Foundations of Vacuum Science and Technology

7/22/2019 Foundations of Vacuum Science and Technology

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Fig. 1.2Plots illustrating Maxwell-Boltzmann distribution laws. Plot fc shows distribution

function for random velocity,c expressed in terms of the most probable velocityα ; plot fx shows distribution function for energy, E , in terms of x = E /(kT ); y corresponds

to the fraction of the total number of molecules for which the random velocity(expressed in terms ofα ) is less than or equal to a given valuec.

ives the fraction of the total number of molecules which have a random velocityequal to or less than thatorresponding to the valuec, or to v = αc. The third and fourth columns in Table 1.2 show values of y and of∆ y, why gives the fraction of the total number which have velocities (in terms ofα as a unit) ranging betweenc and the

mmediately preceding value ofc. Thus, 8.35% of the molecules have velocities betweenc = 1 andc = 1.1, and 42.7ave velocities equal to or less than the most probable value. The values in parentheses are those of (1 y). A plot of yersusc is shown in Fig. 1.2. It is evident that y corresponds to the area under the curve for fc from the origin to theiven value ofc.

rom Eq. (1.53) the distribution formula for translational energy ( E ) can be derived. It has the form

ubstituting the variable x = E /(kT ), Eq. (1.61) becomes






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able 1.2. Values of fc, y, and fx, Illustrating Application of Distribution Laws

fc y ∆ y x fx

0 0 0 0

.10.0223 0.0008 0.0008 0.05 0.2401

.20.0867 0.0059 0.0051 0.1 0.3229

.30.1856 0.0193 0.0134 0.2 0.4131

.40.3077 0.0438 0.0245 0.3 0.4578

.50.4393 0.0812 0.0374 0.4 0.4785

.60.5668 0.1316 0.0504 0.5 0.4839

.70.6775 0.1939 0.0623 0.6 0.4797

.80.7613 0.2663 0.0724 0.7 0.4688

.90.8129 0.3453 0.0790 0.8 0.4535

.00.8302 0.4276 0.0823 0.9 0.4352

.10.8142 0.5101 0.0835 1.0 0.4152

.20.7697 0.5896 0.0795 1.2 0.3722

.30.7036 0.6634 0.0738 1.4 0.3294

.40.6232 0.7286 0.0642 1.6 0.2882

.50.5350 0.7878 0.0602 1.8 0.2502

.60.4464 0.8369 0.0491 2.0 0.2160

.70.3624 0.8772 0.0403 2.2 0.1855

.80.2862 0.9096 0.0324 2.5 0.1464

.9 0.2204 0.9348 0.0252 3.0 0.0973

.00.1652 0.9540 0.0192 3.5 0.0637

.20.0864 0.9784 0.0244 4.0 0.0413

.50.0272 0.9941 0.0157 4.5 0.0266

.00.0024

(4.2 × 104)0.0055 5.0 0.0170

.0 4.1 × 106 (5.1 × 107)6.0 0.0069



.0 7.8 × 1010 (7.9 × 1011)7.0 0.0027

.0 1.9 × 1014 (4.4 × 1016)8.0 0.0011

he last two columns in Table 1.2 give values of fx as a function of x, and Fig. 1.2 shows a plot of this function. By differentiating fx wspect to x and equating the result to zero, it is readily shown that fx has a maximum value for x = 0.5; that is, fE has a maximum valu= 1/2k T . On the other hand, as stated in Eq. (1.9), E av = 3/2kT .

nce

is possible, from the plot for y in Fig. 1.2, to determine the fraction of the total number of molecules which have an energy equaan that corresponding to a given value of E .

follows from the equations above that the value ofv for which fv is a maximum increases withT ½, while that of E for which fE is aaximum increases withT .

alues of va, at 0°C and 25°C, for a number of gases and vapors are given in Table 1.3.




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able 1.3. Masses, Velocities, and Rates of Incidence of Molecules

104 · νa

as or Vapor M 1023m 1010 0°C 25°C 1017 ν1 1020 105G1 1022

2.016 0.3347 0.8878 16.93 17.70 11.23 14.97 0.3759 0.5012

e 4.003 0.6646 1.7631 12.01 12.56 7.969 10.63 0.5297 0.7062

H416.04 2.663 7.063 6.005 6.273 3.981 5.308 1.060 1.414

H317.03 2.827 7.498 5.829 6.089 3.865 5.152 1.092 1.456

2O18.02 2.992 7.936 5.665 5.919 3.756 5.007 1.124 1.498

e20.18 3.351 8.886 5.355 5.594 3.550 4.733 1.190 1.586

O28.01 4.651

12.344.543 4.746 3.012 4.016 1.402 1.868

228.02 4.652

12.344.542 4.745 3.011 4.015 1.402 1.868

ir 28.98a 4.811

12.774.468 4.668 2.962 3.950 1.425 1.900

232.00 5.313

14.094.252 4.442 2.819 3.758 1.497 1.996

r 39.94 6.631

17.593.805 3.976 2.523 3.363 1.675 2.230

O244.01 7.308

19.383.624 3.787 2.403 3.204 1.756 2.342

H3Cl50.49 8.38

22.233.385 3.356 2.244 2.991 1.881 2.508

O264.06

10.64 28.213.004 3.139 1.992 2.656 2.118 2.825

l270.91

11.77 31.232.856 2.984 1.893 2.524 2.229 2.973

r 83.7

13.90 36.852.629 2.747 1.743 2.324 2.422 3.229

7H16100.2

16.63 44.122.403 2.510 1.593 2.123 2.650 3.533

e131.3

21.80 57.822.099 2.193 1.392 1.856 3.034 4.044

Cl4153.8

25.54 67.721.939 2.026 1.286 1.714 3.283 4.377

gb200.6

33.31 (88.33)1.698 1.774 (1.126 1.501 3.750 4.998)

ote : ν1 = rate of incidence of molecules per square centimeter per second, at 0°C and 1 µbar.

= rate of incidence of molecules per square centimeter per second, at 0°C and 1 Torr.

1 = mass of gas corresponding to ν1 (g · cm2 · s1).

= mass of gas corresponding to (g · cm2 · s1).



= mass of molecule (g); = density of gas at 0°C and 1 µbar (g · cm3).

a = average velocity (cm · s1).

Calculated from the valueρ = 1.293 × 103 at 0°C and 760 Torr.Since the vapor pressure of mercury at 0°C is 1.85 × 104 Torr (= 0.247 µbar), the values given in parentheses have no physicalgnificance. Actual values at 0°C, corresponding to saturation pressure, are as follows:ρ = 21.79 × 1010; ν = 2.777 × 1016;G = 9.249 ×06.

3.1

elation between Molecular Velocities and Velocity of Soundis of interest to note that the relations forα , va, and vr can also be expressed in terms of the velocity of sound, which we shall designate u

nce





whereρ1 = density at 1 µbar, and P = P µb, we can write the relations for molecular velocities in the forms

On the other hand,

whereγ = Cp/Cv = ratio of specific heats (per gram-mole) at constant pressure and constant volume. Hence

or mercury and other monatomic gases,γ = 1.667; for diatomic gases (such as H2, N2, and O2),γ = 1.40approximately). Hence,

va/u = 1.236 for monatomic gases= 1.349 for diatomic gases

and

u/α = 0.9124 for monatomic gas.

hus the velocity of sound in a gas approaches molecular velocities very closely.

.3.2Determination of Avogadro's Constant from Distribution of Particles in Brownian Motion

Under high magnification, all suspensions of very fine particles in gases or liquids exhibit ''Brownian" motions1905) suggested that the motion of these particles is essentially that to be expected, on the basis of the kinetic ases, of "large molecules" and therefore subject to the same laws as gas molecules . That is, the average energy pearticle at any given temperatureT is 3/2kT , and the average velocity of the particles is given by the relation

wherem = mass of particle.







pplication of the BoltzmannMaxwell laws leads to the following relation for the distribution of particles at differentgravitational field:

where n0 = number of particles per cubic centimeter ath = 0,n = number of particles per cubic centimeter at heighth (centimeters),

g = 981 dynes,

m′ = apparent mass of particles, which is different from the actual mass because of the buoyancy of themedium.

et m = actual mass of particle. Then

hereρ′ = density of the medium andρ = density of the particles.

ctuallym′ is determined from the rate of settling of the particles, by application of Stokes' law.

hus it is possible to determinek (and consequently the value of NA = R0/k ) from observations on the value ofm′ and thelation betweenn/n0 and h. Using a fine suspension of gum arabic in water, Perrin obtained the value NA = 6.8 × 1023.

quation (1.71) has been applied to the determination of the variation with altitude of the density of the atmosphere.

ssuming an average temperature ofT = 230 K at higher altitudes, we obtain

′/k = M / R0 = (29 × 107)/8.315,nd hence

here P mm, is the pressure in mmHg (Torr) at the altitude H (in meters) above sea level.

4as Pressure and Rate at Which Molecules Strike a Surface

he pressure in a gas is a tensor quantity and has to be defined with respect to an imaginary stationary plane surface phrough a point in the gas. The pressure is defined as the net rate at which momentum normal to this surface is transmcross it per unit area in the positive direction, momentum transmitted in the opposite direction being counted as nega15]. Let∆S represent a small surface element in this imaginary plane surface through which gas molecules included emispherical surface of radius L centered on the center of∆S can pass directly without collision, where L is the mean freath at the prevailing pressure as shown in Fig. 1.3.





Fig. 1.3Diagram illustrating the

calculation of the pressure ina gas. L=the mean free path.v=a particular molecular

velocity.

onsider the gas coming from within the solid angled σ/4π L2, where

a surface element on the hemisphere. For a gas at rest, momentum normal to the surface will bemv cos θ for suchmolecules wherev is the speed of the molecule within the rangev and v + dv, and the rate at which this momentum

ansmitted across the surface ismv2 cos2θ. Then for a gas at rest with respect to this imaginary surface the totalmomentum transmitted will be 2mv2 cos2θ per molecule since the momentum transmitted through∆S from the opp

de is counted as negative. The total momentum transmitted per unit solid angle will be 2nL · ∆S · mv2 cos2θ. Diviy L · ∆S to obtain force per unit area of surface, the quantity L · ∆S cancels out. If the molecular velocities areistributed according to Eq. (1.53), the pressure is given by

his reduces to

sing Eq. (1.9).

n a gas at rest with molecular velocities distributed according to the MaxwellBoltzmann equilibrium distributimolecular flux across a plane surface element A due to all molecules having velocity vectors with directions withmall solid angled ω whose axis makes an angleθ with the normal to A is given by the cosine law [16] formula,







where is the average molecular velocity. While collisions occurring within the solid angled ω may scattemolecules out of the region, in an equilibrium gas the collision processes must result in other molecules enterinegion and having the same direction. If we consider only those molecules crossing an imaginary plane surfaceas in the direction of the positive normal to the surface, or alternatively only those molecules which strike a plr liquid surface and are not scattered backward, then the total molecular flux across or against this surface is

ome of the molecules striking a solid surface will be adsorbed and the remainder are scattered back in variousirections depending on the surface roughness and the intermolecular forces during close approach. The adsorbmolecules eventually reach accommodation with the prevailing temperature of the material at the surface; and hey must acquire velocity components perpendicular to the surface due to molecular vibrations which have maalues ranging from zero to very high values by processes similar to those considered above for orthogonal col

within a gas, some of the molecules will acquire sufficient velocity after a certain time known as theadsorption lifetimo escape the attractive force fields at the surface.

has been shown by Comsa and coworkers [17] that the velocity distribution in the gas from these molecules wesorbed is not necessarily that of a Maxwellian gas. Comsa and several other investigators [18] have shownxperimentally that the angular distribution does not necessarily obey the cosine law. The experiments show thvaporated or desorbed flux is peaked in the direction of the normal to the surface varying as cosnθ with n greater thand as high as 9 for strongly peaked emissions. However, as deduced by Clausing and confirmed by Comsa,

quilibrium conditions the sum of the distribution of the molecules leaving the surface due to various processesadsorptiondesorption, reflection, diffraction, and inelastic scattering) has to obey the cosine law.

pstein [19] has presented a model of the wall boundary condition in terms of the relation between the distribuunctions of the incident and reflected particles, assuming that a certain fraction reflect diffusely (uncorrelated wncident conditions) while the remainder reflect specularly depending on the velocity of the incident particles.

he molecular flux of vapor, as measured in the laboratory frame, in the beam of gas issuing into a vacuum froKnudsen cell, comprising a source of vapor at a uniform temperatureT enclosed in a box with a small thin-edged on one wall, obeys the cosine law approximately, but the mean translational energy per molecule in the beam at 2kT rather than (3/2)kT because the faster molecules have a higher probability of exiting the orifice and the mnergy per molecule involves averaging the translational energy with a velocity distribution function which





ontains the factorv3 rather thanv2. In fact, this value 2kT is characteristic of the mean translational energy in thef molecules in an equilibrium gas against any surface and must be considered when calculating heat transfer.

At very low pressures where the mean free path is much greater than the linear dimensions of the vacuum vesseelocity of the molecules in the gas phase is entirely determined by collisions with the walls and the temperatu

walls. Since such collisions are far less frequent than collisions in a dense gas where the m.f.p is only a small frcm, the relaxation time, or time to restore equilibrium in a gas which has been disturbed from equilibrium byansitory pressure or temperature gradients, is relatively long. Because of outgassing and readsorption at variourfaces within a vacuum system and the removal of molecules by vacuum pumps, equilibrium conditions seldrevail [20], and the pressure measured by a tubulated vacuum gauge will depend on the orientation of the planntrance of the tubulation with respect to mass flow vectors [21]. Pressures measured by an ionization gauge, whe envelope and tubulation removed down to the base mounted inside the vacuum chamber, are less dependenrientation except for the shielding effect of the base.

Muntz [22] has described a method of making localized measurements of the molecular velocity distribution fuarefied gas flows.

rom Eq. (1.78) the incident molecular flux per unit area is

ubstituting forn and va , from Eqs. (1.20), (1.21), and (1.58), we obtain the relations

he volume which strikesunit area per unit time is given by

nd is therefore a constant at all pressures, but varies with (T/M )1/2.

n the literature, especially that originating in Germany, Eq. (1.87) is expressed in the form

whereρ1 is the density at 1 µbar.







he last four columns of Table 1.3 give values ofv1 and G1, the values calculated for a pressure of 1 microbar, an

the values calculated for a pressure of 1 Torrall at 0°C.

he equations given above forv and G are also applicable to the effusion of gasesat low pressures through small hon very thin plates . The requisite condition for the application of Meyer's relation to effusion is that the diameterpening should be small compared with the mean free path.

A comparison of relative values ofv or G for different gases or vapors streaming through such a hole makes it poo obtain relative values of M , since, for constant values of P and T , v varies inversely as M 1/2, andG varies directly

M 1/2.

A good check on the above equations was obtained by Knudsen [23] in some experiments in which hydrogen, nd carbon dioxide, at pressures ranging from 100 to 0.01 Torr, were made to flow into a vacuum through a 0.0ole in a 0.0025-mm-thick platinum strip.

quation (1.87) shows that the volume per unit area per unit time, measured at the pressure P , is always the same. Iollows that FP µb corresponds to the volume at 1 µbar. Hence, if P µb1 and P µb2 (> P µb1) denote the pressures on

wo sides of a very thin-walled orifice of area A, the net quantity of gas (Q) flowing through the orifice per unit timiven by

whereQ = volume in cubic centimeters per second, measured at 1 µbar. That is,Q denotes microbars × cubicentimeters per unit time.

5ate of Evaporation and Vapor Pressure

An interesting application of Eq. (1.84) was first made by Langmuir [24] to the determination of vapor pressurates of evaporation in high vacua. Quoting from Langmuir's original paper,The Vapor Pressure of Metallic Tungsten

Let us consider a surface of metal in equilibrium with its saturated vapor. According to the kinetic theory wlook upon the equilibrium as a balance between the rate of evaporation and rate of condensation. That is, wconceive of these two processes going on simultaneously at equal rates.

At temperatures so low that the vapor pressure of a substance does not exceed a millimeter, we may considthat the actual rate of evaporation of a substance is independent of the presence of vapor around it. That israte of evaporation in a high vacuum is the same as the rate of evaporation in presence of saturated vapor.Similarly we may consider that the rate of condensation is determined only by the pressure of the vapor.

he rate at which molecules will, in general, condense on a surface is given byαv, whereα is known as the

ondensation coefficient or sticking coefficient. It represents the ratio between the rate at which molecules actuondense on the surface and the rate at which they strike the surface. If we let µ denote the rate at which molecvaporate from the surface, then, at equilibrium, we obtain





angmuir [25] has shown that for metal atoms condensing on the surface of a metal the value ofα may be assumede equal to 1. In a later paper on the vapor pressures of high-boiling point organic liquids, Verhoek and Marshahowed that the same assumption is justified in respect to these liquids. Hence, we may, in practically all cases vaporation from the bulk phase, express the relation for rate of evaporation in the form

or the purpose of calculating the vapor pressure of a metal from a determination of loss of weight per unit areme, it is convenient to express Eqs. (1.85) and (1.86) in the forms

whereG = rate of evaporation in grams per square centimeter per second.

As an illustration of the application of these equations, Table 1.4 gives values ofG for tungsten [27] and tantalum [t a series of temperatures (degrees K) together with calculated values of P µb.

or the evaporation from a wire of diameterd ′ (in mils) theloss in weight per second per centimeter length is given

1 = 2.54 × 103πd ′G.

Hence Eqs. (1.92) and (1.93) assume the forms

Table 1.4. Rates of Evaporation and Vapor Pressures of Tungsten and TantalumMetal T (K) G P µbTungstenM = 183.92

2600 8.41×1097.23×104

2800 1.10×1079.81×103

3000 9.95×1079.18×102

3200 6.38×1066.08×101

3400 3.47×1053.41

TantalumM = 180.88

2400 3.04×1092.58×104



2600 5.54×1084.90×103

2800 6.61×1076.07×102

3000 5.79×1065.40×101

3200 3.82×1053.77





quations (1.92) and (1.93) have also been applied by Knudsen and subsequent investigators to the determinatapor pressures fromrates of effusion through a small orifice .

hus let us consider the case in which molecules evaporating from a hot surface pass through a small orifice innother chamber in which they are condensed. If the pressure of residual gas in this "cool" compartment is extrow and theradius of the opening is less than L (the mean free path of the evaporating molecules in the "hot"ompartment), then the rate at which molecules pass through the hole is equal to the rate at which they strike thpening. Consequently, the vapor pressure for any given temperature will be given by Eq. (1.92) or Eq. (1.93), epresents the weight passing through the orifice per unit area, per unit time .

hese equations are, however, strictly applicable only if the thickness (l ) of the wall, in which the orifice of areaπa2ocated, is vanishingly small compared toa . If the orifice consists of a short tube for whichl/a is appreciable, then aorrection factor has to be applied, and instead of Eq. (1.82) we have the relation

where K is a function ofl/a which is less than 1 forl/a > 0. The manner in which the value of K varies withl/a isiscussed subsequently in Chapter 2. Hence, ifG′ denotes the actual loss in weight, at temperatureT , of material ofmolecular mass M , through an opening of area A, over a period oft seconds, then we obtain

hese equations have been applied by a number of investigators for the determination of vapor pressure at lowemperatures, where the values are of the order of a few pascals. The method has been used, for instance, by Eguch metals as zinc, cadmium, mercury [29], and lead [30].

As an illustration let us consider one such determination made for mercury vapor. In this case the area of the opwas A = 0.0335 cm2. At 33.7°C, the loss of mercury through this orifice was 0.7867 g over a period of 2370 morrect for the fact thatl/a was not negligible, the value of K was found (by means of the relations given in Chaptee 0.93.

Hence the corrected value ofG is given by

ince T = 306.9 and M = 200.6, it follows from Eq. (1.93) that P τ = 3.77×103 Torr.

Another interesting application of the above relations, and one which is of increasing importance in industrialhemistry, is provided by the development of





gh-vacuum distillation for the separation of certain organic compounds in the pure state from naturally occurring oilreat advantage of this process arises from the fact that these organic compounds are unstable at higher temperatures aerefore they can be distilled only at lower temperatures, at which the vapor pressures are in the range of 104 to 106 a

n this operation, evaporation takes place from a very thin film of liquid, which is renewed continuously, and condensccurs on an adjacent cooled surface. In a sufficiently high vacuum (pressure of residual gas less than 1 Pa) the rate of

f distilland is in accordance with Eqs. (1.85) and (1.86). As the pressure of residual gas is increased, however, the ratstillation is decreased because of collisions between the molecules of the distilland and those of the gas. This is illuse data shown in Table 1.5, taken from Hickman's paper.

he distilland used was Octoil, which has the chemical formula C6H4 (COOC8H17)2 and molecular weight M = 390.3. Froq. (1.86), it follows that the rate of evaporation,W , in grams per second per square meter , is

hereT is the absolute temperature corresponding to the vapor pressure of P τ in Torr or P pa in pascals.

is evident from these observations, as well as from observations of a similar nature mentioned in the next section, th

olecules leaving the surface of the distilland are prevented from reaching the surface of condensation because of colith the molecules of the residual gas. As a result of such collisions, many of the molecules leaving the hot film are dack, the number of such molecules increasing with the magnitude of residual pressure.

Table 1.5. Variation of Rate of Distillation with Pressure (Hickman)a

Pressure (mTorr) of Residual GasAir)

W (g · s1 · m2)

P τ = 103T = 368 K

P τ = 3×103T = 383 K

P τ = 102T = 393 K

0.3 0.6 1.85 6.4

4.0 0.46 1.59 5.7

7.0 0.38 1.37 5.2

10.0 0.32 1.18 4.6

15.0 0.25 0.95 3.8

25.0 0.21 0.70 2.1

50.0 0.12 0.40 1.67

The values given forT were taken from a plot of log P τ versus 1/T and are therefore only approximate, whichccounts for the fact that values ofW calculated by means of Eq. (1.99) for extremely low pressure are slightly lessor 3×103 and 102 Torr than those given in the first row.





6ree Paths of Molecules

Although the individual molecules in a gas at rest possess very high velocities, as shown previously, it is a mattrdinary observation that gases diffuse into one another very slowly. This is explained on the kinetic point of vssuming that the molecules do not travel continuously in straight lines, but undergo frequent collisions. The tecollision" naturally leads to the notion of free path. This may be defined as the distance traversed by a molecuetween successive collisions. Since, manifestly, the magnitude of this distance is a function of the velocities o

molecules, we are further led to use the expression "mean free path" (denoted by L), which is defined as the averagistance traversed by all the molecules between successive collisions.

However, this definition assumes that the molecules actually collide like billiard balls; that is, the molecules aressumed to be rigid elastic spheres possessing definite dimensions and exerting no attractive or repulsive forcesnother. But this concept can certainly not be in accord with the facts. It is probably impossible to state definiteiameter of a hydrogen atom or molecule, much less that of a poly-atomic molecule. Also there is no doubt tha

molecules exert attractive forces on one another for certain distances and repulsive forces when they approachxceptionally close. Otherwise, how could we explain surface tension, discrepancies from Boyle's law, and a hoelated phenomena? To speak of collisions among molecules, such as these, is impossible. What meaning, there

hall we assign to the free path under these conditions?et us consider att = 0 a group of N 0 "tagged" molecules moving in a given direction. As time goes on, these mo

will suffer random collisions and a number will disappear from the original group. Let N denote the number which,period t , are still identified with the original group, and letω denote the collision frequency. Then

ntegrating this equation, we obtain the result,

f we let l (= vat ) designate the path that has been traversed by a molecule without suffering collision during thethen Eq. (1.101) can be written in the form

urthermore, we can write

where L is a distance covered between collisions. Then it follows that Eq. (1.102) assumes the form





hat is,φ(l ) is the fraction of the original group of molecules that are still traveling without having suffered a con the distancel .

urthermore, it follows from Eq. (1.102) that

epresents the fraction of all the free paths that have a length betweenl and l + dl . (Hence the omission of the negatgn in the differentiation.)

follows from Eq. (1.105) that the average value of the free path is

or l = L, φ(l ) = εl = 0.3679. This result shows that 63.21% of the molecules collide with other molecules in a dqual to or less than L. Furthermore, it is seen from Eq. (1.101) that this 63.21% of collisions occur in the intervτ . Thus 1/ω is a constant of the same nature as the ''decay" constant in radioactive disintegrations, while 1/ L may be

egarded as an "absorption" coefficient similar to the coefficient that measures the decrease in intensity of a beaght in passing through a medium.

quation (1.104) indicates an experimental method for the determination of L′ which has been used by Born [32] aielz [33] and which is described by Fraser [34]. A beam of silver atoms is sent into nitrogen or air, and a deter made of the amount of silver deposited by the beam in a given timet on a surface distantl from the source. If we

0 designate the intensity of the beam at the source, then the intensity at the collector is

where LP is the mean free path of silver atoms in the gas at the pressure in the collecting chamber.

Measurements of the mean free path of potassium in nitrogen have also been reported by Weigle and Plesset [3

As Fraser [34] points out:

With noncondensable gases, it is not possible to measure I 0 directly. We assign therefore to I 0 a differentmeaning: namely, the intensity which the beam would have if it were not, as is actually the case, weakenedthrough scattering by the alien molecules present in the collimator chamber. Now, clearly I 0 is directly proportional to the quantity of gas issuing from the source slit per second; but so also is the pressure P in thecollimator chamber, if a constant pump speed is assumed. We can therefore set I 0 = c· P . On the other hand, LP is inversely proportional to P ; that is, LP = L/P , where if P is measured say in mTorr, L is the mean free path at a pressure of 1 mTorr. I can therefore be expressed as a function of the pressure P ; thus if l is thedistance between source slit and image slit,

I = c · P eP · l/L,





it being assumed that the pressure in the observation chamber is negligibly small. I is a maximum for thatvalue of P which makes P · l/L = 1. To make a measurement, the intensity is plotted as a function of the pressure in the collimator chamber, and the value of the latter at the maximum intensity is observed. Then

LP = L/P = l .

At this value of P , I = 0.3679 I 0.

is of interest to observe, as Fraser emphasizes, that the requisite condition for obtaining a directional effect ofmolecules passing through the slit is that LP must not be less than d , the width of the slit.

he determination of mean free path for hydrogen has been carried out by Knauer and Stern [36]. The value thbtained, however, is only about 0.44 times that derived from viscosity relations (see discussion in the followinection). The reason, as Fraser [34] points out, is that

the standard methods require an intimate encounter in order that the molecules may exchange energy andmomentum in amounts capable of affecting the viscosity or heat conductivity of the gas. The molecular ramethod on the other hand counts as a collision an approach of two molecules sufficiently close to deflect tvery slightly out of their paths; with narrow slits angular deflections of less than 104 are detectable.

n this connection the reader will find an interesting description of the many uses of molecular beams in a papeaylor [37]. As he states, "Molecular beams, narrow rays of molecules formed by a slit system and moving in oirection in an evacuated apparatus, may be used to advantage in many types of research." Among these areeterminations of molecular velocities (involving experimental tests of the validity of the MaxwellBoltzmannistribution law), mean free paths, vapor pressures, accommodation coefficients, and mechanism of chemical rnd of adsorption.

vidently the mean free path must depend upon the molecular diameter, and simple considerations indicate thaength of the mean free path must vary inversely as the total cross-sectional area of the molecules per unit volum

Again, the magnitudes of the coefficients of viscosity, heat conductivity, and diffusivity of gases are intimately p with the length of the free path; whether it be transference of momentum from one layer to another as in visansference of increased kinetic energy of the molecules as in heat conductivity, the rate of this transference mepend upon the number of collisions that each molecule experiences as it passes from point to point. It is theree expected that there should exist very similar relations between the values of the mean free path and those ofoefficients of viscosity, heat conductivity, and diffusion. However, in attempting to deduce such relations, theheoretical physicist has found himself confronted with the problem regarding the laws governing the variationistance of attractive and repulsive forces between molecules. As a result of successive attacks on this problemumber of investigators, the exact forms of these relations have been modified from time to time. The reader iso Chapman and Cowling [1d] for a detailed discussion of the whole problem.





7elation between Coefficient of Viscosity, Mean Free Path, and Molecular Diameter

A gas streaming through a narrow-bore tube experiences a resistance to flow, so that the velocity of this flow dniformly from the center outwards until it reaches zero at the walls. Each layer of gas parallel to the direction xerts a tangential force on the adjacent layer, tending to decrease the velocity of the faster-moving and to incrf the slower-moving layers. The property of a gas (or liquid) by virtue of which it exhibits this phenomenon iss internal viscosity .

As a simple working hypothesis we may assume, as Newton did, that the internal viscosity is directly proportioelocity gradient in the gas. Furthermore, the viscosity must depend upon the nature of the fluid, so that in a miscous fluid the tangential force between adjacent layers, for constant velocity gradient, will be greater than iniscous fluid. We thus arrive at the following definition of thecoefficient of viscosity :

he coefficient of viscosity is the tangential force per unit area for unit rate of decrease of velocity with distance (i.eer unit velocity gradient).

With this definition we are in a position to deduce the approximate form of the relation between the coefficientiscosity and the free path.et u denote the velocity of flow of the gas at a distanced from a stationary surface. In uniform flow along a surfa

he velocity will decrease uniformly to zero as the surface is approached. We can therefore represent (see Fig. 1elocity at distanceOA = d by the ordinate AB = u and represent velocities at intermediate distances by theorresponding ordinates of the lineOB.

We shall imagine the gas divided into layers parallel to the surface, each having a depth equal to the free path, L.

Fig. 1.4Diagram illustrating the derivation of simple

relation between the coefficient of viscosity (η)of gas and the molecular mean free path ( L).







et us denote the tangential force per unit area between adjacent layers by B. By definition:

whereη denotes the coefficient of internal viscosity.

ut, according to the kinetic theory, the tangential force per unit area is measured by the rate at which momentansferred per unit area between adjacent layers. Because of the relative motion of the layers, the molecules moom a faster- into a slower-moving layer possess more momentum in the direction of flow than those moving ipposite direction.

et us consider any layer,CE or EH , of thickness equal to L. We have chosen this particular value of the thicknesshat we may be justified, as a first approximation, in assuming that the molecules starting at either of the planesCD aK reach the plane EF without suffering collisionthat is, without change of momentum.

he momentum, parallel to the surface, of any molecule reaching the plane EF from the planeCD is m(u′ + v), wherenotes the velocity of flow at the planeCD and v is the mean velocity of the molecules.

he momentum, parallel to the surface, of a molecule reaching the plane EF from the plane HK is

m(u′ + v + 2uL/d ).

he number of molecules that cross unit area per unit time in any direction in a gas at rest is equal to (1/6)nv; and thmust be the same for the molecules traveling in a direction perpendicular to the plane EF , because the velocity of fl

assumed to be so small that the density remains constant throughout the different layers.

Hence the net rate of transference of momentum across unit area of the plane EF is equal to

rom Eqs. (1.108) and (1.109) it follows that

he dimensions ofη are evidentlyml 1t 1, and in the cgs system the unit of viscosity is 1 poise = 1 g·cm1·s1 = 1yne·s·cm2. This is the unit of coefficient of viscosity used in this volume.

n deducing Eq. (1.110) it has been assumed that all the molecules possess the same velocityv and the same free pantroducing the law of distribution of velocities, Boltzmann (1881) deduced the relation

whereva = average velocity, and LB is defined as the average free path.





O. E. Meyer, in his Kinetic Theory of Gases , used a different method of calculation and derived a relation of the f

where LM is also defined as the average free path.

rom these equations an interesting conclusion may be deduced regarding the dependence of viscosity on pressas been mentioned, it is evident from very simple considerations that L must vary inversely as the number of molresent per unit volume. Consequently the product pL is constant and independent of the pressure. The velocity,v,epends only upon the temperature and molecular weight. It therefore follows that, for any gas at constant temphe viscosity is independent of the pressure and must increase with the temperature . The confirmation of these twoeductions has been justly regarded as one of the most signal triumphs of the kinetic theory of gases. As is welhe viscosity of all ordinary liquids decreases with increase in temperature. That the viscosity of gases must inc

with temperature was therefore regarded as a remarkable conclusion.

At both extremely low pressures and very high pressures, the conclusion that the viscosity is independent of the not in accord with the observations, but this is due to the fact that the same derivation as has been presented

ot valid under those conditions where either attractive forces between the molecules come into play or the preo low that a molecule can travel over the whole distance between the walls of the enclosure without suffering

oth Eqs. (1.111) and (1.112) have been used by physicists, until comparatively recently, for deriving values o L fro. However, the work of S. Chapman and D. Enskog, since about 1911, has led to the following relations, whiciscussed by Chapman and Cowling [1d] in their treatise.

o derive a more exact relation betweenη and L, it is necessary to introduce the relation between L and δ, the moleciameter, which has been shown to be of the form

wheren = number of molecules per cubic centimeter.

or smooth rigid elastic spherical molecules, it is shown that

ubstituting in this equation the relationsva = (8kT/ p m)½ andρ = mn, it follows that

A further approximation leads to the conclusion that the right-hand side of the last equation should be multiplieactor 1.016, and consequently





ombining this with Eq. (1.113), the result is the relation used in the following discussion:

follows directly from Eq. (1.114) that, for two gases having approximately equal values ofδ, the viscosities shouln the same ratio as the square roots of the molecular masses. This conclusion has been confirmed by observatiohe relative viscosities of H2 and D2 (deuterium) [38]. At room temperature we haveη D2/η H 2 = 1.39, which ispproximately equal to 21/2.

he difference between Eq. (1.116) and the equations of Boltzmann and Meyer arise from the fact that the two nvestigators failed to take into account the existence of forces of attraction and repulsion between molecules. Tccurate form of the relation betweenη and δ has been a topic of considerable discussion by theoretical physicist

One interesting contribution to this subject, to which reference is made in a subsequent section, is the model suy W. Sutherland [40]. Let us assume that the molecules are "smooth rigid elastic spheres surrounded by fieldsttractive force."

he relation between coefficient of viscosity and molecular diameter then has the form

where the constantC is a measure of the strength of the attractive forces between the molecules. In this equationotationδm has been introduced to indicate that the value of the molecular diameter derived in this manner is dom the valueδ used in Eq. (1.114). From a comparison with Eq. (1.114) it follows that Eq. (1.117) is equivale

elation

quation (1.117) leads to the relation, used for calculatingC , which has the form





whereηT and η0 are the values of the coefficient of viscosity measured atT and T 0 respectively. Equation (1.122) lso often expressed in the form

y combining Eqs. (1.123) and (1.118) it is seen that the value ofδm thus deduced is independent ofT and actuallyorresponds to the value of the molecular diameter at infinitely high temperature, whereas, as pointed out belowalue ofδ decreases with increase inT . For this reason, Eqs. (1.118) and (1.119) were used formerly by many wrhis subject. However, following the procedure of Chapman and Cowling and of Kennard, Eqs. (1.115) and (1.sed in the following discussion for the calculations of the values ofδ and L, respectively. The conversion to valueeduced by application of Sutherland's theory may then be made by means of Eqs. (1.120) and (1.121).

rom Eq. (1.116) the following numerical relations are derived:

where P µb and P τ denote the pressure in microbars and Torr, respectively, andη is expressed in poises. These relaave been used to calculate values of L and, from these, values ofδ given in Tables 1.6 and 1.7.

rom Eq. (1.115) we obtain the following relations forδ2 and Sc = πδ2, the latter being defined as the mean equiv

ross section for viscosity [41]:

Whereδ has been determined by some other method [42], an approximate calculation of L may be made by means he relations

Another useful magnitude is thecollision frequency per molecule, which is given by the relation



Values of ω are shown in the last row in Table 1.6.





able 1.6. Mean Free Paths, Molecular Diameters, and Related Data for a Number of Gasesas: H2 He Ne Air O2 Ar CO2 Kr Xe

07η15871 1943 3095 1796 2003 2196 1448 2431 2236

0.69 0.64 0.67 0.79 0.81 0.86 0.95 0.85 0.92

07η0 839 1878 2986 1722 1918 2097 1377 2372 2129

07η25892 1986 3166 1845 2059 2261 1496 2502 2308

038.39 13.32 9.44 4.54 4.81 4.71 2.95 3.69 2.64

11.04 17.53 12.42 5.98 6.33 6.20 3.88 4.85 3.47

9.31 14.72 10.45 5.09 5.40 5.31 3.34 4.06 2.98

12.26 19.36 13.75 6.69 7.10 6.67 4.40 5.34 3.93

08δ2.75 2.18 2.60 3.74 3.64 3.67 4.65 4.15 4.91

84.4 80 56 112 125 142 254 188 252

014 Ns15.22 24.16 17.12 8.24 8.71 8.54 5.34 6.69 4.78

09ω14.45 7.16 1.68 6.98 6.26 5.70 8.61 6.48 5.71

able 1.7. Mean Free Paths, Molecular Diameters, and Related Data for Water and Mercury Vapors

t (°C) P t 105η 108δt 1014 Ns

2O0 4.58 8.69

2.90 6.34 × 104 4.68 5.27

15 12.79 9.26

25 23.76 9.643.37 1.42 × 104

g219.4 31.57 46.66

6.28 1.99 × 104 4.27 6.32

150.0 2.807 39.044.87 1.74 × 103 4.50 5.70

100.0 0.2729 33.56 3.93 1.44 × 102 4.70 5.22

25.0 0.0018 25.402.66 1.45 5.11 4.42

0.0 16.2(J)6.26(J)

ote : In Tables 1.6 and 1.7 the following notation has been used:

τ = vapor pressure att (°C) in Torr.

= mean free path in centimeters at 0°C and 1 Torr.

= mean free path in centimeters at 25°C and 1 Torr.



= mean free path in centimeters att °C and P Torr.

= collision frequency (per second) at 25°C and 760 Torr.

though Sutherland's equation (1.123) has been used most frequently to express the temperature variation of viscosity, several other reve been derived in the literature. The simplest of these is the exponential relation

here a and x are constants characteristic of each gas. This relation has been recommended especially for relatively small ranges of tem

quations (1.123) and (1.133), as well as some other relations, have been tested by Licht and Stechert [43] for a number of typical gasepors, using for this purpose data published in the LandoltBornstein tables [44].





ccording to these investigators, "For twenty-four representative gases and vapors at atmospheric pressure, Sutherland's equation has bfit extensive experimental data with an average error of less than 1 percent." Values of the constantsC and K in Eq. (1.123) and ofa and x in

q. (1.133), taken from the original discussion, are shown in Table 1.8. These constants were used to derive values ofη25 shown in the fifth ghth columns of the table.

he values ofC given in Table 1.6 are those deduced by Schuil [45], and it is of interest to compare them with those given in Table 1.8.

deriving the values of L and δ shown in Tables 1.6 and 1.7, the values ofη used are those given by Kennard [46] for 15°C. Values for 0°

°C (η0 and η25, respectively) were derived from the values for 15°C by means of Eq. (1.133), using the values of x, taken from Kennard'sble, which are given in the second row of Table 1.6. The values ofδ were derived from those ofη0 and therefore apply strictly only at 0°C

ombining Eq. (1.133) with Eq. (1.114), it follows that at room temperature,δ varies asT 0.5( x0.5). Since x is greater than 0.5, it also followat the calculated value ofδ must decrease with increase in temperature.

n interesting method of calculating values of L for air as a function of the temperature has been used by Tsien [47]. From Eqs. (1.116) anfollows that

= 1.255ηγ 1/2/ρu.

hus L may be expressed in terms of the "kinematic viscosity,"η/ρ, and the velocity of sound,u. By means of this relation, Tsien [47] haslculated values of the mean free path for air for the range 0500°C. A few of the values thus deduced (in centimeters) are as follows:

(°C): 0 20 40 100 200 300 400 50006 L( P/P 0): 5.89 6.48 7.06 8.78 11.73 14.86 17.78 20.83

able 1.8. Characteristic Constants for ViscosityTemperature Functionsubstance Temperature

Range (°C)Sutherland Equation Exponential Equation

C 106 K 105η25 106a x 105η25mmonia

77441 472 15.42 10.30 0.274 1.041 10.30

rgon183827 133 19.00 22.67 2.782 0.766 21.83

enzene0313 403 10.33 7.58 0.299 0.974 7.71

arbon dioxide981052 233 15.52 15.03 1.057 0.868 14.86

elium258817 97.6 15.13 19.66 4.894 0.653 20.18

ydrogen258825 70.6 6.48 9.04 1.860 0.678 8.85

Mercury218610 996 63.00 25.03 0.573 1.082 27.20

Methane18499 155 9.82 11.14 1.360 0.770 10.92

itrogen191825 102 13.85 17.80 3.213 0.702 17.60

xygen191829 110 16.49 20.78 3.355 0.721 20.42

Water vapor 0407 659 18.31 9.84 0.170 1.116 9.82





n the lower row, P 0 denotes the standard pressure, 1 atmosphere, and P denotes any other value of the pressure in

tmospheres. The value 5.89 for 0°C is to be compared with the value 5.98 given for in Table 1.6.

n the case of H2O, for which values of L and δ for a series of temperatures are given in Table 1.7, the Sutherlandelation was used withC = 650 andη15 = 9.26 × 105 cgs unit.

n the case of Hg (see Table 1.7), the values ofη used were based on that given by Braune, Basch, and Wentzel [= 219.4°C. Values at other temperatures were derived by means of Sutherland's relation, withC = 942.2 [49]. It she observed that in their publication these authors used Eq. (1.118) to calculate values ofδm.

he value ofη for 0°C is quoted by Jeans (from Kaye and Laby, Physical Constants , 1936 edition) in his book (p.

n addition, Tables 1.6 and 1.7 give values of Ns, the number of molecules per square centimeter, to form amonomolecular layer at 0°C. On the assumption that the spacing is that of a close-packed (face-centered) latticeave

ormulas for the viscosity of mixed gases are given by Kennard [50]. As he points out, the viscosity of a binaryoes not necessarily lie between the values for the pure components; it may be below or above both these value

he relations for collision frequency per unit volume between molecules are of importance in many problems onteraction between molecules. Let ZAA and ZAB denote the number of collisions between like and unlike molecuespectively, per cubic centimeter, per second. Then,

wherenA = number of molecules per cubic centimeter of A at pressure PA (microbars), with similar definition fornBnd δ AB = ½ (δ A + δ B).

or instance, for nitrogen ( M = 28.02,δ = 3.62 × 108) atT = 298.2 K, we have

Z = 8.157 × 1016 cm3·s1 at 1 microbar = 8.357 × 1028 cm3·s1 at 1 atmosphere.







or themean free paths of the molecules A and B in a mixture, the following general relations have been derived

wherevA and vB refer to the average velocity of each type of molecule.

or TA = TB, Eq. (1.138) becomes

nd similarly for 1/ LB.

or and we obtain

or we obtain

or andTA not identical withTB, we obtain

he last equation has been used by Gaede [51] to calculate the mean free path of nitrogen ( A) in the blast of a mercuapor pump. In this case we may assume the following:TA = 300 K; and the temperature of the mercury vapor,TB, 00 K. At this temperature the pressure of mercury vapor is about 1 Torr. Hence,nB = 2.414 × 1016.

rom the data in Tables 1.6 and 1.7, we have

08 · δ AB = ½(3.78 + 4.70) = 4.24.

ubstituting these values and those for MA and MB in Eq. (1.143), the result is LA = 6.73 × 103 cm, whereas from

ata for in Table 1.7 the value derived for the mean free path of mercury molecules in the saturated vapor aL = 4.4 × 103 cm.

.7.1Viscosity at Low Pressures



As mentioned previously, the coefficient of viscosity is not independent of pressure when the pressure decreaseow value. Under those conditions it was observed by Kundt and Warburg (1875) that the damping of a vibratinurface by the surrounding gas is decreased, as if the gas were slipping over the surface. If one surface is at restnother surface, at a distanced , is moving parallel to the first surface with





uniform velocity,u, the viscous drag upon each surface at normal pressures is given in accordance with the def η by the relation

At low pressures, however, the observed value of the tangential force B is less than that given by Eq. (1.144),orresponding to an increase in the value ofd . That is, the equation assumes the form

where ζ is known as thecoefficient of slip .

onsiderations based on the kinetic theory of gases lead to the relation

which, combined with Eq. (1.116), leads to the relation

where f is a numerical coefficient which has a maximum value of 1. It was introduced by Maxwell with an interiven by Kennard [52] as follows:

The value of f , the transfer ratio for momentum, will presumably depend upon the character of the interacti between the gas molecules and the surface; it may vary with the temperature. We can imagine a surface th

absolutely smooth and reflects the molecules ''specularly" with no change in their tangential velocities; in a case f = 0 andζ = ∞, viscosity being unable to get a grip upon the wall at all. On the other hand, we canimagine the molecules to be reflected without regard to their directions of incidence and therefore withcomplete loss of their initial average tangential velocity.

n this case, f = 1 andζ = L [53].

More generally,ζ = β L, whereβ is of the order of unity; and at very low pressures, where Eq. (1.145) b

hus, at very low pressures the rate of transference of momentum from a moving surface to another surface adjnd parallel is directly proportional to the pressure and to the velocity of the moving surface. This conclusion wpplied by Langmuir [54] to the design of a molecular gauge for the measurement of low pressures.

he quantityρva/4, which, as noted previously, corresponds to the mass of gas incident on unit area per unit timeen designated by Kennard as the free-molecule viscosity of the gas between the plates.







he concept of coefficient of slip has also been used to interpret observations on the flow of gases at very low phrough capillaries.

.7.2Molecular Diameters

Mention has been made in the previous section of the two relations for deducing values ofδ and ofδm from viscositmeasurements. These relations are as follows:

As illustrated in Table 1.7 by the values ofδ for mercury, these values exhibit a considerable decrease with increaemperature, and in this case it is found thatδm = 2.50 × 108. The variation withT is obviously greater for thosemolecules for which the Sutherland constantC , has a large value.

n spite of the fact that the values ofδ thus deduced exhibit a variation withT , Chapman and Cowling [1d] have beollowed in this discussion in choosing Eq. (1.150) rather than Eq. (1.151). While, as pointed out by Chapman owling, such a variation in the value ofδ with T "receives a simple explanation on the hypothesis that the molecre centers of repulsive forces, not hard spheres," it is of interest to compare the results obtained by means of E1.150) with those obtained by means of Eq. (1.151) and also by other methods.

here are several such methods, and only a few of the more important ones can be mentioned briefly, together ome of the results deduced.

.7.3Application of the van der Waals Equation

Near the critical temperature and pressure the behavior of gases can be described very satisfactorily by a modiff Eq. (1.14), deduced by van der Waals, which is as follows:

n this equation,V is the volume per mole, the terma/V 2 is a correction term which takes into account the attractivorces between the molecules, and the constantb is a measure of the actual volume of the total number of molecuccordance with the relation





he values [55] of the constantb may be determined for any given gas from the values of the critical temperature (Tc) aritical pressure ( Pc ) by means of the relation

7.4rom the Density of the Solid or Liquid

ssuming that the molecules are closely packed, as in a face-centered cubic lattice, the projected area per moleculey the relation [56]

where m = mass of molecule = M/NA and ρ = density ofcondensed phase.

ut, according to Eq. (1.134),

quation (1.156) has been used to calculate the number of molecules per unit area required to form a unimolecularmonolayer). (See last column of Table 1.9.)

Table 1.9. Values of Molecular Diameter (cm·108)

Gas Fromη Fromb

Fromρ

Electron Collision 1014· Nsfrom ρ

δ0 δm

H2 2.75 2.10 2.76 4.19 2.26.58

He 2.18 1.69 2.66 4.21 1.76.49

Ne 2.60 2.16 2.38 3.40 2.29.98

Ar 3.67 2.42 2.94 4.15 3.66.71

O2 3.64 2.50 2.93 3.73 3.48.30

Hg 6.26 2.50 2.38 3.2610.86

CO2 4.65 3.32 3.24 4.05 4.47.04



H2O 4.68 2.45 2.89 3.48 3.89.53

C6H6 7.65 4.71 4.51 5.893.33

CH4 4.19 3.31 3.24 4.495.73

C2H6 5.37 3.87 3.70 5.014.60

C3H8 6.32 4.45 4.06 5.61 3.67

n-C4H10 7.06 4.84 4.60 6.103.18

n-C5H12 7.82 5.05 4.89 6.452.78

n-C6H14 8.42 5.22 5.16 6.742.54





.7.5ross Section for Collision with Electrons [57]

A cathode-ray beam of initial intensity I 0 is decreased to intensity I , after passing through a layer of the gas of thic in accordance with the relation

where, as shown previously in Eq. (1.104),α is a measure of 1/ Le, where Le = mean free path for electrons = 4(2)½ LHence it follows from Eq. (1.113) that

hus the collision cross section is given byα /n . However, as has been observed experimentally, the value ofα varierather complex manner with the potential used to accelerate the electrons, with the result that it is actually im

o assign a definite value toδ as derived from electron-collision measurements.

he structure of molecules has also been determined from measurements of dipole moments and from electron-iffraction experiments, all of which are discussed at length by Stuart [57] in his book.

able 1.9 gives, for comparison, values ofδ for a number of gases and vapors as deduced by at least four differenelations. The second and third columns give values ofδ0 andδm as deduced by means of Eqs. (1.126) and (1.120espectively, from the values ofη (extrapolated to 0°C) and the values ofC given by Schuil [45]. The fourth columives values ofδ calculated by means of Eq. (1.154) from the values of the van der Waals constant,b; the fifth coluives values deduced by means of Eq. (1.158) from values ofρ at extremely low temperatures (in general for the sate). The sixth column gives values, derived from observed values ofα by means of Eq. (1.160), for 36-volt elec

57], and the last column gives values of Ns calculated by means of Eq. (1.157) from the values ofδ in the fifth colu58]. The values thus derived are to be compared with those deduced in Tables 1.6 and 1.7 from kinetic-theory

8eat Conductivity of Gases

he kinetic theory of gases achieved a great triumph when it led to the conclusion that the viscosity is independhe pressure. It led to still further important results when it predicted the existence of simple relations between troperties of viscosity, heat conductivity, and diffusivity.

rom the kinetic point of view it is the same whether the molecules transfer momentum or translational energy ayer to another. The equations are quite analogous.

As in the case of viscosity, we consider any two layersCE, EH (Fig. 1.4), each of thickness L, between two plateswhose temperatures areT 1 and T 2 and distance apartd . Let cv denote the heat capacity per unit mass at constantolume. The relative temperature drop between the planesCD and HK is equal to

(T 1 T 2) L/d .





Hence the heat transferred per unit area is

herefore the coefficient of heat conductivity

f cv is expressed in calories per gram, the unit ofλ is 1 cal · cm1 · s1 · deg1 · Comparing the last equation with E1.110), it follows that

As in the case of the relation forη , a more careful consideration of the mechanism of energy transfer by means omolecules leads to the relation

where, according to Eucken [59, 60], we have

nd γ = ratio of specific heat at constant pressure to that at constant volume.

or monatomic gases,γ = 5; and for polyatomic gases,γ tends to approach the value 1, with increase in total numtoms per molecule.

Hence

≤ε≤ 2.5.

able 1.10 gives data published by Kannuluik and Martin [61, 62] on values ofλ0 (conductivity at 0°C) and ofε, aserived from observation by means of Eq. (1.164) and as calculated by means of Eq. (1.165). Similar data for tases and a number of others are given in the treatise by Chapman and Cowling [1d].

One important conclusion that follows from Eq. (1.164) is that the thermal conductivity of a gas isindependent ofressure , which is valid as long as the pressure is higher than the range in which molecular flow occurs. (See thollowing section).

With regard to the variation inλ with T the following remarks may be made. To a first approximation the variatioalue ofλ follows that in the value ofη , sinceε exhibits only a slight variation withT . However, for larger ranges occount must be taken of the increase withT in the value ofcv. Denoting themolecular specific heat, atconstant olume, byCv, Partington and Shilling [63] give the relations shown in Table 1.11 for different gases:

ince the variation inη with T is given by the Sutherland relation, Eq. (1.123), it follows that, in terms ofλ0 in caloer centimeter per second per degree,







able 1.10. Values of Heat Conductivity Compared with Coefficients of Viscositya

Gas105λ0 105η0

cv (cal·g1) ε (obs) ε (calc)

He34.3 18.76 0.746 2.45 2.44

Ne11.12 29.81 0.150 2.50 2.44

Ar 3.82 21.02 0.0745 2.44 2.44

H2 41.3 8.50 2.43 2.00 1.90

Air 5.76 17.22 0.171 1.96 1.91

O25.83 19.31 0.157 1.92 1.95

O5.37 16.65 0.178 1.81 1.91

O2 3.43 13.74 0.153 1.64 1.72

N2O3.61 13.66 0.155 1.71 1.73

To convert values ofλ0 from cal · cm1 · s1 · deg1 to watts·cm1 · deg1 multiply values in Table 1.10 by 4.186.

able 1.11. Molecular Specific Heat and Specific Heat Ratio (Partington and Shilling)

Gas γ = Cp/Cv Cv

Air 1.4034 4.924 + 1.7 × 104T + 3.1 × 107T 2

N21.405 4.924 + 1.7 × 104T + 3.1 × 107T 2

O21.396 4.924 + 1.7 × 104T + 3.1 × 107T 2

O1.404 4.924 + 1.7 × 104T + 3.1 × 107T 2

H21.408 4.659 + 7.0 × 104T

O21.302 5.547 + 4.5 × 103T 1.02 × 106T 2

H2O . . . 6.901 1.19 × 103T + 2.34 × 106T 2Hg, Ar, etc.

1.667 2.990

hereα and β are determined from the expression forCv as a function ofT , and l T is expressed in watts per centimeter per degree. Fdrogen ,







imilar expressions for gases for whichλ has not been determined can be derived, as is evident, from determinat, using the observed values ofC and values ofε calculated from those ofγ by means of Eq. (1.165).

will be observed that the heat conductivities of hydrogen and helium are much greater than those of heavier guch as oxygen and carbon dioxide.

or the case of a wire of radiusa and lengthl , suspended along the axis of a cylinder of radiusr , the energy loss per ume due to thermal conduction by the gas is [64]

whereT T 0 is the difference in temperature andr/a is not "excessively" large [65] whilel m is the average conductivver the temperature rangeT T 0.

he units in which E is usually expressed are watts per square centimeter.

he energy loss per unit area per unit time is

nd theenergy loss per unit length of wire per unit time is

ince the total energy loss from a heated wire is the sum of that lost by radiation (which varies as ) aost by conduction of the gas, the former has to be subtracted from the total energy loss in order to obtain the amue to the latter. Furthermore, in the case of short wires especially, a correction has to be made for the loss byonduction at the ends.

or wires of low emissivity, such as platinum, operating at a temperature below about 500°C, the loss due to raegligible compared to that due to conduction.

ince the thermal-conduction loss in the case of mixtures varies with both the nature of the gas and the composact has been applied to the analysis of gases [66]. An instrument devised for this purpose by Shakespear [67], kkatharometer , consists of a platinum spiral filament in a copper block. This instrument has been used extensivnglish investigators for determinations of rates in gaseous reactions and for experiments on thermal transpirat

which is discussed in Section 1.10) [68].

9hermal Conductivity at Low Pressures

As mentioned in the previous section, the heat conductivity of gases should theoretically be independent of prehat this is at least approximately confirmed







y observation is illustrated by the data shown in Table 1.12, obtained by Dickins [69].

he values underW represent the total heat loss (in calories) by conduction, from a platinum wire (a = 3.765 × 103 cm,l = 20m) suspended along the axis of a Pyrex glass tube (inside radius,r = 0.3346 cm). The tube was maintained at about 0°C byxternal cooling, and∆t is the temperature differential between the wire and the wall. The pressure of the gas in Torr is gie third column, and the value indicated byW ∞ represents the heat loss extrapolated for P = ∞. The values underλt give the

ermal heat conductivity at the mean temperature indicated in the last column. The values ofλt (in calories) were derived beans of the relation, deduced from Eq. (1.167),

will be observed that over a range of pressures the values ofW did not exhibit any considerable decrease.

hat the heat conductivity is practically constant over a large range of pressures is also shown by the plots of the energyatts) at constant temperature (about 99°C) from a platinum filament (Fig. 1.5). The filament was a 14-cm length of 3-mcated along the axis of a glass tube 2.54 cm in diameter. The wall temperature was 0°C.

s will be observed, the heat loss in hydrogen was about 10 times that in argon. The loss at a pressure of about 1 m Torr006 W. A comparison of the relative losses in the three gases at 760 Torr yields values which agree, within a few percee values ofλ given in Table 1.10.

Table 1.12. Variation in Thermal Conduction with Pressure (Dickins)

Gas ∆t P τ W W ∞ 105λt t (°C)H2

17.866 625.0 0.21323 0.21494 42.77 9.04

442.0 0.21258

302.3 0.21145

229.9 0.21038

168.2 0.20875129.8 0.20692

Air 23.832 91.7 0.04021 0.04052 6.044 11.94

52.1 0.03997

31.3 0.03961

22.3 0.03926

17.1 0.03891

11.9 0.03825

CO223.80 83.3 0.02461 0.02473 3.694 11.91

40.5 0.02447

19.2 0.02417

11.1 0.02379







hus, over the range 100760 Torr, the heat loss in hydrogen increased only about 7%, whereas in the range belorr the decrease was nearly 100%. Careful measurements show that at very low pressures the thermal conductecreases linearly with the pressure.

he theory of heat conduction at these pressures has been developed from two different points of view. The firshese, due to Knudsen [70], involves a consideration of the mechanism of energy transfer by individual molecuncident on the hot surface.

he second point of veiw, due to Smoluchowski [71], is based upon the concept of a temperature discontinuityhe thermal analogue of the phenomenon of "slip" discussed in Section 1.7.

.9.1ree-Molecule Conductivity (Knudsen)

When molecules originally at a temperatureTi strike a hot surface at temperatureTs (> Ti), complete interchange onergy does not occur at the first collision. In fact



Fig. 1.5Plots illustrating the variation in thermal conductivity

with pressure, for nitrogen, argon, and hydrogen. Ordinatesgive values of total watts conducted from a platinumfilament located along the axis of a cylindrical glass

tube. Scale of watts for hydrogen should be multiplied by 10. Abscissas give pressures in centimeters

of mercury (10 Torr).





may often require many collisions for this to occur. Therefore Knudsen introduced a constant, known as theaccommodation coefficient ,signated byα , which "can be defined as standing for the fractional extent to which those molecules that fall on the surface and are refl-emitted from it, have their mean energy adjusted or 'accommodated' towards what it would be if the returning molecules were issuingeam out of a mass of gas at the temperature of the wall [72].

he molecules re-emitted or reflected from the hot surface consequently possess a mean energy which corresponds to a temperature low, which we shall designate asTr , and the accommodation coefficient is defined by the relation

r α = 1, Tr = Ts ; for α < 1, Ts > Tr > Ti. It should be noted that the temperatureTr is not clearly defined, as Blodgett and Langmuir [73]ve pointed out, unless the molecules leaving the surface have a Maxwellian distribution of velocities.

ecause the faster molecules emitted from a surface carry more energy than the average, the Maxwell distribution function must be rep

= 2(m/2kT )2v3 exp(mv2/2kT )

that the mean translational energy transferred from a surface at temperatureT is given by

nstead of 3/2kT, which is the average energy of the molecules in a volume).

t us now consider heat transfer in a monatomic gas at low pressure:

E 0 = energy transfer from hot to cold surface (at temperatureTi) per square centimeter of hot surface per second

here vi = average velocity atTi.

hus the rate of energy transfer at low pressure is proportional to the pressure and the temperature difference.

r diatomic and polyatomic gases, the molecules striking the hot surface acquire not only increased translational energy but also increamounts of both rotational and vibrational energy. The amount of the vibrational energy possessed by molecules as compared with the a

translational energy is measured by the value ofγ . In these cases, a detailed calculation leads to the relation

hich forγ = 5/3 (case of monatomic gases) becomes identical with Eq. (1.173).





n this equation,α has the value [74]

whereα1 andα2 are the values of the accommodation coefficient for the two surfaces.

ubstituting forvi from the relation in terms ofTi and M , Eq. (1.174) assumes the form

whereΛ0 = free-molecule heat conductivity at 0°C

n terms of calories per second,Λ0 should be multiplied by 0.2389.)

able 1.13 gives values ofΛ0 in watts per square centimeter per degree per mTorr for a number of gases and vapo75], and, for comparison, values of 4.186λ0 (derived from the values in Table 1.10 and from other sources) whiorrespond to the conductivity at 0°C in terms ofwatts per centimeter per degree .

n terms of calories (15°C) per mole, we have

0 = 8.3145 × 107/4.1855 × 107 = 1.9865 cal · deg1 · mol1·



Table 1.13. Values of Molecular Heat Conductivity

Gas M γ 106Λ0 4.186 × 104λ0H2

2.016 1.41 60.72 17.30

He4.003 1.67 29.35 14.36

H2O18.016 1.30 26.49

Ne20.18 1.67 13.07 4.66

N228.02 1.40 16.63 2.38

O232.00 1.40 15.57 2.44

Ar 39.94 1.67 9.29 1.60

CO244.01 1.30 16.96 1.44

Hg200.6 1.67 4.15





ince γ + 1 = (2Cv + R0)/Cv and γ 1 = R0/Cv, whereCv = molar specific heat in calories (at constant volume) and Ras the above value, in all of the above expressions we can set

Hence Eq. (1.177) can be expressed in the form

or coaxial cylinders of radii r 1 and r 2 (r 2 > r 1), the rate of energy transfer per unit area from the inner cylinder wire, at temperatureTs and at low pressures, is given by the relation

nd whenα1 = α2 = α this becomes [76]

eans [77] has pointed out that, according to general dynamical considerations, the constantα should be determinedrelation of the form

wherem′ = mass for molecules striking the surface for which the molecular mass ism.

Morrison and Tuzi [78] have used a molecular beam method with mass spectrometer detector to measure the thccommodation coefficient for translational energy of a number of vapors on Pyrex glass.

or completely roughened surfaces,α = 1. Values ofα which have been observed for different surfaces are givenable 1.14 [79].

Keesom and Schmidt [80] have measured the thermal accommodation coefficients for He, Ne, H2, and N2 onhuringian glass at 0°C at pressures from 0.04 to 0.2 Torr. Average values were 0.335 for He, 0.286 for H2, 0.8

N2, and 0.670 for Ne.



Klett and Irey [81] have measured the thermal accommodation coefficients for air, nitrogen, and helium on comopper surfaces at pressures from 2 × 104 Torr to 4 × 103 Torr, obtaining 0.799 for N2 at 77.4 K, 0.760 for N2

K, 0.823 for air at 77.4 K, 0.698 for air at 243 K, 0.564 for He at 77.4 K, and 0.407 for He at 243 K.





Table 1.14. Values of the Accommodation Coefficient for Several GasesSurface H2 O2 CO2Polished Pt

0.358 0.835 0.868

Pt slightly coated with black 0.556 0.927 0.945

Pt heavily coated with black 0.712 0.956 0.975

H2 N2 Ar Hg Air

Tungsten0.20 0.57 0.85 0.95

Ordinary Pt0.36 0.89 0.89 0.90

.9.2emperature Discontinuity (Smoluchowski)

n Section 1.7, mention was made of the phenomenon of ''slip" which occurs in a gas at moderately low pressuq. (1.145) we introduced a coefficient of slipζ = β L to account for the apparent decrease in viscosity at low pres

An analogous phenomenon was observed by Smoluchowski in the case of thermal conduction at low pressuresarallel plane surfaces separated by a distanced , the heat loss per unit area per unit time may be represented at theressures by a relation of the form

whereλm is the mean conductivity over the rangeT 1 T 0.

n this equation, g is a coefficient defined by the relation

where∆T represents the temperature discontinuity at any one surface, anddT/dx is the temperature gradient normahe surface.

As shown by Kennard,

where the numerical constantε has a value, according to Eq. (1.165), which varies between 1 and 2.5, andβ′ is aumerical constant of the order of unity.



Hence Eq. (1.183) may be expressed in the form

whereα is assumed to be the same for both surfaces, L = c/P , and the symbol E 0 P indicates that the conductivity pnit area is a function of P .





A comprehensive treatment of the heat transport between parallel plates in a gas of rigid sphere molecules for tange of rarefaction conditions from a dense Clausius gas to the extreme rarefaction of a gas with a Knudsen nu

has been published by Frankowski, Alterman, and Pekeris [82]. Willis [83], using a relaxation-type mntermolecular collisions, has derived equations based on the Krook [84] kinetic model for the heat transfer in aas between parallel plates at large temperature ratios. He has also considered heat transfer and shear between ylinders for large Knudsen numbers [85].he problem of heat transfer between concentric spheres in the near free-molecule region has been treated by Hnd Springer [86] and other authors cited in their article.

or a hot wire of radiusa situated along the axis of a cylindrical tube of radiusr , Eq. (1.186) must be replaced by telation

where it is assumed thatα is the same for both the wire and inside surface of the cylinder.or very low values of P , Eq. (1.186) becomes

nd Eq. (1.187) becomes

hat is, at very low pressures E 0 P is independent ofd and varies linearly with P . This conclusion is identical with educed above by Knudsen for the case of free-molecule flow. That Eq. (1.188) is identical with Eq. (1.176) mhown as follows.

ubstituting forβ′ from Eq. (1.185), substituting forλm from Eq. (1.164), and utilizing the relationη = 0.5ρvaL , webtain the result



whereα /(2 α ) takes the place ofα used in Eq. (1.176).





quations (1.186) and (1.187) can be expressed in a form which is very convenient for calculation. We shall cospecially Eq. (1.187), which is more important in practical measurements of heat conductivity. This equation mbviously be written in the form

hat is, if 1/ E 0 P is plotted against 1/ P , a straight line is obtained. From the intercept for 1/ P = 0, which we shallesignate by 1/ E 0 ∞, the value ofλm may be obtained, while the slope is given by the relation

where X is a constant determined by the relation

quation (1.190) thus applies to the transition range of pressures in which E 0 changes from being independent ofressure (at higher pressures) to varying linearly with the pressure (at very low pressures).

n a very interesting paper published in 1912 [87, also see 88], Langmuir formulated a theory of the mechanismonduction from wires (as well as plane surfaces). Observations on the heat losses in hydrogen from tungsten weated to incandescence showed that whether the wire was in a horizontal or vertical position made a differencfew percent (at constant temperature) in the heat loss. "This," states Langmuir, "was strong indication that the

oss was dependent practically only on heat conduction very close to the filament and that the convection curreractically no effect except to carry the heat away after it passed out through the film of adhering gas."

n the case of a wire of radiusa , Langmuir assumed that the energy loss will occur through a "stationary" film ofdherent gas, the outer edge of which is at a distanceb from the axis of the wire. As shown by Langmuir, the valuhen satisfies the relation

nd the energy loss per centimeter length of wire is given by the relation





n whichλ(T ) is given by Eq. (1.166).ntroducing into Eq. (1.195) the relation expressed by Eq. (1.192), it follows that

rom measurements of the energy losses from platinum wires in air [89], Langmuir derived the conclusions that 20°C and 760 Torr, B = 0.043 cm and is "surprisingly independent" ofT . He also concluded that B should beroportional to the viscosity and inversely proportional to the density, "for it is the viscosity that causes the exihe film and it is the difference of density between hot and cold gas (proportional to the density itself) that keeplm from becoming indefinitely large."

he problem of heat conduction at low pressures from a wire of radiusa , suspended coaxially in a glass tube of radwhere r is very much greater thana , has been discussed from the point of view of Langmuir's film theory by Jon

rody and Körösy [90] have shown that although 90% of the wattage lost can be accounted for by assuming puonduction, the film is not "stationary," but convection currents exist with the velocity of convection increasingurface of the filament is approached up to the limit (0.25 mm) of their measurements for incandescent tungstelaments in nitrogen.

10hermal Transpiration (Thermomolecular Flow)

rom Eq. (1.82),

follows that the rate of efflux of a given gas through a small opening varies asρ(T )½. If we have two chambers A , separated by a small orifice, at two different temperatures,TA and TB, transpiration will occur until a steady stastablished at which

he limiting ratio of pressure is

was expected that the same result would be obtained when the chambers are separated by a wall containing alug or by a single long tube of diameter 2a







uch that the Knudsen number because under this "molecular flow" condition the probabassage of a molecule through a long tube is the same in both directions when the molecules enter the ends witosine law distribution. Also, when the effect should be independent of the wall temperature of theonnecting tube. However, Hobson et al. [91] found that, while Eq. (1.199) is obeyed for apertures, this lower lot necessarily reached when the two chambers are separated by a long tube in which the pressure is so low tha

. Their data showed that the measured lower limit wasaRm with a ranging from 1.1 to 1.3, with lower valf a as the tube diameter is reduced and the molecular weight M increased. Miller and Buice [92] attempted to exphe need for the correction factora based on a model in which the faster moving molecules have a higher probabeing specularly reflected. They applied a Monte Carlo method to calculate the flow through the tube with a spf scattering at the wall, but their results were not in good agreement with the experimental data of Hobson andoworkers.

hermal transpiration is of importance in the application of vacuum gauges and vacuum microbalances at low por instance, if the chamber A is a part of a system at liquidair temperature (TA = 90) and the pressure is measured

means of a gauge at room temperature (TB = 300), then the real value of PA is given by the relation

A = PB (90/300)1/2 = 0.55 PB .ecause the envelope of a tubulated ionization gauge is usually at a temperature much higher than room tempe

he gauge is not used under the same temperature conditions as those during its calibration, a correction based o1.199) may be required [93]. Poulis et al. [94] have shown that longitudinal Knudsen forces associated with thanspiration effect can give spurious mass variations in vacuum microbalances when temperature gradients ex

he balance case.

When the mean free path L is very much smaller than 2a , so that collision between molecules become predominaollisions against the walls, then the condition of equilibrium is

here exists therefore a range of pressures in which the pressure ratio PA/PB changes from that given by Eq. (1.20hat given by Eq. (1.199) in the case of an aperture, and toa(TA/TB)1/2 in the case of narrow tubes, witha being anxperimentally determined factor between 1.0 and 1.3.

he theory of the phenomenon was first discussed by Maxwell (1879) and subsequently by Knudsen [95], whoquations for the pressures gradient along the connecting tube as a function of the tube diameter and pressure i

hamber. For the pressures and temperatures in the two vessels, Knudsen proposed





e semiempirical relation

hich for reduces to Eq. (1.199), and for reduces to the equilibrium condition PA = PB . For a temperat

adient along the connecting tube results in a boundary layer flow of gas (thermal creep ) along the wall of the tube from the cold tot side balanced by a return flow through the interior from the hot side to the cold side [96], and complicated theoretical equate thermal transpiration effect in this case have been proposed by various authors.

ennett and Tompkins [97] have recommended that an equation proposed by Liang [98, 99] be used. The equation is supportednetic argument, and Bennett and Tompkins found it to fit experimental data over a wide range. It should be noted, however, thorkers used glass systems. Los and Fergusson [100] observed that the nature of the wall affects the magnitude of the correctioang had predicted [99].

he form of Liang's equation given by Bennett and Tompkins can be expressed as follows:

which

R = the ratio of the pressures in the two regions at different temperatures,TA and TB,b = 1 for connecting tubes of internal diameter,d < 1 cm

= 1.22 for connecting tubes of internal diameter,d > 1 cm, X = PBd ,

αHe = 3.70 (1.70 2.6 × 103∆T )2 (∆T = TB TA),

βHe = 7.88[1 (TA/TB)½] for (TA/TB)½≤ 1,

nd values ofφ g are given in Table 1.15.

ennett and Tompkins also point out thatφ g values may be calculated from the collision diameters,r 0, given by Hirschfelder, Bird,potz [101], by making use of

able 1.15. Experimentalφg Values for Glass Systems (Bennett and Tompkins)Gas: He Ne Ar Kr Xe H2 O2 N2 CO CO2 C2H4

g : 1.00 1.30 2.70 3.90 6.41 1.44 2.87 3.53 3.31 4.52 6.72





he equation

Arney and Bailey [102] studied the thermal transpiration effect for air, argon, and helium for Knudsen numbers.01 up to 100 and for temperature ratios from 1.5 to 3.8 by an unusual technique involving two tubes, one witiameter and the other with small diameter, joined together by an annular junction at which the temperature coaised by an electrical resistance heater while the other ends of the tubes were maintained at a fixed temperatur

water cooling. The pressure at the cold ends of the two tubes was measured for a series of temperature ratios, aressure at the junction was assumed to be that of the cold end of the larger tube as long as the Knudsen numbe0.01 for the larger tube. Then when Kn reached higher values in the larger tube, the pressure ratio between th

nd and the junction could be estimated from the experimentally determined variation of the ratio of pressure atnd of the smaller tube to that at the junction with the Knudsen number for the smaller tube which was determi

Kn for the larger tube was still less then 0.01. Comparison of their results with the predictions of Knudsen's equ103] fordp/dT showed agreement at the upper and lower ends of the range of Kn but somewhat lower values oatio of the pressure at the cold end to that at the hot end for Kn in the middle range from 0.1 to 10. They presef curves, based on their measurements, of pressure ratios versus temperature ratios for a series of Knudsen num

om 0.03 to 10.Hobson [104] compared the experimental data obtained by Edmonds and Hobson [105] for helium and neon efhrough an aperture with 2a = 20 mm,TA = 77.4 K, andTB = 295 K with the values predicted by Eq. (1.201) and 1.202). For the mean free path in Eq. (1.201), Hobson used the relation of Weber and Schmidt [106]:

where ( PL )0 = 0.1339 Torr · mm andn = 0.147 for helium while ( PL )0 = 0.08841 Torr · mm andn = 0.20 for neonwas chosen as 295 K. An appropriate choice of the constantsαHe, βHe, andφ g in Liang's equation gave a curve

ressure ratio R versus PB in very good agreement with the experimental data, while the curve based on the sim1.201) agreed with the experimental data at the lower limit 0.512 and upper limit 1.0 but was slightly higher atf PB in the middle range.

odgurski and Davis [107] obtained results that agreed with Bennett and Tompkins' equation [Eq. (1.202)] for nd xenon but deviated appreciably from this equation for neon and hydrogen at low pressures.

haripov [108] has made extensivse calculations based on a modified Boltzmann equation of the exponentγ in thequation

s a function of the Knudsen number (which he defines as Kn = L/a ) and other factors, for long capillary tubes of r

under conditions of a balance between the





ow due to the pressure gradient and the flow due to the temperature gradient. He tried to compare his calculathe experimental results of Edmonds and Hobson as recalculated using a rarefaction factor proportional to the i

Knudsen number at PB and TB but found a disagreement for different capillaries.

Dietz [109] studied the thermal transpiration effect in the mass spectrometer inlet system for argon in the leak tound that sensitivity response was not affected if gas mixtures and calibrating gases are run at the same pressu

Variable capacitance diaphragm transducers used as transfer standards in an intercomparison of pressure standahe low vacuum region of 1 to 10 Torr are operated at a stabilized elevated temperature to reduce inherent sensmbient temperature changes, and thermal transpiration causes a pressure differential between the transducer anacuum system which must be determined in order to achieve maximum accuracy of calibration comparisons. nd Röhl [110] have studied this problem quantitatively and applied correction procedures based on Eq. (1.202sing both the Liang expression for f ( X ) and the more recent formula of Takaishi and Sensui [111]

where the parameters A*, B*, andC * depend on the gas species and are determined experimentally. The correcticcording to the Liang formula was in poor agreement with their experimental data, but the correction using thf Takaishi and Sensui reproduced the experimental data within about 4%. The degree of agreement seemed ton the material used for the connecting tube, and by adopting an effective temperature (TA)eff and an effective tubeiameter they were able to obtain agreement to better than 0.1%.

Williams [112] derived equations for thermal transpiration in the near-continuum regime starting with the Naviquations and using the slip boundary condition at the wall including thermal creep. Comparison of his equatiohe experimental data of various authors showed good agreement for low Knudsen numbers but gave too smallhe Knudsen number increased.

11hermal Diffusion

he thermal-diffusion effect has been described by Ibbs [113] as follows:

f a temperature gradient is applied to a mixture of two gases of uniform concentration, there is a tendency for teavier and large molecules (massm1, diameterδ1) to move to the cold side, and for the lighter and smaller molemass m2 and diameterδ2) to move to the hot side. The separating effect of thermal diffusion (coefficient DT ) isltimately balanced by the mixing effect of ordinary diffusion (coefficient D12) so that finally a steady state is reacnd a concentration gradient is associated with the temperature gradient. The amount of thermal separation thuroduced by a given difference in temperature depends upon the ratiosm1/m2 andδ1/δ2 and upon the proportion b

olume of the heavier gas f 1 and of the lighter gas





2 (where f 1 + f 2 = 1) and also upon the nature of the field of force operating between the unlike molecules.

he effect was predicted by Enskog (1917) and, independently, by Chapman and Dootson [114]. Following thexperimental investigations of Ibbs and others, Clusius and Dickel [115] devised a continuous method for sepa

mixtures of gases and isotopes which has been applied extensively by subsequent investigators.

n this section the discussion will be limited largely to the experimental data, since the mathematical theory is qomplex and beyond the scope of the objectives of this chapter.

he coefficient of thermal separation is defined by the relation

where DT and D12 have been defined above. Now

f kT is a constant, then we obtain from Eq. (1.207) the relation

or the amount of separation, whereT 1 and T 2 denote the hot and cold temperatures, respectively.

igures 1.6 and 1.7 illustrate results obtained by Ibbs [116] with mixtures of H2 and N2. The concentrations ofhe different mixtures varied from 4.7% for No. 2



Fig. 1.6Relation between degree of separation by thermal diffusion

and log(T 1/T 2) for mixtures of H2 and N2.





Fig. 1.7Relation between composition of H2N2 mixtures

and degree of separation for log(T 1/T 2) = 0.2.

o 50.5% for No. 7. It will be observed that these observations are in accord with Eq. (1.208), since∆ f is found to benear function of log(T 1/T 2). Figure 1.7 shows the variation in value of∆ f with composition for a constant value oatio T 1/T 2.

hapman has shown thatkT can be expressed in the form [117]

where the coefficients A to D are functions of the molecular weights and of the ratioδ1/δ2. These can be calculated

om the force constants s12 in the repulsive force relation F = c/rv , wherev = s12 for unlike molecules andr = 1/2(δ2).

he separation in a mixture of H2 and CO2 was investigated by Ibbs and Wakeman [118] over a range of 600°ny given mixture it was observed that the amount of separation was in accordance with Eq. (1.208). For a conifference in temperature,∆ f increased from 0 for pure H2 to a maximum value of 0.0365 (for∆T = 600°C), for a

mixture containing 61% H2.

According to Chapman,kT in this case should be given by a relation of the form

where f 1 refers to CO2 and f 2 refers to H2. Since this relation is deduced on the assumption that the molecules bs rigid elastic spheres with a force relation in which s12 has a definite value for the interaction between the two tf molecules, it was expected that the observed values ofkT would differ from those calculated. Table 1.16 gives esults of a series of measurements. The last column gives values of a constant defined by the relation







able 1.16. Separation Measurements in a Mixture of H2 and CO2Temperature Range (°C) kT (calc) kT (obs) RT

469Below 144

0.1575 0.0665 0.422

Above 1440.1575 0.0939 0.596

At 470 0.1575 0.1045 0.663

34Below 145

0.1685 0.0695 0.415

Above 1450.1685 0.0929 0.552

r CO2N2 mixture, Chapman's expression forkT is of the form

here f 1 again refers to theheavier gas. (In all the following equations, f 1 has the same significance.)

r f 1 = 0.494, the value ofkT calculated is 0.0564, whereas the value of RT observed varied from 0.247 for temperatures below 144°C to 0r temperatures above 144°C.

r the mixtures ArHe, NeH2, and N2He, relations similar to Eq. (1.210) and Eq. (1.212) forkT have been published by Ibbs and Grew [119l the observed values of RT showed a decrease with decrease in temperature down to 190°C.

ccording to Chapman and Cowling,

ence observations on the values of RT should yield values of s12. In fact the observations on thermal diffusion of gases should revealeresting information on the forces between molecules. Table 1.17 gives values of the repulsive force constant s12, as determined fromserved values of RT , and, for comparison, values of s1 and s2 for the individual gases, as determined from other phenomena.

1938, as mentioned previously, Clusius and Dickel [115] devised an arrangement of hot and cold surfaces that could be utilized practe separation of mixtures of different gases and of isotopes. They used a long vertical tube with a hot wire along the axis. Because of thffusion, the relative concentration of the heavier molecules is greater at the cold wall. Convection causes the gas at the hot surface to e top, where it is deflected to the cold wall. There the gas sinks to the bottom and the cycle is then repeated. As a result, theheaviermponents concentrate at the bottom , whereas the lighter ones concentrate at the top.

r instance, in a chamber 1 meter in height, for a temperature difference of 600°C, it was possible to separate a mixture containing 40%y volume) CO2 and 60% H2, with a yield of practically 100% CO2 at the bottom and 100% H2 at the top. In





able 1.17. Values of ''Force" Constants for Interaction of Moleculesases RT s12 s1 s22H2 0.48

7.3 7.6 11.3

2Ar 0.477.2 8.8 7.35

2N2 0.58 8.2 11.3 8.8

eAr 0.659.0 14.6 7.35

2Ne 0.7411.4 11.3 14.5

2CO2 0.477.2 11.3 5.6

eAr 0.547.9 14.5 7.35

eNe 0.8011.4 14.6 14.5

chamber 2.9 meters in height, for a temperature difference of 600°C, air (21% O2, 78% N2) could be separated, yielding 85% O2 at thttom. Finally, from a mixture of 23% HCl37 and 77% HCl35, a mixture containing 40% of the heavier isotope was obtained at the boe diffusion chamber.

ewer and Bramley [120] used a heated inner tube 1 cm in diameter and an outer cooled concentric tube 2 cm in diameter, each 1 meteith a 350°C difference in temperature, He and Br2 could be separated, so that after 15 min no Br2 could be detected at the top. Undermilar conditions a 5050 mixture of CH4 and NH3 was enriched 25% in NH3 at the bottom. Brewer and Bramley deduced the followination: "Ifl denotes the cylinder length,r the radius of the outer tube, andd the difference in radii, then, to a first approximation, the rate oparation varies asrd and the purity asl/d ."

a thermal-diffusion column developed by Nier [121] for the concentration of C13H4, a Nichrome heating wire threaded through porcsulators was inserted along the axis of a steel tube 3/4 in. in outside diameter, which was concentric with a steel tube 1¾ in. in outsideameter having a wall thickness of 0.035 in. This tube constituted the inner wall of the annular space containing the gas, and the outer nsisted of a 2-in.-outside-diameter brass tube, which was water-cooled. The column, which was 24 ft in length, is used as a return learrent flowing through the Nichrome wire. At the lower end, the two steel tubes were brazed concentrically to a circular steel plate. Therage temperature of the outer wall was 27°C, and that of the inner wall was approximately 375°C. The samples of methane taken at ttom and top were analyzed by means of a mass spectrometer for the ratio of C13H4 to C12H4. At a pressure of 656 Torr and after opr 23.5 hours, the values of this ratio at the bottom and top were 0.0215 and 0.0054 respectively, so that the ratio of C13H4 at the bottothe top was 3.99.

he results obtained were found to be in agreement with conclusions deduced from theoretical considerations by Furry, Jones, and Onsa22]. They derived the relation





where

represent equilibrium concentrations of C13H4 in the lower and upper ends of the column, respeand b are constants for the gas used and the dimensions of the column, and p denotes the pressure. Thusε x orresponds to the separation factor. In the investigation under consideration, this factor was observed to pass t

maximum at p = 0.6 atm, approximately.

he separation of C13H4 and C12H4 has also been investigated, in a column 40 ft in length, by Taylor and Glo123], who found that the separation factor could be represented, in agreement with the theory, by the above eq

he rate at which equilibrium is approached in such a column has been discussed by Bardeen [124] and the coneached have been found to be in good agreement with experimental results obtained by Nier.

Although the above discussion has dealt largely with the separation of gases which differ in value of M , it follows fr

he theory of thermal diffusion that it should be possible by this method to effect a certain degree of separation mixture of gases which have the same value of M but differ with respect to the magnitude of the molecular diameResults in agreement with this prediction have been obtained by Wall and Holley [125].

12heory of Diffusion of Gases

As in the case of viscosity and heat conduction, approximate kinetic-theory considerations lead to the conclusiohe coefficient of self-diffusion, D , is given by a relation of the form

which indicates that, at constant temperature, D varies directly as the mean free path or inversely as the pressure.

ombining Eq. (1.216) with the relation

ntroducing the correction for persistence of velocities and that for Maxwellian distribution of velocities, it is fohe more accurate relation is

According to Chapman and Enskog [126], the coefficient in Eq. (1.217) should have a value lying between 1.2ard spheres and 1.543 for inverse-fifth-power repulsion.





Actually observed values of D yield the following values of the coefficients [127]:

CO, 1.30; H2, 1.37; O2, 1.40; CO2, 1.58.

or the derivation of a relation for the coefficient of interdiffusion, D12 (corresponding to the fact that molecules are involved), we shall follow the StefanMaxwell derivation [128], which, as will be evident, is based on the onsiderations as those used in deriving Eq. (1.216) above.

ettingn1 and n2 represent the number of molecules of each kind per unit volume at a location ( x, y, z ) and assuminhe concentration gradients to occur only with respect to the x-axis, then for a gas at rest we obtain

n1/dx + dn2/dx = 0.

he rate of flow, J 1, of molecules of the first type countercurrent to the flow of molecules of the second type at 2 is defined by

where D12 is the mutual diffusion coefficient orcoefficient of interdiffusion . The Meyer formula [129] for D12 is

wherev1 and v2 are average velocities.

he StefanMaxwell formula for the mean free path, L1, in a mixture of two gases, designated 1 and 2, according t1.140), is

However, as Stefan and Maxwell have pointed out, the collisions between like molecules do not influence diffuence for this case the mean free paths are given by the relations

ince for thermal equilibrium







nd

n this basis it is found that the relation for the coefficient of interdiffusion is

here n = n1 + n2.

is evident that for like molecules this relation becomes

ombining this with the relation

= 0.499ρva /(21/2πnδ2),

e result is

hich is in substantial agreement with Eq. (1.217).

able 1.18 [130] gives the values of D12 (cm2 · s1) observed for several pairs of gases, at 0°C and 1 atm, values ofδ12 calcuom the values of D12 by means of Eq. (1.224), and, for comparison, values ofδ12 calculated from viscosity measurementable 1.6) for each of the two gases.

or the first six pairs, which are comprised of "hard" molecules (with a value for the repulsive force constant greater thagreement is very satisfactory. Even in the case of "softer" molecules the agreement is fair, as shown by the values for tt of five pairs.

Table 1.18. Coefficients of Interdiffusion and Average Molecular Diameters

Gases D12 (obs) 108δ12 (calc from D12) 108δ12 (calc fromη)H2air

0.661 3.23 3.23

H2O20.679 3.18 3.17

O2air 0.1775 3.69 3.68

O2N20.174 3.74 3.70

COH20.642 3.28 3.25

COO20.183 3.65 3.70

CO2H20.538 3.56 3.69



CO2air 0.138 4.03 4.20

CO2CO0.136 4.09 4.22

N2OH20.535 3.57 3.69

N2OCO20.0983 4.53 4.66





ummerhays [131] has used the katharometer (see Section 1.8) to measure the diffusion coefficient of water vair. The value observed was D = 0.282 cm2 · s1 at 16.1°C.

As will be noted, Eq. (1.224) indicates that the interdiffusion coefficient should be independent of compositionHowever, a series of experiments carried out at Halle [132] to test this conclusion show that there is a variation more than a few percent with variation in the ration1/n2.

Mention should be made in this connection of a relation for the coefficient of interdiffusion, given by Loeb [13 of the form

n whichβ is a numerical factor, the value of which is between 1.00 and 1.50, andn = n1 + n2.

rom the equations for D it follows that to a first approximation D should vary asT 3/2 and as P 1. Since, however,ηaries withT in accordance with Sutherland's relation, Eq. (1.122), it is expected that the exponent ofT would excee/2. Lonius [132] gives the following relation for D as a function ofT :

where DT = value atT (in degrees Kelvin) and P t (in Torr) and D = value at 15°C and 760 Torr. The values of x useonius for several binary mixtures are all in the neighborhood of 1.75.

vakin and Suetin [134] have measured the temperature dependence of the diffusion coefficients of 18 pairs of ghe temperature range 290470 K. Using their experimental data they calculated the interaction potential parameotential functions of the Lennard-Jones type and of the modified Buckingham type and also for point center re(r ) = d/r δ. For the latter case they used the formula

12 = D0TN ,

where D0 is given by a complicated formula taken from the treatise by Hirschfelder, Curtiss, and Bird [135], w N/2 + 2/δ. The calculatedδ values ranged from 4.33 for H2Ar to 14.29 for Heair. For comparison they also preseotential parameters obtained from viscosity measurements and the second virial coefficient. The potential parbtained from the diffusion equations gave the best fit to the temperature behaviour.

.12.1MaxwellLoschmidt Method for Determination of Diffusion Coefficients

n view of the fact that in vacuum technique a problem arises occasionally regarding the time required for gaseis of interest to review briefly one method which has been used for the determination of D for gases.





tube of lengthl is divided by means of a wide-bore stopcock into two parts of equal length. This is mounted in a vertical positioavier gas ( A) is put in thelower part, and thelighter gas ( B) is put in theupper part. At timet = 0 the stopcock is opened and diffuslowed to occur for a definite period,t . The stopcock is then closed, and the proportions of A and B are measured in each compartme

Let U = amount of A expressed as the fraction of the total number of moles in the lower compartment,Q = amount of A in the upper compartment, expressed similarly.

hen, on the basis of the equations for diffusion,

or instance, in the case of H2O2 mixture, forl = 99.93 cm andt = 1800 s we obtainU = 0.5982 andQ = 0.4018 at 14.8°C and 749.3 ence, at 15°C and 760 Torr, D = 0.788.

able 1.19 gives values ofUQ for two different values ofl as a function of Dt , along with values oft , for l = 100 cm, assuming D = 0.21.

or l = 100, only the first term in the series on the right-hand side of Eq. (1.229) is of importance for values of Dt > 500. Forl = 25, onst term is of importance for Dt > 100. Equation (1.230) shows that for values ofl and Dt for which the first term only is sufficientlycurate,t varies asl 2 for constant value of (U Q).

ering and Sheinblatt [136] have considered diffusion theory for both thermal gradients and density gradients in rarefied gases vtire pressure range from the continuum domain to the free-molecular-flow domain as applied to

able 1.19. Illustrating the Application of Eq. (1.229)t l = 100 cm

U Ql = 25 cm

U Qt (min) for D = 0.2 cm2 · s1

100 0.9550 0.2063 8.33

200 0.8401 0.0425 16.67

300 0.7514 0.0088 25.00

400 0.6771 33.34

500 0.6118 41.67

700 0.5014 58.67

1000 0.3728 83.83

1500 0.2276 125.00

2000 0.1390 166.67

3000 0.0518 250.00

5000 0.0071 416.67





molecules which obey a center of repulsive force F = K 12/rv, wherev = 5 (Maxwell molecules) and in the extremegid-sphere molecules,v = ∞.

unningham and Geankoplis [137] have presented equations for diffusion in three-component mixtures in the tegion between Knudsen and molecular diffusion in an open system. Solution of the equations is, by trial and eided by computer.

.12.2ffect of Pressure of Gas on Rates of Evaporation of Metals

n Section 1.5, equations were derived for rates of evaporation in avacuum . These equations have been applied, aslustrated in the above connection, to the calculation of vapor pressures of high-melting-point metals from obsn rate of loss in weight as a function of the temperature. However, in the presence of a gas which does not reahemically with the metal, the observed rate of evaporation is lower; as is well known, this fact was utilized byangmuir in the invention and development of the gas-filled tungsten-filament lamp. This phenomenon has bexplained by Langmuir by assuming the existence of a film adjacent to the evaporating surface through which vaporated from the surface diffuse.

onda [138] has shown that this theory accounts very satisfactorily for his observations on the rate of evaporatiungsten in the presence of argon at various pressures, and the following remarks on the mechanism of evaporander these conditions are quoted from his paper:

The filament is considered to be surrounded by tungsten vapor at the same pressure as would be present invacuum. The atoms of this vapor, however, instead of being projected directly from the filament, as in avacuum, are pictured as diffusing through the stationary film of gas. Once an atom reaches the outer boundof the film, it would be carried away in the convection current of gas and would be lost to the filament; bu path within the film is so irregular that an atom may in fact return to the filament and be deposited on it, thleading to a reduced evaporation as compared with that in a vacuum.

et dc/dr denote the concentration gradient at the surface of the wire, wherer is the distance from the axis, and let Denote the diffusion constant. Assuming uniform distribution over the surface of the wire, the rate of diffusion per unngth of the wire is

where D is given by Eq. (1.224).

ince the value ofn for tungsten atoms is negligible compared with that ofn for argon gas, the expression for D ecomes identical with Eq. (1.216), where L and va refer to the values of the mean free path and average velocityespectively, of the tungsten atoms at the temperature of the filament. Thus D varies inversely as the pressure, P ofrgon, and Eq. (1.231) becomes

where A is a proportionality constant.





r a wire of diameter 2a and gas film of diameter 2b, it follows, from the same considerations as those that lead to Eq. (1.192) for the hea

t m denote the rate of evaporation in grams per square centimeter per second. Then it follows from Eqs. (1.232) and (1.233) that

here ca and cb are the concentrations of the tungsten atoms atr = a and r = b, respectively.

ble 1.20 shows results obtained by Fonda for the rate of evaporation from a filament in a mixture of argon and nitrogen, such as is uss-filled lamps. The valuem = 230 × 109 g · cm2 · s1 observed for P = 0 is in agreement with the value 250 × 109 observed by Langmuirnes, and Mackay [139].

s Fonda states: "The expressionmaP cm log (b/a ) is sufficiently constant at pressures above 10 cm (100 Torr) to allow of credence beinge hypothesis developed above."

he constancy of the expression has a further significance, because, as is evident from its derivation, it denotes a constant difference bee vapor pressure of tungsten at the surface of the filament and at the surface of the film of gas. For constant filament temperature this

at the concentration of tungsten vapor at the surface of the stationary film of gas should be constant for all pressures above 10 cm. It ipor which constitutes that which effectively evaporates from the filament, because the rising convection currents of gas carry it off toposited on the bulb. The rate of evaporation at different pressures should be determined therefore by the area of the assumed film of ge concentration of vapor at its border is in

able 1.20. Rate of Evaporation (m) of Tungsten in 86% Argon, 14% Nitrogen at 2870 K a

cm 109m b (cm) 109maP cm log(b/a ) 109m/b

0 230

1 57.5 9.68 3.9

5 23.5 2.42 6.3

10 20.5 1.31 9.8 15.6

25 10.3 0.63 10.4 16.250 5.4 0.36 9.6 14.8

70 4.2 0.28 9.6 14.8

165 2.0 0.15 8.8 13.5

Diameter of filament (2a) = 0.00978 cm; P cm = pressure in cm of Hg.





act a constant. The constancy of the ratiom/b is therefore a further confirmation of the validity of the theory. Othvidence, based on the appearance of the surface of the filament, has also been shown by Fonda to be in agreemhe views expressed above.

rom Eq. (1.234) it also follows that at constant pressure and for filaments of different diameters the expressionma b/a ) should be constant. The validity of this conclusion was confirmed by Fonda in a series of observations maoth pure nitrogen and a mixture of nitrogen and argon [140]. In these cases the value actually used for B (the thicknf the film for a plane surface in gas at atmospheric pressure) was the same as that obtained from data on heatonduction in nitrogen.

13andom Motions and Fluctuations [141]

et us consider the case in which a group of N molecules start from the plane z = 0, at the instantt = 0, and diffusehrough the gas. The differential equation for the diffusion is

At any instant,t , the distribution of these molecules along the z axis is given by the relation

which satisfies the condition

Hence, the average value of z is

And similarly it can be shown that the root-mean-square value is given by the relation

hat is, thetotal net displacement in any given direction varies ast 1/2.

hese equations are of special importance in the determination of diffusion coefficients from observations on thrownian motion of small particles.





We can also express Eqs. (1.237) and (1.238) in terms of the mean free path L, on the basis of the relation

ubstituting in the above equations we obtain the relations

he collision frequency per molecule is

= va/ L,while the total length of path actually traversed by a molecule in timet is

hat is, thetotal length of path varies as the square of the net displacement from the point of origin att = 0.

As an illustration of the above equations let us consider the case of molecules in air at 25°C and atmospheric prince L = 6.69 × 106 andva = 4.67 × 104, it follows from Eq. (1.239) that D = 0.104 cm2 · s1, and fort = 60 s webtain zr = 3.53 cm, whilel = 6.98 × 109t = 4.19 × 1011 cm.

hat l = 1.19 × 1011 zr is obviously due to the fact that after each collision the probability of a displacement towower (or more negative) values of z is just as great as that of a displacement toward more positive values of z .

he equations for random motion have been applied to determine the value of Avogadro's constant from observn rates of diffusion of Brownian particles. It may be demonstrated that the rate of diffusion of spherical particliven by the relation



where a = radius of particle andη = viscosity of medium.





Also, the mean square of the displacement per second is expressed as

Values of NA obtained by application of these relations, though not nearly as accurate as those obtained frometerminations of the unit electric charge (the method used by Millikan), are in good agreement with them.

14cattering of Particle Beams at Low Gas Pressures

As calculated on the basis of classical collision theory of smooth elastic spheres, a neutral projectile particle of aveling with uniform velocityw1 before scattering by a target molecule of massm2 moving with average speed,w

much smaller than the magnitude of the projectile velocity so that we can setw2 = 0, will suffer a fractional loss ofnergy (see Section 1.3.).

o that, using Eqs. (1.39) and (1.44),

whereθ is the angle of incidence betweenw1 and the line of centers at collision in the laboratory system.

When the target particle is at rest in the laboratory system, the center of mass moves in this system with the conelocity

n the center-of-mass coordinate system, CM, the velocity of the projectile particle isw1 w12 and the velocity of tharget particle isw12. By combining the various vectors in both systems in one diagram it can be shown [142] th

whereβ is the angle of scattering in the center-of-mass system. Then the fractional energy loss can be written a

whereβ L is the angle of scattering in the laboratory system.





or a parallel monoenergetic beam of projectile particles uniformly distributed in a plane normal to the directiomotion, the probability of a particle being scattered in the angle betweenβ L and d β L is

o that the integral of this probability over all angles from 0 toπ equals 1. There is no backwards scattering from anitially stationary target particle in the laboratory reference frame.

When as in the case of elastic scattering of an electron, the scattering angleβ L is approximately equal tnd the laboratory system is almost the same as the center-of-mass system.

or a molecular beam emerging into a ''perfect vacuum" there will still be some scattering as the faster moleculvertake the molecules moving more slowly. By dividing the beam molecules into two groups, each with a narange of differing velocities but following a Maxwellian law of distribution, Troitskii [143] has calculated that ee path for collision of molecules within a unidirectional beam (far from the source opening) is about three tim

mean free path in a stationary gas of the same particle density as in the beam, neglecting second collisions withiffusely scattered by a first collision.

When the projectile particles are charged and moving with very high speeds, the target particle becomes the nun atom in the gas, and the scattering is designated asCoulomb scattering. At pressures of 106 Torr in the vacuumhamber of a synchrotron, or the beam tube of particle accelerators in general, the mean free path for a hydrogen nitrogen might typically be of the order of 104 cm, but the "mean free path" for collision of a hydrogen nuclproton) with the nucleus of a nitrogen atom might be more like 107 cm, depending on the velocity. When the particle is charged, the effect of scattering is compensated to a large degree by focusing magnetic fields which he particle away from the walls while being accelerated by electromagnetic fields over a total path length of ne

where ta is the acceleration time. Forta = 1 s, this path length is 3 × 1010 cm, so that many collisions with the nuas molecules at 106 Torr will occur. Without magnetic focusing, even deflection through a small scattering angβ

would be sufficient to scatter the projectile particle into the wall of the vacuum chamber.n the presence of the magnetic fields, elastic scattering gives rise to "betatron" oscillations with amplitudes whncrease slowly with time until the particle is captured by the wall of the vacuum chamber. Blachman and Courn 1948 published formulas which make possible an estimate of the fraction of the original particles in a circulaynchrotron which is scattered to the wall. They begin with the Rutherford formula for the scattering cross sectdf a particle of chargee by the nucleus of a target particle with charge Ze, into any solid angle,d ω, at the angleβ,

wherem is the relativistic mass of the projectile particle andv0 is its velocity. Because of the finite size of the nuchere is an upper limit onβ given byλ /b , where





= h/mv0 is the de Broglie wavelength andb is the "radius" of the nucleus. These authors give an equation for thllowable pressure in Torr inside the vacuum chamber of a synchrotron which is directly proportional to the pa

when the effects of damping are included, where is the mean square maximum amplitude of the vertical scillations and A is the vertical semiaperture of the chamber cross section. If no more than a 10% loss through cattering is to be permitted, thenη must be no more than 0.089 and the calculated upper limit of pressure is of tf 1.3 × 104 Pa (106 Torr) in typical synchrotrons. In 1949 Blachman and Courant [145] derived new equationo the "racetrack" modification of the synchrotron by the insertion of straight sections.

n 1951 Greenberg and Berlin [146] considered the gas scattering problem for protons and for electrons in greand estimated the limiting pressures at which 50% of the protons are lost and at which 10% of the protons are lrookhaven and Birmingham Synchrotrons. The values depend on the method of particle injection, but in gene

ndicate that pressures less than 1.3 × 104 Pa (106 Torr) are required to avoid loss of more than 10% in these mimilar calculations were made in 1955 by Moravcsik and Sellen [147] for the strong focusing electron synchr

ornell.n 1953 Courant [148] revised the previous gas scattering theory to include effects of scattering through angles nough for immediate particle loss. Kheifets [149] has used scattering formulas to estimate the lifetime in a stoevice of a beam of electrons. Various methods for computing particle loss by gas scattering in cyclical acceler

were compared by Didenko and Serdyutskii [150] in 1963. Orlov and Kheifets [151] have used revised formulappropriate boundary conditions for estimating the particle loss due to multiple Coulomb scattering in a cyclicaccelerator.

References and Notes

. In connection with this chapter, use has been made of the following treatises:

a. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics . McGraw-Hill, New Y1938.

b. L. B. Loeb, Kinetic Theory of Gases . McGraw-Hill, New York, 1934.

c. J. H. Jeans, An Introduction to the Kinetic Theory of Gases . Macmillan, New York, 1940; Cambridge UnivPress, Cambridge, UK, 1960.

d. S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases . University Press, CambrUK, 1939; 3rd ed., 1970.

Some other treatises which are recommended for further details are:

G. A. Bird, Molecular Gas Dynamics . Oxford University Press (Clarendon), Oxford, 1978.

C. Cercignani, Mathematical Methods in Kinetic Theory . Plenum, New York, 1969.

E. A. Guggenheim, Elements of the Kinetic Theory of Gases . Pergamon, New York, 1960.

M. N. Kogan, Rarefied Gas Dynamics . Plenum, New York, 1969.

L. C. Woods, An Introduction to the Kinetic Theory of Gases and Magnetoplasmas . Oxford University Press,Oxford, 1993.



T. Wu, Kinetic Equations of Gases and Plasmas . Addison-Wesley, Reading, MA, 1966.





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2. A. Roth,Vacuum Technology , p. 45. North-Holland Publ., Amsterdam, 1976; 3rd ed., 1990.

3. M. S. Kaminsky and J. M. Lafferty, eds., Dictionary of Terms for Vacuum Science and Technology, Surface

cience, Thin Film Technology and Vacuum Metallurgy , p. 71. AIP Press, Woodbury, NY, 1980.4. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics , p. 101. McGraw-Hill, N

York, 1938.

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H. de Leeuw, ed.), Vol. 1, p. 315. Academic Press, New York, 1966.

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Namur, Belg., 1958, E. Thomas (ed.), pp. 323328 Pergamon, London (1960); D. H. Holkeboer,10th Natl. Vac. Symp92, Macmillan Co., New York (1963).

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6. F. Knauer and O. Stern, Z. Phys . 53, 766 (1929).

7. J. B. Taylor, Ind. Eng. Chem . 23, 1228 (1931); also see W. H. Bessey and O. C. Simpson,Chem. Rev . 30, 2391942).

8. A. C. Torrey, Phys. Rev . 47, 644 (1935); A. B. Van Cleave and O. Maass,Can. J. Res., Sect. B 12, 57 (1935); 1384 (1935).

9. This topic is discussed at length by Chapman and Cowling [1d ] in their treatise on this subject. It will be obserhat LM = 1.611 L = 1.131 LB and LB = 1.425 L.

0. S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases , Sect. 10.41. University Presambridge, UK, 3rd ed., 1970.

1. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics , p. 147. McGraw-Hill, NYork, 1938.

2. See sub-section 1.7.2 on molecular diameters in Section 1.7.

3. W. Licht, Jr. and D. G. Stechert, J. Phys. Chem . 48, 23 (1944).

4. LandoltBornstein Physikalisch-Chemische Tabellen , 5th ed., Springer, Berlin, 19231935.

5. A. E. Schuil, Philos. Mag . [7] 28, 679 (1939). This paper gives data on values ofη for gases and vapors over thange 0250°C.




7. H.-S. Tsien, J. Aeronaut. Sci . 13, 653 (1946).

8. H. Braune, R. Basch, and W. Wentzel, Z. Phys. Chem. Abt. A 137, 447 (1928).

9. Value given in Ref. [48], which differs somewhat from that given in Table 1.8.

0. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics , pp. 160162. McGraw-HiNew York, 1938.

1. W. Gaede, Ann. Phys . ( Leipzig ) [4] 46, 357 (1915).


3. A. Timiriazeff [ Ann. Phys . ( Leipzig ) [4] 40, 971 (1913)] assumed that f , which may be regarded as anccommodation coefficient for transfer of momentum, has the same value for any gas-surface combination asα theccommodation coefficient for heat transfer (discussed in Section 1.9.1); but B. Baule [ Ann. Phys . ( Leipzig ) [4] 44, 1914)], disagreed with this assumption and concluded that the value of the ratio betweenζ and L [denoted byβ in E1.148) and (1.149)] must be a complicated function of the diameters of the molecules in the gas and those conhe surface. The theoretical





investigations on this topic are discussed by Kennard and Loeb. Loeb quotes results obtained by R. A. Mil[ Phys. Rev . 21, 217 (1923)], which lead to values of f ranging from 0.87 to 1.00.


5. Values ofb for a large number of gases and vapors are given in the Handbook of Chemistry and Physics , publishy CRC Press, Boca Raton, FL. Since these values are expressed in terms of the volume at 0°C and 1 atm as unhould be multiplied by 22,414 to give values for use in Eq. (1.154).

6. H. K. Livingston, J. Am. Chem. Soc . 66, 569 (1944); also S. Brunauer,The Adsorption of Gases and Vapors , p. 2rinceton University Press, Princeton, NJ, 1942.

7. H. A. Stuart, Molekülstruktur , pp. 49et seq . Springer, Berlin, 1934.

8. See also P. H. Emmett and S. Brunauer, J. Am. Chem. Soc . 59, 1553 (1937).

9. A. Eucken, Phys. Z . 14, 324 (1913).

0. L. B. Loeb, Kinetic Theory of Gases , pp. 234252. McGraw-Hill, New York, 1934.1. W. C. Kannuluik and L. K. Martin, Proc. R. Soc. London, Ser. A 144, 496, (1934).

2. See also the following references on this topic: H. Gregory and C. T. Archer, Proc. R. Soc. London, Ser. A 110, 91926); 121, 284 (1928); H. Gregory and S. Marshall,ibid . 114, 354 (1927); 118, 594 (1928); B. G. Dickins,ibid . 1417 (1934); H. A. Daynes,Gas Analysis by Measurement of Thermal Conductivity . Cambridge University Press,ambridge, UK, 1933, gives a very comprehensive table of relative thermal conductivities (air = 1) for a large f gases, including hydrocarbons.

3. J. R. Partington and W. G. Shilling,The Specific Heat of Gases . Benn, London, UK 1924; see also G. N. LewiM. Randall,Thermodynamics , p. 80. McGraw-Hill, New York, 1923; Bulletin 30, Cornell University, Engineering

xperiment Station, October, 1942, gives specific heats of a number of gases over a wide range of pressures anemperatures.

4. ln = loge = 2.303 log10.

5. The exact meaning of this requirement will appear in the subsequent discussion.

6. See A. Farkas and H. W. Melville, Experimental Methods in Gas Reactions , p. 190. Cambridge University Preambridge, UK, 1939; also A. Farkas,Orthohydrogen, Parahydrogen, and Heavy Hydrogen . Cambridge Universitress, Cambridge, UK, 1935, for illustration of the application of this method.

7. G. A. Shakespear, Proc. R. Soc. London, Ser. A 97, 273 (1920); see also the comprehensive discussion of thisnstrument by H. A. Daynes,Gas Analysis by Measurement of Thermal Conductivity . Cambridge University Press,ambridge, UK, 1933.

8. See especially a description of a modified construction by T. L. Ibbs, Proc. R. Soc. London, Ser. A 99, 385 (192lso 107, 470 (1925); W. E. Summerhays [ Proc. R. Soc. London 42, 218 (1930)] has used the katharometer to meahe coefficient of diffusion of water vapor.

9. B. G. Dickins, Proc. R. Soc. London, Ser. A 143, 517 (1934).

0. M. Knudsen, Ann. Phys . ( Leipzig ) [4] 31, 205 (1910); 32, 809 (1910); 33, 1435 (1910); 34, 593 (1911); [5] 61930); see also Loeb [1b, pp. 310325] and Kennard [1a, pp. 311320].



1. M. von Smoluchowski, a number of papers published before 1911 and Ann. Phys . ( Leipzig ) [4] 35, 983 (1911); iscussed by Loeb [1b] and Kennard [1a].

2. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics , pp. 311312. McGraw-HiNew York, 1938.

3. K. B. Blodgett and I. Langmuir, Phys. Rev . 40, 78 (1932).






5. A table of values ofγ is given by Loeb [1b, p. 445]; also see Partington and Shilling [63].

6. M. von Smoluchowski, Ann. Phys . ( Leipzig ) [4] 35, 983 (1911).

7. J. H. Jeans, An Introduction to the Kinetic Theory of Gases , p. 193. MacMillan, New York, 1940.

8. J. A. Morrison and Y. Tuzi, J. Vac. Sci. Technol . 2, 109 (1965).

9. The data for platinum are from Loeb [1b, p. 321]. The data for tungsten are from H. A. Jones and I. LangmGlectr. Rev . 30, 354 (1927)], while those for "ordinary" platinum are from B. G. Dickins [ proc. R. Soc. London, Ser. A43, 517 (1934)]. That the value of the accommodation coefficient is greatly affected by the nature of the surfaas been shown by K. B. Blodgett and I. Langmuir [ Phys. Rev . 40, 78 (1932)]. In the case of a tungsten wire inydrogen at 0.20 Torr, the value ofα changes from 0.534 for bare tungsten to 0.094 for tungsten with an adsorbef oxygen. The general problem of the interaction between molecules and solid surfaces, which is obviously inhe interpretation ofα , has received considerable attention from a number of investigators. For detailed discussispecially with regard to the role ofα in adsorption phenomena, see Loeb [1b, p. 311] and also J. K. Roberts (Someroblems in Adsorption . Cambridge University Press, Cambridge, UK, 1939). Values ofα for air and a number ofifferent metals having etched, polished, and machined surfaces have been determined by M. L. Wiedemann [Trans.SME 68, 57 (1946)]. These values range from 0.87 to 0.97.

0. W. H. Keesom and G. Schmidt, Physica ( Amsterdam ) 3, 590, 1085 (1936).

1. D. E. Klett and R. K. Irey, Adv. Cryog. Eng . 14, 217 (1969).

2. K. Frankowski, Z. Alterman, and C. L. Pekeris, Phys. Fluids 8, 245 (1965).

3. D. R. Willis, in Rarefied Gas Dynamics (J. A. Lauermann, ed.), Vol. 1, pp. 209225. Academic Press, New Yo963.

4. P. L. Bhatnager, E. P. Gross, and M. Krook, Phys. Rev . 94, 511 (1954).

5. D. R. Willis, Phys. Fluids 8, 1908 (1965).

6. J. C. Havekotte and G. S. Springer, AIAA J . 7, 782 (1969).


8. H. A. Jones,Gen. Elec. Rev . 28, 650 (1925).

9. Of course the loss due to radiation was subtracted from the total observed energy loss.

0. I. Brody and F. Körösy, J. Appl. Phys . 10, 584 (1939).

1. J. P. Hobson, T. Edmonds, and R. Verreault,Can. J. Phys . 41, 983 (1963); T. Edmonds and J. P. Hobson, J. Vac.ci. Technol . 2, 182 (1965).

2. G. A. Miller and R. E. Buice, J. Phys. Chem . 70, 3874 (1966).

3. Tentative Recommended Practice for Ionization Gauge Application to Space Simulators , ASTM E296-66T,Appendix A2. Am. Soc. Test. Mater., Philadelphia.

4. J. A. Poulis, B. Pelupessy, C. H. Massen, and J. M. Thomas, J. Sci. Instrum . 41, 295 (1964).

5. M. Knudsen, Ann. Phys . ( Leipzig ) [4] 31, 205, 633 (1910); 83, 797 (1927).



6. L. B. Loeb, Kinetic Theory of Gases , p. 358. McGraw-Hill, New York, 1934.

7. M. J. Bennett and F. C. Tompkins,Trans. Faraday Soc . 53, 185 (1957).

8. S. C. Liang,Can. J. Chem . 33, 279 (1955); J. Phys. Chem . 57, 910 (1953).

9. S. C. Liang, J. Appl. Phys . 22, 148 (1951). See also J. P. Hobson, J. Vac. Sci. Technol . 7, 351 (1970) for measurffect of surface roughness.

00. J. M. Los and R. R. Ferguson,Trans. Faraday Soc . 48, 730 (1952).

01. J. O. Hirschfelder, R. B. Bird, and E. L. Spotz, J. Chem. Phys . 16, 968 (1948);Chem. Rev . 44, 205 (1949).





02. G. D. Arney and A. B. Bailey, AIAA J . 1, 3863 (1963).

03. M. Knudsen, Kinetic Theory of Gases , p. 37. Methuen, London.

04. J. P. Hobson,Vacuum 15, 543 (1965).

05. T. Edmonds and J. P. Hobson, J. Vac. Sci. Technol . 2, 182 (1965).

06. S. Weber and G. Schmidt, Kamerlingh Onnes Laboratory, Commun. No. 246C. University of Leiden, 193

07. H. H. Podgursky and F. N. Davis, J. Phys. Chem . 65, 1343 (1961).

08. F. Sharipov, J. Vac. Sci. Technol. A 14, 2627 (1996).

09. L. A. Dietz, Rev. Sci. Instrum . 27, 817 (1956).

10. W. Jitschin and P. Röhl, J. Vac. Sci. Technol. A 5, 372 (1987).

11. T. Takaishi and Y. Sensui,Trans. Faraday Soc . 59, 2503 (1963).

12. J. C. Williams, III, J. Vac. Sci. Technol . 8, 446 (1971).

13. T. L. Ibbs, Physica ( Amsterdam ) 4, 1135 (1937).

14. S. Chapman and F. W. Dootson, Philos. Mag . [6] 33, 248 (1917); see also Jeans [1c, p. 251]. A mathematicaeatment of the subject is given by Chapman and Cowling [1d, pp. 140147, 351], as well as by W. H. Furry, Rones, and L. Onsager [ Phys. Rev . 55, 1083 (1939)] and R. Clark Jones and W. H. Furry [ Rev. Mod. Phys . 18, 1511946)]. A "simple theory" has been published by L. J. Gillespie [ J. Chem. Phys . 7, 530 (1939)], and a much morelaborate mathematical discussion by S. Chapman [ Proc. R. Soc. London, Ser. A 177, 38 (19401941)].

15. K. Clusius and G. Dickel, Naturwissenschaften 26, 546 (1938); 27, 148 (1939).16. T. L. Ibbs, Proc. R. Soc. London, Ser. A 107, 470 (1925).

17. See L. J. Gillespie, J. Chem. Phys . 7, 530 (1939), for a discussion of the derivation of this equation.

18. T. L. Ibbs and A. C. R. Wakeman, Proc. R. Soc. London, Ser. A 134, 613 (1932).

19. T. L. Ibbs and K. E. Grew, Proc. R. Soc. London, Ser. A 43, 142 (1931).

20. A. K. Brewer and A. Bramley, Phys. Rev . 55, 590 (1939).

21. A. O. Nier, Phys. Rev . 57, 30 (1940).22. W. Furry, R. Clark Jones, and L. Onsager, Phys. Rev . 55, 1083 (1939).

23. T. I. Taylor and G. Glockler, J. Chem. Phys . 8, 843 (1940).

24. J. Bardeen, Phys. Rev . 57, 35 (1940).

25. F. T. Wall and C. E. Holley, J. Chem. Phys . 8, 949 (1940).

26. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics , pp. 195196. McGraw-HNew York, 1938.



27. J. H. Jeans, An Introduction to the Kinetic Theory of Gases , p. 216. MacMillan, New York, 1940.

28. J. H. Jeans, An Introduction to the Kinetic Theory of Gases , pp. 207210. MacMillan, New York, 1940.


30. J. H. Jeans, An Introduction to the Kinetic Theory of Gases , pp. 217218. MacMillan, New York, 1940.

31. W. E. Summerhays, Proc. Phys. Soc., London , 42, 218 (1930).

32. The results are summarized by A. Lonius, Ann. Phys . ( Leipzig ) [4] 29, 664 (1909).

33. L. B. Loeb, Kinetic Theory of Gases . McGraw-Hill, New York, 272 (1934).

34. B. A. Ivakin and P. E. Suetin,Sov. Phys.Tech. Phys . ( Engl. Transl .) 9, 866 (1964).





35. J. Hirschfelder, C. Curtiss, and R. Bird, Molecular Theory of Gases and Liquids . Wiley, New York, 1954.

36. S. Ziering and M. Sheinblatt, Phys. Fluids 9, 1674 (1966).

37. R. S. Cunningham and C. J. Geankoplis, Ind. Eng. Chem., Fundam . 7 (August issue), 429 (1968).

38. G. R. Fonda, Phys. Rev . 21, 343 (1923).

39. I. Langmuir, H. A. Jones, and G. M. J. Mackay, Phys. Rev . 30, 211 (1927).

40. G. R. Fonda, Phys. Rev . 21, 343 (1923).

41. E. H. Kennard, Kinetic Theory of Gases with an Introduction to Statistical Mechanics , Chapter 7. McGraw-HiNew York, 1938.

42. E. W. McDaniel,Collision Phenomena in Ionized Gases . Wiley, New York, 1964.

43. V. S. Troitskii,Sov. Phys.JETP ( Engl. Transl .) 14, 281 (1962).

44. N. M. Blachman and E. D. Courant, Phys. Rev . 74, 140 (1948).

45. N. M. Blachman and E. D. Courant, Rev. Sci. Instrum . 20, 596 (1949).

46. J. M. Greenberg and T. H. Berlin, Rev. Sci. Instrum . 22, 293 (1951).

47. M. J. Moravcsik and J. M. Sellen, Rev. Sci. Instrum . 26, 1158 (1955).

48. E. D. Courant, Rev. Sci. Instrum . 24, 836 (1953).

49. S. A. Kheifets, Instrum. Exp. Tech . ( Engl. Transl .) 6 (June), 873 (1961).

50. A. N. Didenko and V. A. Serdyutskii,Sov. Phys.Tech. Phys . ( Engl. Transl .) 7, 679 (1963).

51. Y. F. Orlov and S. A. Kheifets,Sov. Phys.Tech. Phys . ( Engl. Transl .) 7, 671 (1963).





low of Gases through Tubes and Orifices

R. Gordon Livesey

he nature of gas flow in pipes and ducts changes with the gas pressure and its description is generally dividedhree parts orregimes . The flow dynamics are characterized byλ, the molecular mean free path, in relation to somharacteristic dimension such as the diameter of a pipe. The flow regime cannot be determined from the mean flone but only from the relation of this parameter to the characteristic dimension. The relation is known as the Knudsumber , defined as*

hree regimes are generally identified:. Free Molecular Flow . The mean free path is of the same order as, or greater than, the characteristic dimensionange of relatively large Knudsen numbers), and gas dynamics are dominated by molecular collisions with the he retaining vessel or pipe.

. Continuum Flow . The mean free path is small compared with the characteristic dimension (the range of smallKnudsen numbers), and intermolecular collisions are much more frequent than wall collisions. In this regime th

roperties of the gas

* In the literature the Knudsen number may be variously defined, for a cylindrical tube, asλ /d, d/ λ , λ /R, or R/ λ.

Foundations of Vacuum Science and Technology , Edited by James M. Lafferty.ISBN 0-471-17593-5 © 1998 John Wiley & Sons, Inc.





mperature, density, flow velocity) do not vary significantly over several mean free paths and the gas can be considered a continuoushe gas dynamics are therefore described and analysed hydrodynamically. Flow in this regime is often referred to asviscous flow , although e circumstances (such as flow through short ducts) in which. viscosity plays no part.

Transitional Flow . The transition between continuum and free molecular flow occurs at intermediate values of the Knudsen number th wall collisions and intermolecular collisions are influential in determining the flow characteristics.

xpressed in terms of pressure and characteristic dimension the Knudsen number is

r air at 20°C, withd in mm and P in mbar we obtain

ble 2.1 shows the generally accepted range of Knudsen numbers for the three regimes. There is no sharp transition between the regimmewhat different values may be quoted by different authors. The gas factor Fg in the table, used to correct for different gases, is the ratie mean free path for air to that of the gas under consideration (at the same pressure and temperature) and can be calculated from

lues of the gas factor for a number of common gases are shown in Table 2.2.

pplications of vacuum technology range from the lowest pressures attainable (< 1014 mbar) through to around atmospheric pressure,the regimes described are of interest to workers in this field. One of the main aims of this chapter is to enable calculation of flow unange of conditions as possible, so that a large number of flow equations is presented. The widespread availability of scientific calculrsonal computers, and mathematical software means that some of the more cumbersome formulae are considerably less daunting thast. However, the "back of an envelope" is still a much favored tool of scientists and engineers and rough calculations are often sufficat approximations will be given wherever possible. Equations for the molecular, continuum and transitional

able 2.1. Flow Regimes versus Knudsen Number and Pressure

egime Kn (λ /d ) P (mbar),d (mm)Molecular

Kn > 0.5 PdFg < 0.133

ransitional0.5 > Kn > 0.01 0.133 < PdFg < 6.6

ontinuumKn < 0.01 PdFg > 6.6





able 2.2. Properties of Some Common Gases at 20°Cas Relative Molecular Mass Viscosity

Pa·s × 106Viscosity Ratio (Air/Gas) Fg

22 8.8 2.07 0.543

e4 19.6 0.929 0.345

2O (vapor)18 9.7 1.88 1.48

228 17.6 1.03 1.02

ir 29 18.2 1 1

232 20.4 0.892 0.937

r 40 22.3 0.818 0.959

O244 14.7 1.24 1.53

gimes are discussed in Sections 2.2, 2.3, and 2.4, respectively. For the most part, derivations are not given since there are textbooks anpers where the basic theories are discussed extensively; several references are listed in each section for the reader interested in studyibject in more detail.

l equations are written at least once in the text in SI units; where numerical coefficients are given, the units used are stated.

xcept for the discussion of adiabatic compressible flow, it is generally assumed throughout this chapter that isothermal conditions appl

ow Conductance, Impedance, and Gas Throughput

the field of vacuum science and technology it is common practice to express gas flow rate asthroughput in pressurevolume units. The sym

is normally used and the throughput of gas at a particular pressure is then

the volumetric flow rate is due to a pump

here S is the speed (or volumetric rate) of the pump at the pressure P .

he pumping speed available at a chamber will be affected by restriction due to connecting pipework. One of the most common problemcuum technology is to estimate the loss in speed due to such restrictions (system design is covered in Chapter 9).nudsen [1] first introduced the notion of a pipe as an impedance or resistance in the electrical sense and Dushman [2] introduced the cconductance , which is defined by the relation





where Pu is the upstream pressure and Pd is the downstream pressure. These pressures normally refer to values inperhaps notional) plenums at the entrance and exit of a duct or a system fitting such as a valve. Gas flow cond

thus analogous to electrical conductance, with pressure difference being the analogue of voltage difference analogue of current. The reciprocal of conductance (resistance or impedance, Z = 1/C ) could equally well be used;owever, conductance has come into common usage in vacuum technology mainly because of its intuitive relatolume flow rate and pumping speed.

Applying this concept to a set of pipes or components in series, the net conductance is found from

he net speed of a pump in series with a component or pipe is found in a similar way:

n practice it is seldom quite so easy as these equations imply. Some care is needed with combinations of compnd this is discussed in Section 2.2.10 in relation to molecular flow. In continuum flow, conductance depends iomplicated way on the flow conditions, and a better approach is to calculate the pressure ratio ( Kp) across a compor series of components.

is usually assumed that continuity applies through a system; that is, the throughput is the same through all sehis will be the case as long as sufficient time has elapsed (from opening a valve or starting a pump for exampl

here are no temperature differences between the points of interest. In many common situations, steady conditioeasonable assumption. (Some cases of unsteady molecular flow are covered in Section 2.2.11.) If Pd is the inletressure to a pump of speedS which is connected via a pipeline or component to a chamber, then, assuming stea

onditions, the speed (Sn) and pressure ( Pu ) at the chamber are simply related by

n this way, the net pumping speed can be found if the pressure ratio can be calculated.

rom the definition of conductance

Dividing through by the downstream pressure Pd and rearranging gives







his calculation is often easier than taking the reciprocal of a sum of reciprocals, and Kp is the factor by which theumping speed is reduced.

2Molecular Flow

One of the fundamental assumptions in the derivations of molecular flow conductance is that molecules scatterurface according to a cosine distribution. This is also referred to as diffuse or random scattering and means thare no favored directions. A scattered molecule has the same probability of emerging in any direction, and this nrelated to its direction of incidence. There are special circumstances in which nondiffuse scattering may occu

microscopically rough surfaces the diffuse scattering law is well established theoretically and experimentally [3

igure 2.1 shows the distribution of molecules emerging from an aperture and from tubes of various lengths. Tengths of the vectors are proportional to the number of molecules emerging in that direction. It is noticeable thonger the tube, the more heavily weighted is the emerging flux to the tube axis. This is an indication of what onside a tube. An observer close to the entrance (looking upstream) will see the entrance plane as a diffuse sournside the tube an observer will see a perturbed flux which is peaked toward the axis. This is often referred to aeaming effect of a tube.

he aperture in Fig. 2.1 acts as a plane cosine emitter, and the molecular flux shows a spherical distribution. Atngles to the plane the flux of molecules is reduced,

Fig. 2.1Angular distribution of molecules

exiting tubes of various length-to-diameterratios. Reproduced with permission fromL. Valyi, Atom and Ion Sources , p. 86.

Copyright 1977, Akadémial Kiadó, Budapest.







ompared with larger angles. This is not because there is a preferred direction but is a consequence of the anglehe emitting plane does not appear ''dimmer," simply smaller.

n the molecular regime, solution of gas flow problems can be reduced to finding the conductance of the elemenvolved since conductance is independent of pressure or flow conditions. The derivation of conductance, by thr analyticostatistical methods, assumes that molecules arrive at the entrance plane of a duct from a chaotic gashe entrance plane effectively behaves as a diffuse (cosine) emitter. When vacuum components are connected ihis may not be the case and some correction is needed; this will be covered in Section 2.2.10.

lausing [6] first introduced the concept of transmission probability, denoted byα . If N 2 molecules arrive at thentrance plane of a duct then the number of these which reach the exit plane is N 2α , and N 2(1 α ) return to the entraimilarly, of N 1 molecules striking the exit plane (from a downstream chamber), N 1α reach the entrance. Thenet fluf molecules from entrance to exit is then ( N 2 N 1)α . Although proportional to the pressure difference across the dhe net flux is not driven by a pressure difference; it actually consists of two independent fluxes, and there is non the usual sense of the word. Some of the molecules which enter the duct will return to the entry plane after o

more wall collisions. The flow dynamics are thus very different to the continuum flow case in which all molecurossing the entrance plane will leave the exit (apart from the possibility of back diffusion which can occur in sircumstances).

xpressions for conductance are usefully formulated in terms of transmission probability, so that the conductanuct (or other component) is given by the entrance aperture conductance multiplied by the transmission probab

.2.1onductance of an Aperture

he molecular flow conductance of a thin aperture is directly related to the rate of impingement of molecules operture area A (discussed in Chapter 1):

where R0 is the universal gas constant,T is the thermodynamic (or absolute) temperature, and Mm is the molar mas., 0.028 kg/mole for nitrogen).

his gives the familiar result that the molecular flow conductance of an aperture for air at 20°C is 11.6 liters peer square centimeter.

or air at 20°C, Eq. (2.15) can be written in the convenient form

nd Table 2.3 gives values of the constantka for several combinations of commonly used units.





Table 2.3. Aperture Conductance for Air at 20°C in Various UnitsCa = kaA

Ca ka A

m3·s1 115.6 m2iter·s1

11.56 cm2

iter·s10.1156 mm2

m3·h10.4163 mm2

cfm0.245 mm2

cfm158.1 in.2

iter·s174.62 in.2

.2.2General Considerations for Long Ducts

Molecular flow in long ducts was first studied experimentally and theoretically by Knudsen [7]. He deduced a elationship for a long duct of lengthl , varying cross-sectional area A and perimeter B, which can be written as

whereva is the mean thermal velocity of molecules.

However, as discussed by Steckelmacher [8, 9], Eq. (2.17) gives the correct result only in the case of a long cylube and leads to erroneous results for all other cross sections.

A correct expression was derived by Smoluchowski [10] which may be written

whereρ is a chord making an angleθ with the normal to the perimeter s. Expressions for a number of different croections have been derived from Eq. (2.18).

.2.3General Considerations for Short Ducts



or small values ofl it is clear that the long duct relation will give values for conductance which are too high. Aength tends to zero the conductance apparently tends to infinity. Reasoning from the point of view that the entuct can be considered as a vacuum circuit element with resistance Za = 1/Ca in series with the duct proper (regard"long" duct), of resistance Zml = 1/Cml , the net conductance is [applying Eq. (2.8)]





Using this principle, the net transmission probability of a short duct then becomes

wherea l is the long duct transmission probability.

his principle was originally applied by Dushman [2] to short circular cross-sectional tubes as anapproximate methf correcting for the end effect. A similar logic is often applied to short ducts of other cross sections. The maximrror for a cylindrical tube is about 12% (too high). Errors of this order are expected for blocky cross sections, ther cross sections the errors may be more serious. In the case of narrow rectangular ducts the errors can be grhan 50%. The most accurate results are obtained using transmission probabilities which have been derived for umber of different shapes either theoretically or via Monte-Carlo methods.

ransmission probability data for cylindrical tubes, from the results of Cole [11], are shown in Table 2.5. It is ahat the transmission probability for a unit length increases as the length of the duct increases. Consider a unit len

1 for whichα = 0.514. For two unit lengths (l/d = 2) the transmission probability, expected from the shorter lenwould be 0.257, whereas the actual value is 0.357. At 10 unit lengths the transmission probability is almost twixpected value. This reflects the effect of the random molecular distribution near the entrance compared with th

eamed distribution which evolves further down the tube.

.2.4ube of Uniform Circular Cross Section

ong Tubes. The familiar expression for the conductance of a long cylindrical tube of diameterd was first presentedKnudsen [7] in 1909:

can be seen from Eq. (2.21) that the transmission probability for a long cylindrical tube is

erman [12] derived the solution as an asymptotic expansion, the first four terms of which are

or this reduces to Eq. (2.22) (which needs significant correction forl < 50 d ).

able 2.4 lists values of long tube and aperture conductance for a number of gases.





able 2.4. Conductance of Long Cylindrical Tubes and Apertures for Air at 20°Cas Relative Molecular

MassCml (l/d 3) liter · s1

(mm)Ca/A liter · s1

(mm)Ca/d 2 liter · s1

(mm)2

2 0.461 0.440 0.346

e4 0.326 0.311 0.245

ir 29 0.121 0.116 0.0908

r 40 0.103 0.0985 0.0773

ort Tubes. Transmission probabilities for short tubes derived by Cole [11] are shown in Table 2.5. Berman [12] presented equations forect calculation ofα for any length.

able 2.5. Transmission Probabilities for Cylindrical Tubes

l/d α (Cole [11]) α [Eq. (2.20)] % Error

0.05 0.952399 0.963855 1.20

0.150.869928 0.898876

3.33

0.250.801271 0.842105

5.10

0.350.743410 0.792079

6.55

0.450.694044 0.747664

7.73

0.50.671984 0.727273

8.23

0.6 0.632228 0.689655 9.08

0.70.597364 0.655738

9.77

0.80.566507 0.625000

10.33

0.90.538975 0.597015

10.77

10.514231 0.571429

11.12

1.50.420055 0.470588

12.03

20.356572 0.400000

12.18

2.50.310525 0.347826

12.01

30.275438 0.307692

11.71

3.50.247735 0.275862

11.35

40.225263 0.250000

10.98

4.50.206641 0.228571

10.61



50.190941 0.210526

10.26

100.109304 0.117647

7.63

150.076912 0.081633

6.14

200.059422 0.062500

5.18

250.048448 0.050633

4.51

30 0.040913 0.042553 4.01

350.035415 0.036697

3.62

400.031225 0.032258

3.31

450.027925 0.028777

3.05

500.025258 0.025974

2.83

5000.002646 0.002660

0.51

efining





we obtain

his gives results which agree with the Cole [11] data to within 0.13%.

anteler [13] devised a simpler and more convenient formulation and calculates the transmission probability as

where le is an "equivalent length" and

his gives transmission probabilities with a maximum error of less than 0.7% relative to the Cole data.

.2.5Duct of Uniform Rectangular Cross Section

he convention used to denote dimensions of rectangular (and elliptical) ducts is as follows:a and b are the cross-

ectional dimensions, withb ≥ a , and l is the length in the direction of gas flow. Thus the cross-sectional area is A =o avoid any confusion, equations quoted from various authors have been recast to conform with this conventi

ong Ducts. The transmission probability, due to Smoluchowski [10] is

whereδ = a/b and

A useful approximation is

his is accurate to better than 1% for aspect ratios (b/a ) up to almost 100. The error increases slowly with aspect rut is still only 1.9% and 2.4% for aspect ratios of 1000 and 10,000, respectively.





Pa

ort Ducts. There appear to be no general expressions which cover the whole range of lengths and aspect ratios. Data are availablonte Carlo calculations of Levenson et al. [14]. The results of Santeler and Boeckmann [15], which cover a greater range of lengpect ratios, are shown in Table 2.6 (for short ducts the original data are listed to six significant figures). Also shown for compari

able 2.7 are some of the results of Cole [16], derived using a complementary variational method which gave upper and lower boue values listed are the means and are accurate to 1.2% or better.

able 2.6. Transmission Probabilities for Rectangular Ductsa

l/a b/a

1 1.5 2 3 4 6 8 12 16 24

0.010.9902 0.9918 0.9926 0.9934 0.9938 0.9942 0.9944 0.9946 0.9947 0.9948

0.020.9807 0.9839 0.9854 0.9870 0.9878 0.9885 0.9889 0.9893 0.9895 0.9897

0.040.9626 0.9685 0.9715 0.9744 0.9759 0.9774 0.9782 0.9789 0.9793 0.9797

0.070.9370 0.9467 0.9515 0.9564 0.9589 0.9613 0.9625 0.9638 0.9635 0.9650

0.1

0.9131 0.9260 0.9326 0.9392 0.9425 0.9458 0.9475 0.9491 0.9500 0.9508

0.20.8428 0.8645 0.8757 0.8869 0.8926 0.8982 0.9011 0.9039 0.9053 0.9067

0.40.7334 0.7659 0.7829 0.8004 0.8093 0.8182 0.8227 0.8272 0.8295 0.8317

0.70.6178 0.6575 0.6793 0.7022 0.7140 0.7260 0.7321 0.7381 0.7411 0.7442

10.5363 0.5786 0.6026 0.6285 0.6421 0.6560 0.6631 0.6702 0.6737 0.6773

20.3780 0.4192 0.4444 0.4733 0.4893 0.5063 0.5150 0.5240 0.5285 0.5330

40.2424 0.2759 0.2977 0.3245 0.3404 0.3583 0.3679 0.3781 0.3833 0.3885

70.1596 0.1848 0.2020 0.2242 0.2380 0.2545 0.2639 0.2742 0.2796 0.2852

100.1195 0.1397 0.1537 0.1723 0.1843 0.1991 0.2078 0.2177 0.2230 0.2287

200.0655 0.0776 0.0864 0.0984 0.1066 0.1171 0.1238 0.1319 0.1366 0.1419

400.0346 0.041 0.0464 0.053 0.058 0.0652 0.0695 0.075 0.078 0.083

700.020 0.024 0.0275 0.032 0.035 0.039 0.042 0.046 0.048 0.052

1000.014 0.017 0.019 0.023 0.025 0.028 0.030 0.033 0.035 0.038

From Santeler and Boeckmann [15].



able 2.7. Transmission Probabilities for Rectangular Ductsa

a b/a

1 5 10 20 50 100 1000 10000

10.53619 0.66722 0.68266

40.24233

100.11930 0.21280 0.2372 0.2400

200.11207

400.07234

800.04464

1000.01438 0.0320 0.0438 0.0464 0.0468

2000.0224

4000.01295

From Cole [16].





or short slits (or large flat plates ): Values of transmission probability were first calculated by Clausing [6]. Ber12] devised equations for the direct calculation of transmission probability to a greater accuracy than the tabullausing values.

or and and putting x = l/a we obtain

f (long, closely spaced slot, again with ), this equation simplifies to

.2.6Uniform Elliptical Cross Section

and b are the minor and major axes,

ong Ducts. The expression derived from Eq. (2.18) by Steckelmacher [8] is

the complete elliptic integral, and

teckelmacher [8] has shown that, for the same aspect ratio and cross-sectional area, the expressions for a rectauct (Eq. (2.26)] and an elliptical duct are in close agreement. The rectangular duct approximation was derivedasis, so that a similar approximation is available for the elliptical duct:



he constant is chosen to give the correct result forb = a (circular) and minimises the errors for practical aspect rap to 10 (although the errors are less than 1% even for unrealistically large aspect ratios up to 1000).





Generally for ducts which have cross sections intermediate between rectangular and elliptical we have

whereα r is the rectangular duct transmission probability and

hort Ducts. No data are available for short ducts of elliptical or similar cross section. However, it is expected thmilarity between long elliptical and rectangular ducts (of the same cross-sectional area and aspect ratio) will apply to short ducts. It is suggested that approximate transmission probabilities can be found from

or very short ducts this reduces toα s = α r since the transmission probability of an aperture is independent of sh

.2.7ylindrical Annulus (Flow between Concentric Cylinders)

ong Ducts.

where K (e2) and E (e2) are the complete elliptic integrals of the first and second kinds. X (e) is listed for a range ofalues ofe in Table 2.8.

hort Ducts. Table 2.9 presents the results of Berman [17], who calculated transmission probabilities over a largsing the variational method. Berman also obtained an empirical expression which is more convenient for compalculation.





Table 2.8. The Function X (e) for a Long Cylindrical Annulus [Eq. (2.31)] = d 1/d 2:

0 0.1 0.2 0.3 0.4 0.5

X (e):1.3333 1.231 1.1238 1.0116 0.8942 0.7711

= d 1/d 2:0.6 0.7 0.8 0.9 0.95 1.0

X (e):0.6416 0.5044 0.3576 0.1966 0.1071 0

efining x = l /(d 2 d 1), we obtain

he expression is valid in the range 0≤ x ≤ 50 and 0≤ e ≤ 0.9.

2.8niform Triangular Section (Equilateral)

ong Ducts.

hort Ducts. Approximate transmission probabilities can be obtained using the entrance correction principle [Eq. (2

2.9ther Shapes



ransmission probabilities for a number of geometries are shown in graphical form in Figs. 2.2 [18], 2.3, and 2.4. Ioting that the transmission probability for an




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P

Table 2.9. Transmission Probabilities (× 104) for Cylindrical Annulusa

y = l /( R2 R1) R1/ R2

0.1 0.20.25

0.40.5

0.60.75

0.80.9

0.95

0.5 8017 8022 8030 8037 8043 8046

1.0 6737 6754 6783 6808 6829 6842

1.5 5842 5867 5915 5958 5997 6020

2.0 5175 5206 52665295

53245365

5378 5413

2.5 4655 4690 4758 4826 4894 4926 4940

3.0 4237 4274 4348 4423 4501 4558

3.5 3893 3931 4007 4087 4174 4241

4.0 3604 36423661

37203761

38043872

3896 3972

5.0 3123 3181 3260 3347 3448 3507 3538

6.0 2791 2828 29062948

29943071

3100 3201

7.0 2513 2548 2625 2712 2820 2929

8.0 2286 23212339

23952436

24812559

2589 2704

9.0 2099 2132 2204 2288 2496 2515

10.0 1914 1973 20422081

21242200

2230 2304 2352

12.01819 1933

14.0 1617

15.0 1414 1440 1499 1569 1666 1740 1792

16.01381 1456 1559

18.01325

20.01216 1310

1404

25.0 921.7 941.1 984.5 1038 1116 1180 1230

30.0 1019

35 897

40 802

50 496.0 507.6 533.9 567.4 618.2 700.4

100 258.9 265.4 280.1 299.2 328.9 380.5

200 132.7 136.1 144.0 154.3 170.6 200.1



500 53.97 55.4 58.69 63.04 70 82.99

1000 27.15 27.88 29.56 31.77 35.34 42.09

104 2.733 2.807 2.978 3.204 3.57 4.273

105 0.2735 0.2809 0.298 0.3207 0.3575 0.4282

a From Berman [17].

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Fig. 2.2Molecular transmission probabilities of an elbow,from the results of Davies [18].

lbow is almost the same as two short tubes (with length measured at the inside of the elbow) connected by a laolume. The effect of the elbow is to randomize, at least partly, the molecular distribution.

.2.10ombinations of Components

f two components, with transmission probabilitiesα1 andα2, are connected in series, then the usual method ofetermining the net transmission probability is







Fig. 2.3Molecular transmission probabilities of a cylindricaltube with restricted openings, from the results of Davies [18].

onsider two identical, short tubes, of transmission probabilityα , connected via a large volumeV as shown in Fig. he inlet of tube 2 and the outlet of tube 1 are also connected to large volumes and, for convenience, the downressure is taken to be zero. It is supposed that there is no beaming between the tubes, and the effect of the larg to randomize the molecular distribution between the tubes.



he net flux of molecules through tube 2 is ( N 2 N 1)α , and the net flux through tube 1 is N 1α . Under steady conditihese must be the same, so that N 1 = N 2/2 and the number of molecules transmitted is N 2α /2. The overall transmissrobability of the system is thenα /2. The conclusion is the same if the transmission probabilities are combined a2.38).





Fig. 2.4Molecular transmission probabilities of a chevron baffle.Reproduced with permission from Levenson et al. [14]

Copyright 1963, Société Française d'Engenieurset Techniciens du Vide.

Now consider Fig. 2.5b, in which the two tubes (each withl/d = 1) have been brought together. The transmissionrobability of each tube separately is (from Table 2.5) 0.514. However, the transmission probability for the join/d = 2) is 0.357 and not 0.514/2 = 0.257.

learly the method of combining transmission probabilities for the joined tubes is incorrect. In this case every mwhich crosses plane AA also crosses plane BB and vice versa, but this is not so when the tubes are separated byolume.

Oatley [19] discussed the correct method of combining transmission probabilities,α1 andα2, for two joined tubes he same cross section and showed that the net transmission probability is given by



n the example above, this gives the overall transmission probability as 0.346, which is much closer to the correhe Oatley method gives results with a maximum error of 5% or 6% forl/d ~ 2. It is, perhaps, surprising that the

method gives such good results, since the derivation assumes random gas entry into the second tube and thus igeaming effect. However, in short ducts the molecular distribution is





Fig. 2.5Combination of two short tubes.

ot too seriously perturbed from a chaotic distribution, and in long ducts the entrance effect is relatively small.

he transmission probabilities for each of the two tubes, in effect, includes an entrance correction. Thus, when 2.38) is applied, the overall transmission probability includes two entrance effects. This is correct when the twre separated by a large volume but not when they are joined and the Oatley method is equivalent to removing he two corrections.

A typical case is illustrated in Fig. 2.6, in which a pump is connected to a chamber via a tube of the same size aump inlet. The pump speed (S ) has beenmeasured , so that any entrance effects are already accounted for (at leasrinciple). A pump can be regarded as a conductance with a transmission probabilitya H equal to its Ho coefficientatio of the pump speed to the conductance of the pump inlet aperture). IfCa is the pump and tube aperture conducnd α is the tube transmission probability, thenS = a HCa and the tube conductanceC equalsa Ca . The net speed athamber is thenSn = a nCa , where

Alternatively,

he effect of this procedure is to remove an entrance correction.






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Fig. 2.6Pump connected via a tubeof the same diameter.

f the pump speed is 300 liter · s1 and the connecting tube is 200 mm long and 100 mm in diameter, thenCa = 908 ls1 (for air),α (for l/d = 2) = 0.357, and

which givesSn = 188 liter · s1 [instead of 155 liter · s1 using Eq. (2.34)].

An addition theorem developed by Haefer [20] enables the calculation of multiple components of differing diamhe overall transmission probability ofn elementsα1n is related to the individual transmission probabilitiesa i and ireas Ai by

he overall transmission probabilityα1n is expressed in terms of the inlet tube aperture.

ome cases of the application of this theorem will be discussed with reference to Fig. 2.7.

a)eries Arrangement of Tubes of Different Diameters (Fig. 2.7a). The overall transmission probability is







Fig. 2.7Combinations of components.

he diameter increases from tube 1 to tube 2 so thatδ2, 1 = 0, butδ3, 2 = 1 since the diameter decreases from tube. If l/d = 2 for each tube and the diameters are 15 mm, 25 mm, and 20 mm for tubes, 1, 2, and 3 respectively, tαvaluates to 0.214. The aperture conductance of tube 1 (15-mm diameter) is 20.4 liter·1, so the conductance of rrangement is 0.214Ca 1 = 4.38 liter·1. If the order of the tubes is reversed (20 mm, 25 mm, 15 mm),α1n nowvaluates to 0.121. The inlet aperture conductance (for 20-mm diameter) is now 36.3 liter·s1, so the overall con 0.121 × 36.3 = 4.38 liter·s1 as expected. The conductance of an arrangement cannot be changed by reversingrder of components; but note that if the tubes were rearranged in ascending order of size, thenα1n = 0.224. It isenerally the case that the highest conductance for a series of components is achieved when they are physicallyrranged in order of size. In a calculation, the temptation to reorder the components for mathematical conveniehould be resisted since this can lead to incorrect results.

quation (2.42) relating transmission probabilities can be expressed in terms of conductances:

which is more convenient if conductance values are given for components.δ has the same meaning as in Eq. (2.42

he first summation in Eq. (2.44) contains the ''tube only" conductanceCmt discussed by Holland et al. [21]:

hat is, a tube with its entrance correction subtracted. If the conductance quoted for a component is the "tube onhen the entrance correction should not be subtracted. A typical example would be a quarter swing valve whichesigned for direct connection to a large chamber but is normally connected via a manifold. Similar remarks apq. (2.42) if the tube only transmission probability is given.





ither of Eqs. (2.42) or (2.44) can be used to find the net speed of a pump in series with a set of components.

b)ump Connected to a Chamber via Two Tubes or Components (Fig. 2.7b).

ince Cm3 = α HCa 3 = S , this reduces to

which can be written

Written in terms of "tube only" conductances, this becomes

he second term on the right-hand side of this equation can be seen as the total correction required to account fiffering sections (remembering that a correction for A3 is inherent in the pump speed).

f, in Fig. 2.7b, tubes 1 and 2 and the pump all have the same aperture size of conductanceCa , then Eq. (2.48) beco

ach tube has its entrance correction subtracted and only one correction, inherent in the pump speed, is applied

)ump Connected to a Chamber Via a Second Chamber (Fig. 2.7c). This case is equivalent to makingCa 2 and Cm2 arge in Eq. (2.47), giving

n this case the entrance correction for tube 1 is retained.



.2.11ases of Unsteady Flow

onsider a system in which a pump is connected to a vessel via a valve and a pipe of some significant length. Ihat, at the instant that the valve is opened, the throughputs at the pump and vessel must be





ifferent. Some time is required for continuity to be established. Usually this is very short compared with the tior exhaust of the vessel, especially at continuum flow pressures where the pipe conductance is relatively high.

However, if the "vessel" is a long pipe, then steady conditions are never achieved.

Unsteady flow is of most interest under molecular flow conditions and is particularly relevant to filling, exhausesting of long pipelines. Mathematically, unsteady molecular flow in a constant section duct is analogous to heonduction in an infinite slab. Both can be treated as one-dimensional since there is no transverse flow. The casescribed here are intended only as a small sample to illustrate the kind of unsteady flow problems that can be olutions for many heat conduction cases, which have practical parallels in molecular flow, are available in theterature; Carslaw and Jaeger [22] is a good source of reference.

n the equations which follow,V is the volume andC the conductance of the pipe, assumed to be long. Given a reor pressure distribution, the throughput (from or into the pipe) can be obtained from the pressure gradient at thpipe:

ase 1. Pipe with uniform initial pressure P 0, closed at x = 0. x = l opened to an environment maintained at constaressure Pe at t = 0.

his covers both exhaust and filling of a pipe. Lawson [23] discussed the application of this and similar cases tumping of trapped volumes and leakage.

he time constant for the first (slowest) term is

ontrast this with the time constant of chamber of volumeV pumped at speedS or through a restrictive conductanccovered in Chapter 9).

or air at 20°C (l and d in meters) we have

nd for helium we have







A 1-meter-long pipe, 10 mm in diameter would have a time constant for helium of ~100 msec. For a pipe lengtmeters, this increases to ~10 sec. Leak testing can be difficult with a detector at the downstream end of such lon

nce any leak will be located at the position of the helium probe several seconds prior to the indication on the etector gauge.

he series converges quite rapidly and taking only the first term is a good approximation fort > 0.3τ0. Thus, takingnly the first term we obtain, at x = 0

nd the throughput

ase 2 . Pipe, with constant initial pressure P 0, closed at x = 0 and pumped at the other end by a pump of constant for t > 0.

where r = S/C and φn are the roots of

A good approximation for the first root is

ccurate to within 3% in the worst case.

aking only the first term of the series for throughput, we obtain

or the time constant becomesV/S and the case reduces to the simple pumpout of a large chamber.



ase 3 . Pipe with zero initial pressure. Constant leak into the pipe at x = 0 and constant pumping speedS at x =or t > 0.





his is again relevant to leak test of a long pipeline since the initial partial pressure of He will be zero.

where r = S/C and φn has the same meaning as in Case 2.

aking only the first term, the throughput from the pipe is

3ontinuum Flow

n the continuum regime, calculation of gas flow through ducts is complicated by the different types of flow whccur. Flow may be broadly distinguished into two major types, referred to asviscous laminar flow and turbulent flowince flow through a duct is driven by a pressure difference, all gas flow is compressible. There are circumstan

which gas can be treated as incompressible, and this leads to considerable simplification of the equations descrow. However, there are also many circumstances in which compressibility cannot be ignored, socompressible flow

will also be discussed.

ontinuum (or viscous) flow is often thought of as occurring at relatively high pressures. But consider air flowhrough a 100 mm (4 inch) diameter pipe. From Eq. (2.2) the Knudsen number Kn is < 0.01 (and hence the flowontinuum) down to pressures of about 0.1 mbar. Thus many vacuum processes will operate at pressures whereontinuum flow conditions prevail.

At relatively low velocities, gas flows smoothly in stream lines, generally parallel to the duct walls, and the flowo be laminar. In long ducts, viscosity of the gas is a controlling factor in the flow rate; this is not the case in shlthough the flow may still be laminar. As the flow velocity is increased, there comes a critical point at which treaks up into turbulent eddies. These two types of flow, viscous laminar and turbulent, are described by differquations. It is important to distinguish these flow types in calculation of flow rates; failure to do so can lead tonaccurate results. In short ducts, or in longer ducts at high flow velocities, compressibility becomes important f incompressible flow formulae can also lead to serious errors.

he primary controlling parameter in the viscous behavior of Newtonian* fluids is the dimensionless Reynolds

* Newtonian fluids are those in which the shear stress is proportional to the transverse velocity gradient. Mcommon fluids (water, oils, and gases) are newtonian.





whereρ is the density of the fluid,η is its viscosity, andu is the flow velocity. Dh is the hydraulic diameter* of theapplicable to any cross section) defined by

where A is the cross-sectional area and B is the perimeter.

or a circular cross-sectional tube we obtain

o that the hydraulic diameter is simply the actual tube diameter.

or a concentric annulus we have

Note that, in calculating B, the perimeter of all "wetted" surfaces must be included.

is useful to write Re in terms of the throughput:

n the case of a circular cross-sectional tube, B = πd . For air at 20°C, Eq. (2.67) can conveniently be written as

nd Table 2.10 lists values for the units conversionkR for a variety of commonly used units.

As shown by the work of Senecal and Rothfus [24], the transition from viscous laminar to turbulent flow beginRecrit ~2000, although there is no sharp boundary, and flow is normally fully turbulent at a Reynolds number o

n very smooth pipes with well-rounded entrances, the transition to turbulence may be delayed to higher valuesUsing the value Recrit = 2000, the value of throughput for the onset of turbulent flow is

* Re defined in terms of diameter is the most commonly used convention. Some texts define Re in terms oradius and make use of hydraulic radius rather than diameter. When making comparisons, note that hydraudiameter = 4 × hydraulic radius (yes, 4!).







o for air at 20°C the flow will become turbulent if

Values of kT for a variety of units are given in Table 2.11.or a cylindrical tube for example, withQT in mbar·liter·s1 and tube diameter in mm, we obtain

or example, in a 25-mm-diameter tube the conditions will be turbulent if the throughput exceeds 600 mbar · lif this tube size were used with a 20 liter · s1 pump, then turbulent flow would persist down to about 30 mbar.

n the continuum flow regime, conductance may be a function of pressure, pressure ratio, or rate of flow depenhe type of flow and particular circumstances. The termconductance is useful as a conceptual toolto say, for examhat the conductance of some tubulation is too small does provide a succinct means of characterizing a flowonditionbut has limited practical value. Calculation of conductance is generally a means to an endcalculation hroughput (when the end pressures are known) or calculation of pressure difference (when throughput is knowxample. Thus, relations will be presented for throughput and pressure ratio where these can be expressed expl

Table 2.10. Units Conversions for Reynolds Number and Throughput [Eq. (2.68)] for Air at 20°C

B kR

Pa · m3 · s1m 2.615

mbar · m3 · h1mm 72.64

mbar · liter · s1mm 261.5

orr · liter · s1mm 348.6

orr · liter · s1in 13.73

orr · cfmin 6.478



Table 2.11. Units Conversions for Turbulent Throughput [Eq. (2.70)] for Air at 20°C

B kT

Pa · m3 · s1m 764.8

mbar · m3 · h1mm 27.53

mbar · liter · s1 mm 7.648orr · liter · s1

mm 5.736

orr · liter · s1in 145.7

orr · cfmin 308.7





efore proceeding to discuss the equations of continuum flow, it is convenient to define

his collection of terms occurs frequently in equations of continuum flow. As is evident, the term is closely rela , the molecular flow conductance of an aperture [Eq. (2.15)], differing only by a numerical factor. The term as units of volumetric flow rate and provides a succinct means of expressing many continuum flow relations.

he long tube equations which will be presented for laminar and turbulent flow are of limited practical applicathere are few circumstances in which straight tubulation is employed of sufficient length to meet the long tubeo be discussed later). In vacuum technology, "short and wide" is beautiful! The long tube equations will be dirst since they form the basis for expressions which apply to ducts of any length. This will be followed by disc

he equations for compressible flow and then of approximations which are sufficiently accurate for many practiurposes.

.3.1Viscous Laminar Flow

he simplest solutions for viscous flow, in ducts of constant cross section, are based on four assumptions: (1) T incompressible; (2) the flow is fully developedthat is, the flow velocity profile is constant throughout the len

he flow is laminarthat is, in one direction only parallel to the duct axis and there are no turbulent motions; (4) telocity at the walls is zero.

he assumptions may appear restrictive but are true for newtonian fluids flowing in long ducts at relatively lowelocities. Except for the assumption of incompressibility, this also includes gases, but even for gases it can be hat compressibility can be ignored if

where Ma is the Mach number of the flow, defined as the ratio of the flow velocity to the local velocity of sounenerally accepted criterion is Ma < 0.3.

When fluid flows into the entrance of a duct, the flow velocity is approximately uniform over the entrance areauid moves down the duct, shear stress due to viscous friction retards the flow near the walls and the fluid deveelocity profile which, after some entry length, becomes constant and the flow is said to be fully developed. In f a circular cross section, for example, the profile is a parabola of revolution with the greatest fluid velocity at xis. The pressure drop over the entrance length is greater than that for fully developed flow because of the inchear stress and the kinetic energy needed to accelerate the flow. Shah and London [25] have given the followiorrelation for entry length:





he first term is significant only at very low Reynolds numbers, and the condition is usually expressed as

At the transition to turbulent flow, with Re = 2000, this gives an entry length of 112 diameters for a circular piphe viscous laminar flow equations are valid only for fully developed flow, some correction is required unless tength is much greater than the entry length. Corrections for entrance effects and long tube criteria are discusseections 2.3.4 and 2.3.7.

Viscous laminar flow has proved irresistibly attractive to theorists since the fundamental equations of flow can olved analytically; a wealth of solutions is available for an amazing variety of cross-sectional shapes. A few o

more practical shapes will be discussed.

or incompressible fluids, equations are usually presented for volumetric flow rate which is proportional to theifference across the pipe. For gases, density varies along the duct, so equations are normally given for througherms of the average pressure which reflects the average density.

f Cv is written for the viscous flow conductance, then

where the conductance is proportional to the average pressure

nd kV is a constant for the particular duct, containing the numerical factors, viscosity and geometric terms.

he throughput is then

Given a relationship forkV , it is no particular problem to determine the throughput if both end pressures are knowhe throughput is given (because, for example, the downstream pumping speed at a given pressure is known), itasy to calculate the pressure drop because both pressures are required by Eq. (2.76). However, the equation caxpressed as, for example,

where KP = Pu/Pd is the pressure ratio across the duct.

he termkVPd has the same units as conductance (i.e., volumetric flow rate); it can be thought of as the conduche duct calculated at the downstream pressure





nstead of the average pressure). In order to express flow equations in a form convenient for calculation, it is uefine two artificial conductances:

Cvu = viscous flow conductance calculated at the upstream pressure,Cvd = viscous flow conductance calculated at the downstream pressure.

his artifice enables the equations of flow to be expressed in terms of quantities which are known.

When both end pressures are known, the throughput can be written as

f the downstream pressure and pumping speed (i.e., the volumetric flow rate) are known, then the pressure ratihe duct can be found from

f the upstream pressure and downstream pumping speed are known, we obtain

v, Cvu, and Cvd can be calculated, for different geometries, from the equations that follow, and Eqs. (2.78) to an be used to calculate throughput or pressure ratio.

ircular Cross-Sectional Tube. The HagenPoiseuille equation for a long circular pipe is probably the best-knowquation in viscous flow. The throughput is

ence the conductance is

or any gas, this can be written as







alues of the units conversion constantkv are given in Table 2.12 for a variety of commonly used combinations of u

should be apparent from the previous discussion that, for a circular pipe for example, the artificial conductanceCvd is

ectangular Cross Section.

lthough only the first three terms are needed for good accuracy, this expression is rather cumbersome. A goodpproximation is [21]

his expression, valid for all aspect ratios, is accurate fora = b and and it shows a maximum error of <3% atntermediate aspect ratios.

oncentric Cylindrical Annulus.

ccentric Cylindrical Annulus. It is worth noting that flow rate (for the same pressure difference) increases significa

he inner cylinder is offset from the axis. In the extreme case of a narrow annulus with maximum he flow rate is increased by a factor of 2.5. This explains the observation that flow rate can be very difficult to adjn almost closed needle valve.

Table 2.12. Units Conversions for Viscous Flow Referenced to Air at 20°C [Eq. (2.84)]

Cv d l P kv

m3·s1m m Pa 54,963

iter·s1mm m mbar 5.496 × 103

iter·s1mm mm mbar 5.496

iter·s1mm m torr 7.326 × 103

iter·s1mm mm torr 7.326

m3·h1mm m mbar 0.01978



m3·h1mm mm mbar 19.78

cfmin ft torr 21,195

cfmin in torr 254,363





.3.2urbulent Flow

Although particular solutions of the fundamental equations of fluid flow are known (viscous laminar flow, for eo general analysis of fluid motion has been successfully developed. The reason is the dramatic change in fluid

which occurs at a critical Reynolds number when the flow becomes turbulent. The chaotic, fluctuating nature ourbulent flow has defied theoretical analysis since it was first observed by Hagen in 1839. The flow equations ave been developed are semiempirical, describing the gross mean properties of the fluid and ignoring small-scuctuations. The DarcyWeisbach (1850) equation for head loss in a pipe can be expressed as

where∆ P is the pressure difference,u is the fluid velocity, and fD is the Darcy* friction factor. The friction factor fDot a constant (would that life were so easy!) but varies with the Reynolds number and is also a function of the ectional shape.

he Blasius relation holds for smooth pipes:

However, most real pipes are not smooth. Haaland [26] devised a useful general relation which takes surface ronto account. Jones [27] showed that the optimum friction factor correlation with Re for rectangular ducts is baffective hydraulic diameter of Deff = ( Dh/SF ) which leads to an effective Reynolds number of Re/SF to be used inalculating the friction factor. This approach is recommended by White [28] for all noncircular ducts. Haaland'xpression, modified to incorporate this proposal, is

whereε is the surface roughness, typically 0.0015 mm for the drawn tubing commonly used for system pipewo

F is the shape factor, given by

nd Ge is the numerical constant and cross-sectional geometric terms in the viscous flow conductance equationection 2.3.1.

* The Fanning friction factor is also in common use in the literature on fluid flow. Darcy friction factor = 4(Fanning friction factor).





ircular cross section :

ectangular cross section :

oncentric annulus :

he shape factor for some cross sections is shown in Fig. 2.8.

igure 2.9 shows (for circular cross section) the friction factor plotted against Re for three pipe diameters withε =.0015 mm. Also shown for comparison is the Blasius smooth pipe relation. Larger-diameter pipes (d > 25 mm)pproach the smooth pipe curve for values of Re up to ~ 105, but there is significant deviation for smaller pipe

or viscous laminar flow the friction factor is a simple function of the Reynolds number:

or a circular tube we haveSF = 1, so that fD = 64/Re.



Fig. 2.8Shape factor for some cross sections.





Pa

Fig. 2.9Friction factor for a cylindrical tube.





or a very narrow rectangular duct we haveSF = 3/2, so that fD = 96/Re.

f the relation for fD is substituted into the turbulent flow Eq. (2.88), then the viscous laminar flow equations apwould be convenient if fD were independent of cross-sectional geometry, because then laminar flow solutions fohape could be derived from Eq. (2.88). Unfortunately, the laminar flow solutions must be known in order to fihape factor.

or turbulent flow in a long duct, Eq. (2.88) can be rearranged to give the throughput as

Written in terms ofCz [defined by Eq. (2.72)], we obtain

xpressed in this latter form, it is immediately apparent that throughput equates to the product of a volumetric erm (Cz ) and a pressure. In calculating throughput from this relation, it is only necessary to calculateCz and expreshe pressure in whatever units the user finds convenient. The terms under the square root sign are either dimensr dimensionless ratios.f throughput and downstream pressure are known (and hence the pumping speed or volumetric flow rate), thenressure ratio across the duct can be found from

alculation is straightforward in this case; since the throughput is known, Re and hence fD are readily found. Howehe nature of the variation in friction factor with Re complicates calculation of throughput. A value of fD must be

hosen and calculated, Re can then be calculated, and a new value of fD obtained from Eq. (2.90). The process hen repeated to obtain to the desired degree of accuracy. This procedure is painful for hand calculation, alth a simple matter to program on a personal computer. Often a single iteration will be sufficient and, if only a rostimate is needed, a constant value fD ~ 0.03 can be used. In vacuum pumping lines, Re seldom exceeds 105 ansually be less. Vacuum system pumping lines are often sized to avoid significant performance loss at the loweperating pressure. This usually means that losses are small at pressures where turbulent flow occurs, and accuralculation may be unnecessary. If accurate calculation is needed, then one simply has to go through the pain (oo a friendly programmer). This is not the





east of calculation problems that may be faced: It should be emphasized that the equations described thus far ao long pipes without obstructions to the flow (such as bends and pipeline components) and to flow velocities o.3.

he entry length in turbulent flow is

At Re = 3000 for example, this gives an entry length of 17 diameters for a circular pipe. The criterion for a lonwill be discussed in Section 2.3.7.

.3.3ompressible Flow

Unlike other common fluids, such as water and oils, the flow of gases can involve significant changes in densityoted in the discussion on flow in long pipes, the effects can be ignored for small flow velocities (Ma < 0.3). Aow velocities and in short pipes the effects of density changes become significant. Density is related to both pnd temperature, so that in analysis of gas flow the laws of thermodynamics must be considered in addition to tf motion and continuity.

he flow relations will be discussed with reference to Fig. 2.10, which relates to an adiabatic process. When gauct (from a large volume) the flow accelerates across the entrance, and this is associated with a fall in both temnd pressure. As the gas proceeds down the duct, pressure and temperature continue to fall and the gas continuccelerate, reaching its maximum velocity at the duct exit. If the pressure upstream of a duct is kept fixed and townstream pressure is reduced, then the flow rate will increase. As the pressure is reduced further, the flow raecomes constant when the pressure ratio across the duct reaches a critical value. Further reduction in the downressure will produce no further increase in rate of flow. This is due to the limiting velocity which can be achieas flowing in a duct of constant cross sectionMach 1, the speed of sound.* In this condition the flow is said tohoked (or blocked). The flow rate can be changed by changing the upstream pressure; but once the critical preatio is reached, the flow rate becomes completely independent of the pressure on the downstream side of the derm choked flow is used because the mass flow rate has reached the maximum value that it is physically possibchieve for a given upstream pressure and the duct behaves as though something is preventing, or choking off, aurther increase in flow. The phenomenon is particularly apparent with a small orifice restricting the inlet of a p

Once the pumping speed exceeds a certain value, the throughput will become constant and cannot be increasedmatter how large a pumping speed is used. Orifices, nozzles, and short or long ducts can become choked; the nondition is that the flow velocity of the gas reaches the speed of sound. For any particular duct there is a specif pressure ratio at which choking will occur; this critical pressure ratio is generally referred to as thechoked pressureatio . In the case of an orifice or very short duct, the choked pressure ratio is independent of pressure or flow

* Supersonic velocity can be achieved downstream of the throat of a convergingdiverging duct.





Fig. 2.10Compressible flow through a duct.

onditions. In longer ducts the choked pressure ratio, because of its dependence on the friction factor, will chanhe pressure and type of flow (laminar or turbulent). Note that if the gas flow velocity in a duct does reach Mar

will do so at the duct exit. It is not physically possible for an initially subsonic flow (in a constant section duct)March 1 at any other point.

n the flow of gases through apertures or short ducts, or through longer ducts at high flow velocities, there is liteat exchange between the gas and its surroundings and the process is approximately adiabatic. In longer ducts

may be significant heat exchange and the flow may be approximately isothermal.

he thermodynamic theory of high-speed flow shows that isothermal conditions cannot be maintained at flow vlose to the limiting value because the required rate of energy input to the gas tends to infinity. Approximatelyothermal conditions may prevail for part of the flow through a duct but cannot be sustained if the flow becomhoked. In long ducts the results of isothermal analysis and adiabatic analysis converge; in short ducts, adiabatihe most reasonable assumption. Some of the results of compressible flow analysis will be quoted without proo

asic theory is covered in a number of textbooks on fluid dynamics [2830].Using results of thermodynamic analysis, it can be shown that throughput, velocity, and pressure at any pointa alonhe duct are related by

whereCz is defined by Eq. (2.72). The throughput is referenced to the stationary (or stagnation) conditions in thpstream chamber (because of temperature changes, throughput is not constant through the duct).

or subsonic flow, the duct exit pressure ( Px ) must be the same as the downstream chamber pressure ( Pd ); so,earranging Eq. (2.100)

ince Ma x≤ 1, it is apparent that the flow will be choked if







his is a general relation, true for a duct of any length. If the pumping speedS at the downstream end of a duct isnown, it can be immediately determined if the flow is choked.β is simply used as a convenient way of writing therms inγ .

can be shown that the relationship between throughput and entry velocity is

nd it can be shown further that the relationship between entry and exit velocity is given by

hoking is a property of this equation in that the variation of flow rate with Mach number exhibits a maximum

.or a finite length duct, the equations of compressible flow cannot be rearranged to give an explicit relation be

hroughput and pressure. They can be solved for choked and nonchoked, laminar and turbulent flow, but complerative procedures are needed. Sadly, envelopes (no matter how large) must be discarded and resort made to crogramming. However, an approximate treatment, giving explicit equations accurate to a few percent, is coveection 2.3.6.

is instructive to examine how the rate of flow varies with duct length and an example is shown in Fig. 2.11. Throughput (normalized to the throughput of an aperture) is plotted for a 10% pressure difference across a 12.5-iameter tube; flow conditions were arranged to be viscous laminar and turbulent. The normalized molecular flhroughput is also shown for comparison. The striking difference

Fig. 2.11Variation of normalized throughput with tube length for a12.5-mm-diameter tube and a pressure difference of 10%.







etween the molecular and continuum flow cases illustrates the relative insensitivity to length of continuum flohort ducts. For larger pressure differences the reduction in continuum flow throughput with length is even sma

3.3.1low through an Aperture or Short Duct

ince there is no frictional work and the process is adiabatic, flow through an aperture is often referred to asisentropiow.

or a duct of zero length, the right-hand side of Eq. (2.104) is zero and an obvious solution is Man = Ma x.

he critical pressure ratio for choked flow can be found by combining Eqs. (2.101) and (2.103) along with Man = M1:

he maximum throughput for choked flow, from Eq. (2.103), is

ypical values of Kpca , γ , and the functionG(γ ) are shown in Table 2.13 for several gas types. The values ofγ areypical of monatomic, diatomic, and so on, gases; but more accurate values can be found in Kaye and Laby [31xample.

or sharp-edged apertures the throughput is reduced by a factor of ~ 0.85 because the flow narrows to avena contract

which has a cross section smaller than the duct inlet area. This entry loss can be reduced to negligible proportioadius on the entrance edge of ~ 0.2 diameters (or 0.2 × smallest dimension for noncircular ducts).

is apparent from Eq. (2.106) that a choked aperture has aconstant speed , given by

A choked aperture (or short nozzle) is often used a convenient means of providing a constant volumetric flow rpeed, which is independent of pressure. Such a nozzle might be used to provide a 'soft start' pumpdown, to avisturbances due to turbulence or pressure fluctuations in a process chamber during the initial stages of roughinisturbances occurring in the inlet ducting to the pump (downstream of the choke) will travel at the speed of soannot travel upstream through the sonic choke and hence cannot be communicated to the chamber.



Table 2.13. Some Thermodynamic Properties of Gases

Gas Type γ Kpca G (γ )Monatomic

1.66 2.0490.7252

Diatomic1.4 1.893

0.6847

Triatomic1.3 1.832

0.6673

Polyatomic1.1 1.71

0.6284





or air at 20°C,Sa = 20 A liter·s1, with A in cm2. Compare this with 11.6 A liter·s1 for the molecular flowconductancf an aperture.

he downstream pumping speed needed to choke an aperture is [cf. Eq. (2.102)]

or air at 20°C,Sca = 37.5 A liter·s1, with A in cm2. Once the pump speed exceeds this value, the pumping speedhamber will remain constant atSa no matter how large the pump.

At pressure ratios smaller than the critical value, the throughput is given by

r, if the downstream pressure and pumping speed are known, the pressure ratio can be found from

he net speed at the inlet of the aperture will then be

here is no particular value in expressing the conductance of an aperture, since this varies with the pressure ratxample, an aperture which is just choked (pressure ratio 1.89 for air) has a conductance of 42 A liter·s1 (with A in cm

educing to 20 A liter·s1 for a very large pressure ratio The conductanceC increases as the pressure reduced andC →∞ as Kp→ 1.

or a choked aperture, it is interesting to note that for a given pressure difference the throughput is reduced by with two apertures (of the same area) in series compared with a single aperture. In molecular flow the throughp

e reduced by 50%

emperature Changes . In adiabatic flow, the temperature at any point along a duct is

which indicates that there can be significant temperature changes in high-speed flow. For example, in the case iatomic gas such as air, the temperature will fall from 20°C to 29°C if the gas reaches sonic velocity. This can eezing up of choked nozzles due to condensation of water vapor initially present in the source air.

ime to Vent a Chamber Through an Aperture or Short Duct . This useful result can be derived from the choked anonchoked throughput relations given above. The







ource pressure (e.g., atmospheric) is assumed constant and much greater than the initial chamber pressure. Thehe chamber pressure to equalize with the source pressure is then

whereCz is defined by Eq. (2.72) andCa is the molecular flow conductance of an aperture [Eq. (2.15)].

he derivation assumes that the temperature of the gas, after entering the chamber, is the same as the source gaemperature. In fact the gas temperature in the chamber will be greater, and this will reduce the equalization tim

Although the entering gas cools due to adiabatic expansion at the throat of the inlet aperture or nozzle, reheatins the gas comes to rest in the chamber. If the process were entirely adiabatic (i.e., no exchange of heat betweend walls of the chamber), then the temperature rise (above the external ambient air temperature ofT 0 Kelvin) wou0(γ 1). For an ambient temperature of 293 K, this implies a temperature rise of about 100 K.

ractically, such large temperature rises are not observed due to heat exchange, especially since the thermal caphe gas is much lower than that of the chamber. As an example, rapid venting (< 1 s) of a 22-liter chamber led tbserved temperature rise of about 40°C. Greater temperature increases may be observed in larger chambers whented rapidly.

3.3.2pproximation for Flow through an Aperture

A simple approximation for nonchoked flow through an aperture can be obtained from Bernoulli's equation:

aking downstream values forρ and u leads to

r, if the downstream pumping speed is known,

he maximum errors occur at the choked pressure ratio and are 2.5% (γ = 1.66), 3.1% (γ = 1.4), 5.5% (γ = 1.3), and

0.9% (γ = 1.1). At lower pressure ratios the errors are less..3.4orrections for Flow Obstructions

n most practical circumstances, gas and vacuum lines include obstructions such as bends, valves, or other comhe basis for corrections is Bernoulli's equation





nd the observation that pressure head losses are proportional to the square of the mean flow velocity over the cection.

wherenc is the loss coefficient, or number of corrections. This relation is commonly used to estimate head lossencompressible flow. The same principle is applied here for gases, with the velocity taken to be the mean valuength of the flow path.nc can apply to more than one component, and the corrections are simply summed for alomponents in the pipeline. The implication of taking the mean velocity is that the separate obstructions are regvenly distributed through the pipeline. It appears that the positioning of flow obstructions makes little differenverall pressure loss. For example, withnc = 4 and maximum flow rate the variation in pressure loss is only abou

wherever the obstructions are located. This is likely to be smaller than the uncertainties in applying corrections

or ducts longer than the entry length, the loss coefficient [32] isnc ~ 0.7 (flat plates) and 1.25 (cylindrical tube), iscous laminar flow. About half of this is due to excess shear over the entry length and the remainder due to thdditional pressure difference needed to accelerate a uniform flow into the developed velocity profile. This lossddition to the kinetic energy needed to accelerate the flow from zero velocity. In ducts shorter than the entrancorrection is more complex; the subject is discussed in some depth by Shah and London [25]. The additional enoss appears to be less important in turbulent flow. It is suggested to takenc ~ 1 to account for entrance losses. Nott high velocities in short ducts the kinetic energy needed to accelerate the flow is much more important than virag.

able 2.14 lists suggested corrections to be used in the equations that follow. These are in addition to the kinetillowance built into the equations which thus assume that gas enters a duct from a large volume.

.3.5ApproximationsEntrance Correction Model

n a similar fashion to Dushman's original treatment of short ducts in molecular flow, entrance correction modemagine a real duct to consist of an aperture in series with an ideal duct.

he total pressure drop is then taken to be the sum of the pressure drop across the entrance plus viscous losses uct:

u Pd = ( Pu Pi ) + ( Pi Pd ) = entrance loss + viscous loss.

Table 2.14. Loss Coefficients Due to Flow ObstructionsObstruction nc

Sharp-edged entrance0.5

Mitred (90°) elbow 1Standard (90°) elbow

0.8

Tee (used as elbow)1

Tee (in-line flow)0.25

Right-angle valve (fully open)3







anteler [33] discussed a similar model but with the loss considered as an exit loss. For nonchoked flow, as shoreviously, it makes little difference where the correction is placed. Applying the isentropic equation for an apehis model, the variation in calculated pressure difference between aperture-at-entrance and aperture-at-exit isfor any length of duct). For a duct with a choked exit the Santeler model makes more intuitive sense since an eannot be choked.

n continuum flow this model is equivalent to allowing for the kinetic energy required to accelerate the gas to tow velocity:

As discussed previously, this can be generalized for any number of corrections:

Using this expression the following equations can be derived.

iscous Laminar Flow. When the two end pressures are known the throughput can be found from

When the throughput and downstream pressure are known we obtain

urbulent Flow. When the two end pressures are known we obtain

When the throughput and downstream pumping speed are known we obtain

hese equations will be found useful in many practical circumstances. Strictly speaking, they should not be usehoked flow or for very short pipes. In this case errors in calculated throughput can be up to around 50% (for aperture), although even this may be acceptable for a rough estimate. These equations do not show







maximum with pressure ratio; that is, the equations do not exhibit a choke property unlike the thermodynamiquations and those which follow.

.3.6ApproximationsKinetic Energy Model

he main deficiency of the previous approximations is the failure to take proper account of the kinetic energy ay the gas. The entrance correction approach is valid for an incompressible fluid which must reach its final velhe duct entrance. If the fluid density is constant and the mass flow rate through the length of the duct is constaan be no change in velocity. In contrast, a gas flowing in a duct reaches its final velocity at the duct exit. Thusinetic energy accounting must relate to the exit velocity.

n this case, the viscous loss term relates to mean density and velocity, but the kinetic energy correction appliesensity and velocity at the duct exit.

he flow equations derived from this expression show a maximum in the throughput with pressure ratio. In othhe equations exhibit the property of choking in the same way as the compressible flow relation. Unfortunately,xplicit expression cannot be found for the critical pressure ratio, and the value of approximate equations is nulerative methods are required for solution. However, with a little analytical trickery, a solution is found by borresult from the thermodynamic theory, namely

btained from Eqs. (2.101) and (2.103) with Ma = 1.

A set of equations can then be derived covering both nonchoked and choked flow including allowance for flowbstructions. Iteration is needed to find the friction factor for turbulent flow when the two end pressures are knohe throughput is to be calculated. Otherwise, all the relations are explicit and iteration procedures are not requihese equations give calculated flow rates and pressure differences to within 7% of values predicted by the

hermodynamic equations.

iscous Laminar Flow. (a) With both end pressures known, the choked pressure ratio is given by

f Kp > Kpc , so the flow is choked, then the throughput can be found from Eq. (2.123).





f the flow is not choked, then

b) If the throughput and downstream pressure are known, then the test for choked flow is [Eq. (2.102)]

≥βCz .

f the flow is choked, then the choked pressure ratio in terms of the known downstream conditions is

nd the upstream pressure can then be found from

f the flow is not choked, then the pressure ratio is

urbulent Flow. The choked pressure ratio is

a) Both end pressures known : If the flow is choked, then the throughput is given by [Eq. (2.123)]

f the flow is not choked, then the throughput is







b) Throughput and downstream pressure known : The flow will be choked if [Eq. (2.102)]

f the flow is choked, then the upstream pressure can be found by rearranging Eq. (2.123):

f the flow is not choked, then the pressure ratio is

is interesting to consider the case of flow from atmospheric pressure through a hole, of diameter 0.1 mm and0 mm, in a vacuum chamber. This might be, for example, a pinhole leak in a weld. With a pressure of 103 mbhamber, it is generally assumed that the flow changes from viscous through transitional to molecular at the vaf the hole. The flow is most likely to be viscous laminar, so Eq. (2.124) can be used to calculate the choked pratio. In this case,Cz = 2.276 × 103 liter·s1 [Eq. (2.72)],Cvu = 1.349 × 103 liter·s1 [Cv of Eq. (2.83) but calculatedhe upstream instead of the average pressure], and (forγ = 1.4)β = 1.296 [Eq. (2.102)]. Putting these values into E2.124) gives Kc = 5.55, so the pressure at the hole exit is 160 mbar and the flow is continuum through the whoength. The throughput [from Eq. (2.123)] is calculated to be 0.532 mbar·liter·s1; turbulent flow [from Eq. (2.7

would require mbar·liter·s1, so the flow conditions are viscous laminar as assumed. An almost identiesult is obtained from solution of the thermodynamic equations.

.3.7ong Duct Criteria

n setting out the simple equations for turbulent and viscous laminar flow, it was said that these were applicableong ducts. This raises the obvious question as to what constitutes ''long." This is most easily answered by conshe approximate equations derived from the kinetic energy model. Equation (2.130) is quite general, covering burbulent and viscous laminar flow (with appropriate choice of the friction factor). A duct can be considered loniscous drag is the dominant effectin other words, if the viscous drag term greatly exceeds the kinetic energy tehat kinetic energy losses can be ignored. The long duct condition is then

he maximum pressure ratio is achieved when the flow is choked. Substituting the expression for the choked patio [Eq. (2.129)] in this inequality leads to





nterestingly, the right-hand term of this inequality is the (approximate) choked pressure ratio for an aperture.Depending on the value ofγ , this then gives

ow-speed flows imply a small pressure difference, Kp ~ 1, so that

ubstituting for the friction factor fD in Eq. (2.134) gives

or example, with Re = 250 the criterion givesl 7.8d , meaning that the tube should be at least 78 diameters lonaking "much greater than" to mean a factor of 10). The case is illustrated in Fig. 2.12, for which a set of presshosen (using the thermodynamic equations) to maintain constant throughput in a 10-mm-diameter tube under iscous laminar flow conditions. Throughputs were then calculated using the entrance correction [Eq. (2.118)] inetic energy [Eq. (2.123)] models and the uncorrected Poisseuille equation [Eq. (2.82)]. Even atl = 78d the



Fig. 2.12Comparison of throughput calculated using various equations

and illustrating the long duct criterion.





rror in the Poisseuille values is still 19%, so the criterion is, if anything, rather conservative. The entrance corrmodel gives improved accuracy and does not give the wildly inaccurate values for smaller lengths. The kineticmodel gives values within a few percent of the correct value over the whole range.

hus, for viscous laminar, high-speed flows the long duct criterion is

or air at 20°C, flowing in a cylindrical tube the criterion can be expressed as

or high-speed flows, the likely error is still about 20% and the length would need to be increased by a factor ochieve errors of less than 10%. For low-speed flows which also meet the incompressible criterion (Ma < 0.3), n calculated values should be within 10%.

or high-speed, turbulent flow the long tube criterion is

he friction factor varies from 0.04 at Re = 4000 to 0.02 at Re = 50,000, givingl > 500 Dh to 1000 Dh . For low-speeows the values are halved; that is,l > 250 Dh to 500 Dh . With these criteria the error in calculated values should b

within 10%.

he conclusions to be drawn from this analysis are that a "long" duct is much longer than is commonly though generally unsafe to use the simple uncorrected viscous and turbulent flow equations.

4ransitional Flow

n the transition regime, gas flow dynamics are intermediate between free molecular flow and continuum flow.hort ducts transition occurs between molecular and isentropic flow and in long ducts between molecular and vaminar flow. The flow cannot be turbulent at or near transitional flow pressures as is easily shown.

he maximum flow velocity possible is equal to the speed of sound, and the Reynolds number at this velocity i

ombining this with Eq. (2.2) for the Knudsen number Kn gives





Kn = 0.01 marks the high-pressure boundary of transitional flow, so the maximum possible value of Re is ~ 16ess than the value (~ 2000) at which turbulent flow occurs.

Molecular flow analysis is concerned with the effect of bounding walls on the free flight of individual moleculontinuum flow analysis is based on hydrodynamic and thermodynamic considerations. It is clear that an analynification between the regimes presents considerable difficulty, but a number of attempts have been made. A nf analyses based on numerical solution of the Boltzmann equation have been described [3436]. Since, at the mundamental level, gas flow dynamics is determined by molecular interactions, attempts [37, 38] have been maxtend Monte Carlo methods into the transition regime by taking account of moleculemolecule collisions. Howhese methods require considerable computing power even for the simplest geometries. Scherer-Abreu and Abreveloped a probabilistic three-dimensional model requiring more modest computing power and obtained goodgreement with published results.

.4.1ransitional Flow in Long Ducts

n spite of the significant amount of work, there have been no general derivations of flow equations which are ased on first principles. The state of theory was reviewed by Thompson and Owens [40] who discuss, in parti

heory and empirical methods of obtaining an equation for the total flow regime. In viscous laminar flow, a statayer of fluid is assumed to exist adjacent to the duct walls. Slip theory supposes that the velocity of this layer ionzero, essentially due to a degree of specular reflection of molecules at the surface. One of the equations for ube, discussed by Thompson and Owens, derived from slip theory can be written as

whereCm is the long-tube molecular flow conductance [Eq. (2.14) or (2.21)] andδ is the fraction of molecules diffcattered at a surface. For large values of Kn the conductance tends to the molecular flow value, and for small v

Kn the first term inside the brackets becomes dominant and the conductance becomes equal to the Poiseuille, vow conductance [Eq. (2.83)]. The best correlation with experimental data (for glass and copper tubes) is achie= 0.84.

here is considerable evidence thatδ ~ 1 under molecular flow conditions, and there is no evidence of slip in theiscous regime (the Poiseiulle equation has been verified to a high degree of accuracy). Equation (2.141) has thharacter of a linear combination of viscous and molecular flows with a suitable weighting function to achievegreement with observation. The theory of slip flow is not entirely consistent, and there is some question whethctually occurs; the concept was introduced primarily as a means of extending solution of the NavierStokes equnto transitional flow. Slip theory does not appear to give any better results than empirical methods.





Knudsen [7] was the first to develop an empirical expression for transitional flow in a long circular cross-sectiowhich can be written as

whereCv is the Poiseuille long-tube conductance [Eq. (2.83)],Cm is the molecular flow conductance [Eq. (2.21)],K is given by

xpressed in terms of the Knudsen number, we have

With pressure in millibars and diameter in millimeters, Eq. (2.142) becomes

where the first term inside the brackets isCv/Cm and Fg is the gas factor defined by Eq. (2.4). At low and highressures the conductance tends to the molecular and viscous conductances respectively, as expected.

able 2.15 shows values of the conductance (as a ratio to the molecular flow conductance) and the term Z 1 for a ranf values of Kn together with the average

Table 2.15. Ratio of Conductance of Cylindrical Tube (Ct ) for That for Molecular Flow (Cm) as aFunction of Knudsen Number

Kn P mean (mbar)for d = 25 mm

Z 1 Ct/Cm

104 26.440.809

737.1

103 2.644 0.810 74.44

0.01 0.2640.811

8.174

0.1 0.02640.821

1.557

0.2 0.01320.831

1.199

0.5 5.289 × 1030.856

1.003



1 2.644 × 1030.884

0.958

1.55 1.706 × 1030.905

0.952

2 1.322 × 1030.917

0.954

5 5.289 × 1040.955

0.970

10 2.644 × 104 0.974 0.982

20 1.322 × 1040.986

0.990

50 5.289 × 1050.994

0.996

100 2.644 × 1050.997

0.998





ressure (for air at 20°C) in a 25-mm-diameter tube. For Kn < 0.01 the flow is almost entirely viscous, whereas0.5 the conductance has fallen to the molecular flow value. This is the justification for the values of Kn, delimow regimes, discussed in the introduction.

he pressure versus conductance results are also plotted in Fig. 2.13 for a 1-meter-long, 25-mm-diameter tube.ressures the conductance passes through a shallow minimum; the slope then rises through the transition regionncreasing to 45° in the viscous laminar flow region when conductance becomes proportional to pressure. At prbove 10 mbar the conductance has increased to more than 1000 liter·s1 and it might be thought that this size oould be used with a 50- or 100-liter·s1 pump with little loss in speed. However, Fig. 2.13 also shows the effecthis pipe with a 50-liter·s1 pump. At pressures ~ 1 mbar, the conductance begins to deviate from the long tubeonductance and flattens sharply at around 10 mbar as the flow becomes turbulent. At 100 mbar the conductan80 liter·s1 rather than ~ 5000 liter·s1. If a 100 liter·s1 pump were used, the conductance would be reduced to ~ter·s1. Even at a length of 40 diameters the pipe is not "long," as discussed in Section 2.3.7, and it cannot be a

hat conductance always continues to increase with pressure.

As an illustration of the application of the Knudsen equation, it is of interest to calculate the rate of leakage of atmosphere through a small hole into a vacuum chamber at 20°C. The pressure in the chamber is assumed to bower than atmosphere (say, 1000 mbar), so the mean pressure is 500 mbar. Consider two sizes of holes:

. l = 1 mm,d = 2 × 103 mm. The Knudsen number is 0.066, so flow is in the transition regime. The apertureonductance (from Table 2.3) is 3.63 × 107 liter·s1 andα = 0.00265 [Eq.(2.25)], soCm = 9.64 × 1010 liter·s1.

Applying Eq. (2.145) gives the conductance asCm × 1.93 = 1.86 × 109 liter·s1, so the throughput is 1.86 × 106mbar·liter·s1.

. l = 1 mm,d = 0.02 mm. The Knudsen number is now 0.0066, so the flow is still transitional.Cm = 9.24 × 107ter·s1. Applying Eq. (2.145) gives the conductance asCm × 11.95 = 1.1 × 105 liter·s1, so the throughput is 0.011

mbar·liter·s1. To maintain a pressure of 104 mbar with this leak rate would require a pumping speed of 110 lite

As will be observed, the ratio of transitional to molecular flow conductance is greater for the larger-bore capillahese examples serve to illustrate the fact that, even for a very fine hole, the rate of leakage can be substantial.

he conductance minimum observed by Knudsen at intermediate pressures (Kn ~ 1.6) may not always occur atalue and may be entirely absent. Pollard and Present [41] have offered a qualitative explanation for the minimave shown that it should depend on the length of the tube. When the pressure is sufficiently low that the mean much greater than both the diameter and the length of the tube, subpopulations of molecules occur which havxial velocity components on entry to the duct or after scattering from a wall. These molecules, which can travistances before a further wall collision, make a disproportionately large contribution to the transmitted flux. Aressure is increased, the mean free path





Fig. 2.13Variation of long-tube conductance with pressure and effect of

50 liter·s1 pump for a 25-mm-diameter, 1-meter-long tube.





ecomes smaller relative to the tube length, and the paths of these molecules are disrupted by intermolecular coAt the same time, the effect of the increased number of intermolecular collisions is to initiate an overall drift ve

ollard and Present reasoned that, since the development of continuum properties (and hence a drift velocity) dn λ/d , the decrease in flow due to the shortened mean free path will outweigh the increase due to a drift velocithe mean free path is more closely comparable with the tube diameter than with its length. The implication of th that a conductance minimum is likely to occur for long tubes but may not occur for short tubes or, at least, wronounced.

he conductance minimum is evident in the computed results of Sharipov and Seleznev [42] who presented tabalues of normalized flow rate for a range of Knudsen numbers, based on solution of the Boltzmann equation. abulated values can be used in calculation of conductance or throughput over the transition region and give res

which are a maximum of about 6% lower (at round Kn ~ 1) than those given by the Knudsen equation.

he term Z 1 in the Knudsen equation varies between 1 and 0.81, depending on the pressure. A simple approximhe Knudsen equation takes Z 1 = 1, so the equation becomes a straightforward summation of viscous and molecuows:

alculation of throughput is then straightforward, using

f the downstream pumping speed and pressure are known, then the pressure ratio can be found from

here appears to be little information on transitional flow in ducts of noncircular cross section. Dong and Bromiscussed transition and slip flow and developed empirical equations for rectangular and annular cross sectionslthough it is difficult to know how to interpret their results or to say whether the empirical relations are applicaucts with lengths and aspect ratios different to those used in their experiments.

is therefore suggested that the Knudsen Eq. (2.142) [or the simple approximation of Eqs. (2.146) to (2.148)] s a rough approximation for transitional flow in other cross sections, takingCv as the viscous conductance for thearticular duct shape.

An alternative to the Knudsen equation is

ike the Knudsen equation, this also exhibits a minimum in the transition region, although significantly deepermay be more appropriate for narrow rectangular





ucts which are known to show a more pronounced minimum than circular cross sections [43]. The basis of thiormulation will be covered in Section 2.4.3.

.4.2ong Duct Criterion in Transitional Flow

or continuum, high-speed flow, it was shown previously [Eq. (2.132), Section 2.3] that the worst-case conditiong tube is

o that, for a circular cross-sectional tube in laminar flow we have

ombining this with the result of Eq. (2.140) for the maximum Reynolds number leads to (for high speed flow

At the high-pressure limit of transitional flow (Kn ~ 0.01, at the duct exit), this gives

epending on the value ofγ . As discussed under continuum flow, this suggestsl long ~ 40d even at sufficiently lowressures that conditions at the duct exit are close to transitional. Since the Knudsen equation is a combination iscous and molecular flows, it is expected that a similar criterion is applicable through the regime. This implieong becomes smaller as the pressure is reduced and flow conditions become transitional (Kn > 0.01). At moleow pressures the kinetic energy term must vanish, so the criterion becomes irrelevant.

haripov and Seleznev [42] showed that the conditions of applicability of their solution of the Boltzmann equa

where Kn is the Knudsen number at the mean pressure and∆ P is the pressure difference across the tube. The resulhis solution agree well with those calculated using the Knudsen equation. Thus, these conditions should also ahe Knudsen







quation and to other empirical transitional flow formulations which are based on a combination of viscous andmolecular flows. These conditions imply that solutions are valid for relatively short tubes if the pressure differemall. However, one of the main assumptions underlying solutions of the Boltzmann equation is that the tube isufficiently long that end effects can be neglected and the flow considered as one-dimensional. This suggests thl hould not be less than about 20d even well into the transitional flow regime. It is difficult to be more specific bef the dearth of experimental and theoretical information on transitional flow in short ducts.

.4.3ransitional Flow through Apertures and Short Ducts

ransitional flow through a thin slit was studied by Kieser and Grundner [44], who gave an empirical fit to datat 20°C, which can be written as

whereCa is the molecular flow aperture conductance,a is the short dimension of the slit,λ is the mean free path at

mean pressure,k 1 = 0.5, andk 2 = 0.3412. In their experiments, ; thus the equation only describes the trom molecular to continuum, choked flow. The authors noted fluctuations of the measuring points in the high-

ange, which they attributed to small alterations of flow pattern as a function of pressure. The equation gives thmaximum flow rate as 85% of the theoretical isentropic flow rate through an aperture [Eq. (2.106)], which is tyhin, sharp edged apertures.

As noted earlier (Section 2.3.3.1), the theoretical flow rate can be achieved with a small radius on the inlet edgength ducts. It is suggested that the equation can be generalized for any gas and for apertures with radiused ed

1 = 0.5 and

o that, at high pressures, Eq. (2.155) will give the theoretical value for an orifice.

Kieser and Grundner [44] also studied flow, at large pressure ratios, through rectangular ducts. They regard theeries combination of entrance aperture and the duct itself. In the modified form suggested by O'Hanlon [45] thate can be found from





whereCt is essentially the Knudsen transitional flow conductance, given by Eq. (2.142) withCv as the viscous flow

onductance for a rectangular duct. As for the aperture, this equation is valid only for the case when .

anteler [33, 46] suggested the following formulation for transitional flow through an aperture (again valid onlyarge pressure ratios):

where the subscriptsma and 0c refer to molecular flow [Eq. (2.15)] and isentropic flow [Eq. (2.106)] respectivel a weighting function which can be written, in terms of Kn at the mean pressure, as

he best fit to the results of Eq. (2.155) is obtained withks ~ 12 (Santeler usedks = 28). In a fashion similar to thatq. (2.19), short ducts are considered to consist of an ideal duct in series with an exit aperture. The total pressuhen due to purely viscous losses in the duct plus the pressure drop across the transitional/isentropic aperture.

f the formulation of Eq. (2.158) is applied to a finite length duct, then

where are the molecular and viscous flow throughputs. For a long circular section tube, it is intereote that

f ks = 128/3π is taken as the basis for the weighting factorθ, the result is Eq. (2.149).

An expression, due to DeMuth and Watson [47], for nonchoked transitional flow through orifices is

where [Eq. (2.109)] is the isentropic and ma the molecular flow throughput of an aperture. The Knudsen n calculated at the mean pressure. The equation is based on studies of air flowing through apertures at pressure

anging from 1.1 to 1.4. Since the authors appear to define the Knudsen number as R/ λ, their equation has beenmodified to conform with the definition in this chapter.

or large pressure ratios, the duct + isentropic exit (or entrance) models appear to give good results for short du principally because high-speed flow through short ducts is very insensitive to length (as illustrated in Fig. 2.1

he isentropic aperture conductance is independent of pressure. But this type of model breaks down at lower preatios. As the pressure ratio is reduced, the isentropic aperture conductance increases and tends to infinity at vamall pressure ratios. The







entropic term, in Eq. (2.158) for example, then makes a disproportionately high contribution to the total flow. For examponsider a pressure ratio Kp across an aperture. Using the approximation of Eq. (2.114) for continuum flow through an aperviding Eq. (2.158) by the pressure difference gives the conductance as

or a small pressure difference (say Kp = 1.01) and with Kn = 1 (molecular flow) so thatθ = 0.93 [Eq. (2.159) withks = 13], thves

he enhancement factor from Eq. (2.162) is 1.83 for the same conditions. It seems unlikely that the aperture conductance nhanced by such a large a factor under essentially free molecular conditions.

learly, simple combinations of isentropic and molecular flow and aperture + entrance models are not a good basis for genmpirical equations applying to short ducts. As discussed under continuum flow, in short ducts a term must be included tor the kinetic energy required to accelerate the gas. It is suggested that approaches to empirical equations in the transition

ould be based on formulations which force the kinetic energy term to vanish under molecular flow conditions.

ymbols

ymbol Meaning Section

Duct cross-section dimension, minor axis of ellipse 2.2.5

A Cross-sectional area 2.2.2

Duct cross-sectional dimension, major axis of ellipse,b ≥ a 2.2.5Cross-sectional perimeter (includes all wetted surfaces) 2.2.2

C Conductance 2.1Ca Molecular flow conductance of an aperture 2.2

Cm Molecular flow conductance of a duct 2.2

Cn Net value conductances in series 2.1

Ct Transitional flow conductance of a duct 2.4.1

Cv Viscous flow conductance 2.3.1

Cvd Viscous flow conductance, calculated at downstream (lower) pressure 2.3.1

Cvu Viscous flow conductance, calculated at upstream (higher) pressure 2.3.1

Cz The term 2.3Diameter of a cylindrical tube Introduction

Dh Hydraulic diameter 2.3

able continued on next page)





able continued from previous page)


D Darcy friction factor 2.3.2

g Gas factor IntroductionGe Numerical constant and cross-sectional geometry terms in viscous conductance equations 2.3.2

G(γ ) Function ofγ defined by Eq. (2.106) 2.3.3.1Generally used for constants and units conversions

Kn Knudsen number Introduction

Kp Pressure ratio: (higher pressure)/(lower pressure) 2.1

Kpc Choked pressure ratio 2.3.6

Kpca Choked pressure ratio for an aperture 2.3.3.1Length of a duct (in direction of gas flow) 2.2.2

e Equivalent length used in Eq. (2.25) 2.2.4entry Entry length 2.3.1

Ma Mach number (ratio of flow velocity to local velocity of sound) 2.3.1Man Mach number at duct entrance 2.3.3Ma x Mach number at duct exit 2.3.3

Mm Molar mass (e.g., 0.028 kg·mole1 for nitrogen) Introduction Number density of molecules Fig. 2.5

c Loss coefficient or number of corrections for flow obstructions 2.3.4

N Number of molecules striking an area 2.2

Mean pressure 2.3.1Pressure Introduction

d Downstream (lower) pressure 2.1

u Upstream (higher) pressure 2.1

Throughput (in pressure × volume units) 2.1

Choked throughput for an aperture 2.3.6

Value of throughput at onset of turbulent flow 2.3Generally used for ratios

R Radius of a cylindrical tube 2.2.4Re Reynolds number 2.3

R0 Universal gas constant (8.314 J·mole1·K1) IntroductionPumping speed 2.1

a Speed of a choked aperture 2.3.3.1



ca Pumping speed required to choke an aperture 2.3.3.1

F Shape factor 2.3.2

n Net speed of a pump in series with conductances 2.1Time 2.2.11

T Thermodynamic temperature IntroductionFlow velocity [and dimensionless terms in Eq. (2.36)] 2.3

a Mean thermal velocity of molecules 2.2.2

V Volume 2.1

Gas flow impedance 2.1

1 Term in Knudsen transitional flow Eq. (2.142) 2.4.1

Transmission probability 2.2

n Net transmission probability of components in series 2.2.10

able continued on next page)





able continued from previous page)


H Ho coefficient of a pump 2.2.10

The term 2.3.3

Ratio of the principal specific heats for a gas 2.3.3

Dimension ratio used in Eq. (2.26), diffuse scattering fraction in Eq. (2.141), and factor in Eq.(2.42)

Wall roughness 2.3.2

Mean free path Introduction

Viscosity of a gas Introduction

Gas density 2.3Angle in Eq. (2.18) and weighting factor in Eq. (2.158)

Time constant 2.2.11

eferences

M. Knudsen, Ann. Phys . ( Leipzig ) [4] 28, 9991016 (1909).

S. Dushman,Scientific Foundations of Vacuum Technique , Chapter 2. Wiley, New York, 1949.

W. Steckelmacher,Vacuum 16, 561584 (1966).W. Steckelmacher, Proc. Int. Vac. Congr., 6th , Kyoto Japan, 1974; J. Appl. Phys., Suppl . 2 (Part 1), 117125 (1974).

W. Steckelmacher and M. W. Lucas, J. Phys. D 16, 1453 (1983).

P. Clausing, Ann. Phys . ( Leipzig ) [5] 12, 961 (1932); J. Vac. Sci. Technol . 8, 636646 (1971).

M. Knudsen, Ann. Phys . ( Leipzig ) [4] 28, 75 (1909).

W. Steckelmacher,Vacuum 28, 269275 (1978).

W. Steckelmacher, Rep. Prog. Phys . 49, 1083 (1986).

0. M. Smoluchowski, Ann. Phys . ( Leipzig ) [4] 33, 1559 (1910).

1. R. J. Cole, Rarified Gas Dyn . 10 (Part 1), 261272 (1976).

2. A. S. Berman, J. Appl. Phys . 10, 3356 (1965); erratum, ibid. 37, 2930 (1966).

3. D. J. Santeler, J. Vac. Sci. Technol. A 4(3), 338 (1986).

4. L. L. Levenson, N. Milleron and D. H. Davies,Vide 103, 42 (1963).

5. D. J. Santeler and M. D. Boeckmann, J. Vac. Sci. Technol. A 9(4), 2378 (1991).

6. R. J. Cole, Proc. R. Soc. Edinburgh 82A, 211223 (1979).



7. A. S. Berman, J. Appl. Phys . 40, 4991 (1969).

8. D. H. Davies, J. Appl. Phys . 31, 1169 (1960).

9. C. W. Oatley, Br. J. Appl. Phys . 8, 15 (1957).

0. R. A. Haefer,Vacuum 30, 217 (1979).

1. L. Holland, W. Steckelmacher and J. Yarwood,Vacuum Manual . Spon, London, 1974.

2. H. S. Carslaw and J. C. Jaeger,Conduction of Heat in Solids . Oxford University Press, London, 1959.

3. J. D. Lawson, J. Sci. Instrum . 43, 565 (1966).

4. V. E. Senecal and R. R. Rothfus,Chem. Eng. Prog . 49, 533 (1953).





5. R. K. Shah and A. L. London, Laminar Flow Forced Convection in Ducts . Academic Press, New York, 1978.

6. S. E. Haaland, J. Fluids Eng . 105, 89 (1983).

7. O. C. Jones, J. Fluids Eng . 98, 173 (1976).

8. F. M. White, Fluid Mechanics , 2nd ed. McGraw-Hill, New York, 1986.

9. B. S. Massey, Mechanics of Fluids , 5th ed. Van Nostrand-Reinhold, Wokingham, Berkshire, England, 1983.

0. A. H. Shapiro,The Dynamics and Thermodynamics of Compressible Fluid Flow , Vols. 1 and 2. Ronald Press, NYork, 1953.

1. G. W. C. Kaye and T. H. Laby,Tables of Physical and Chemical Constants , 15th ed. Longman, New York, 198

2. F. M. White,Viscous Fluid Flow . McGraw-Hill, New York, 1991.

3. D. J. Santeler, J. Vac. Sci. Technol. A 4(3), 348 (1986).

4. C. Cercignani and F. Sernagiotto, Phys. Fluids 9, 40 (1966).

5. C. Cercignani,Theory and Application of the Boltzman Equation . Scottish Academic Press, Edinburgh, 1975.

6. S. K. Loyalka, T. S. Storvick and H. S. Park, J. Vac. Sci. Technol . 13(6), 1188 (1976).

7. Masahiro Ota and Hiroyoshi Taniguchi,Vacuum 44, 685 (1993).

8. L. Fustoss,Vacuum 31, 243 (1981).

9. G. Scherer-Abreu and R. A. Abreu,Vacuum 46, 863 (1995).

0. S. L. Thompson and W. R. Owens,Vacuum 25, 151 (1975).

1. W. G. Pollard and R. D. Present, Phys. Rev . 73, 762 (1948).

2. F. M. Sharipov and V. D. Seleznev, J. Vac. Sci. Technol. A 12, 2993 (1994).

3. W. Dong and L. A. Bromley,Trans. Natl. Vac. Symp . 8, 1116 (1961).

4. J. Kieser and M. Grundner,Vide 201, 376 (1980).

5. J. F. O'Hanlon, J. Vac. Sci. Technol. A 5, 98 (1987).

6. D. J. Santeler, J. Vac. Sci. Technol. A 12, 1744 (1994).

7. S. F. DeMuth and J. S. Watson, J. Vac. Sci. Technol. A 4, 344 (1986).





ositive Displacement Vacuum Pumps

A positive displacement pump is a vacuum pump in which a volume filled with gas is cyclically isolated from the gas being then transferred to an outlet. The first pumps of this type were piston pumps, but in 1905 Gaede [ntroduced the modern rotary vane (blade) vacuum pump. It has developed in many ways over the last 90 yearsnd very early on, it was oil-sealed and then a number of improvements were incorporated, including reductionnd vibration, handling of condensibles and corrosive materials, elimination of oil being sucked back when stoirect drive (running at 1450 or 1800 rev/min), and so on.

Another type of pump which has been widely used, primarily in the chemical industry, is the liquid ring pump he pumping action is developed by a rotating liquid. Pumps of this type produce nearly isothermal compressioandle dry gases or vapor gas mixtures. By reason of the isothermal compression, it is possible to handle exploases or gases subject to polymerization. With the pumping of vapor-laden gases, condensation occurs in the puesulting in an enhanced capacity.

n the early 1980s it became clear that the pumping of corrosive and inflammable materials, combined sometimbrasive dust, was complicating the operation of the oil-sealed rotary pump and much reduced its normal long lerformance. It was also becoming necessary to take precautions against backstreaming of the oil into some vaystems to reduce system contamination. These two requirements led to the search for pumps which did not useealing in their pumping mechanisms. The resultant pumps were referred to as ''dry vacuum pumps" because ofbsence of liquid sealing. The first pumps were based on a number of stages working either on the Roots Princcirca 1861) or on the more recent Claw Principle (circa 1930), but there are now a number of other mechanismnd these are described in a later






ection. An attempt is made to indicate the relative merits of the various mechanisms, but due to the rapid deven this field they are likely to be modified with time by design changes.

When a positive displacement pump is used to back a secondary pump which has high pumping speed, but in aressure region, the forepressure requirement of the secondary pumps must be satisfied. In recent years the intrf turbo pumps with integral molecular drag stages has resulted in pumps requiring a forepressure of around 10two-stage diaphragm pump is sometimes used. When choosing a forepump it is always necessary to ensure thffect on the performance of the secondary pump is taken into account (see Chapter 9).





art IOil-Sealed Vacuum Pumps

Nigel T. M. Dennis

1il-Sealed Vacuum Pumps

apacities available: 1 to 1500 m3/hr

Operating pressure range:

Single-stage: 1000- to 5 × 102-mbar total and partial pressureTwo-stage: 1000- to 103-mbar total pressure

1000- to 104-mbar partial pressure

otal pressure is influenced mainly by the type and quality of the oil charge, while the partial pressure is due toansfer of gas within the pump.

.1.1ump Design

here are two basic designs of oil-sealed rotary pumps, and these are illustrated in Fig. 3.1. Figure 3.1a shows the twane pump where gas is trapped between the vanes and the stator before it is swept out through the outlet valve.1b illustrates the rotary piston pump where a single vane is slotted into the stator by the use of a hinge pin andf a sleeve which fits around the rotor. The vane is hollow and acts as an inlet valve, closing off the pumping com the inlet when the rotor is at top center. Smaller pumps tend to be of the two-vane design, while larger pum

more frequently of the rotary piston design. Foundations of Vacuum Science and Technology , Edited by James M. Lafferty.ISBN 0-471-17593-5 © 1998 John Wiley & Sons, Inc.





Fig. 3.1Two basic designs of rotary pump mechanism. (a) Two-vane pump.

(b) Rotary piston pump. A, rotor; B, stator casing; C, rotor sleeve andsingle vane; D, vane; E, hinge pin; F, gas ballast port; G, outlet valve;

H, gas entering the swept volume; J, the gas being compressed.

n the two-vane design the main path of leakage between the inlet and the outlet is the rotor to stator gap at theetween these two ports. To reduce this leakage to a minimum, it is usual to use a long path seal which is proviroove in the stator which is of the same diameter and on the same center as the rotor. This gives a long path clwhich is sealed with oil between the inlet and the outlet and reduces carryover of gas between the two ports to

minimum.

n a two-stage pump it is normal to feed outgassed oil from the outlet stage to seal and lubricate the inlet stage,nsuring that the best ultimate can be achieved.

.1.2Gas Ballast [2]

his is a feature useful in reducing the extent of vapor contamination of the oil. Atmospheric air or, if required,nert gas is admitted to the pump during the compression stage (see Fig. 3.2) to increase the proportion of

oncondensable gas in the pump by the time compression has progressed to a point (about 1200 mbar) when thalve lifts. By this means the partial pressure of the vapor being pumped, at the time when the outlet valve liftsxceed its saturated vapor pressure at pump temperature, so that the vapor is discharged without liquefaction.urthermore, due to the extra work done in compressing the gas introduced as gas ballast, the pump temperaturnd further assists in preventing vapor condensing within the pump. Gas ballasting is a useful technique for purump oil of condensed or dissolved vapor; it should proceed for a minimum of 20 minutes to allow the pump tp completely. Gas ballasting is very useful for pumping vapors that do not dissolve in the pump oil and is stillalue for vapors that do dissolve.





Fig. 3.2Method of introducing gas ballast to a bladed rotary pump.

he gas ballast flow is generally about 10% of the free air displacement of the pump. Because the effectivenessallast is very dependent on pump temperature, it is desirable to run the pump as hot as possible. Typically, runemperatures are 60°C to 90°C.

ondensation will occur when the temperature in the pump outlet line reaches the saturated vapor pressure of that is being pumped. It is, therefore, important that a catch pot is fitted immediately adjacent to the outlet port uid condensed in the outlet line does not run back into the pump oil box.

he ultimate pressures attainable when gas ballast is used are as follows:



Single-stage pump: about 0.5-mbar total pressureTwo-stage pump: about 102-mbar total pressure





o calculate the minimum (maximum) safe pumping rate it is assumed that the ballast gas just becomes fully sawith vapor at the end of the compression as it is forced through the outlet valves and that the vapors are insolub

ump oil [3]. It is therefore necessary to know the volume flow rate, the partial pressure, and the absolute tempf the vapor under these conditions (this may be assumed to be the temperature of the pump itself). The partial hen the saturation vapor pressure at the pump temperature (T , K), and its value is available from vapor pressure dPs , mbar). If the total pressure reached under the outlet valve is PT (mbar), the partial ballast gas pressure is PT Ps .

he volume rate of flow for the vapor is the same as for the ballast gas and is therefore obtained by calculatingolume flow rate for the ballast gas, in terms of its measured flow rate (V , m3/h) into the pump at atmospheric prend temperature ( PA and t , K).

hus we have the volume/hour of emerging gas:

f the maximum pumping rate isW (kg/h) and if the vapor density of the saturated vapor atT (K) is ρ s (kg/m3), then

he ordinary perfect gas equation is used to obtainρ s with adequate accuracy in this pressure range; thus for wateapor we obtain

aking PA as 1013 mbar and assuming that the pressure PT under the outlet valve when the mixture is expelled ismbar andt = 293 K, then for water vapor we obtain

Knowing Ps (the vapor pressure for water) at the pump's temperatureT and the volume rate of flow of the ballast g

now possible to calculate the maximum safe water vapor pumping rate in kg/h. Knowing the speed of the puSm3/h), it is then possible to calculate the maximum safe inlet pressure of water vapor:





f the ballast air is humid, then Ph (mbar) is the partial water vapor pressure, the true mass flow rate of air is reduhe ratio ( PA Ph )/ PA , and water vapor is also entering the pumps with the ballast air at a rate of

quation (3.1) must be changed to allow for the reduced true ballast air flow and the additional water vapor enwith the ballast air; thus

his is only applicable when pumping water vapor. If other vapors are pumped, the moisture contributes usefulhe effect of ballast humidity is small at the normal gas-ballasted pump temperature of 70°C or higher and is gisregarded.

As the vapor pressure of water is rapidly increasing at these higher temperatures, the pump temperature is verymportant in determining its water vapor capacity. In the standard on determining this part of the pump perform indicated that an initial test is carried out allowing air to be substituted for water vapor at the likely safe inlet

o that the pump temperatureT is adjusted.

High or low ambient temperature has an effect which can be appreciable if it is more than a few degrees away .

An alternative to gas ballast is the use of extremely small air bubbles passing through the oil to carry the contamway. This has the advantage of minimal loss of pump oil and a normal ultimate vacuum. The amount of contahat can be removed by this method is much less than by normal gas ballasting and does require a small air pumroduce the bubbles.

.1.3ump Oil [4]

he type most widely used is normally highly refined hydrocarbon oil. For very-heavyduty applications, syntherganic fluids are used, and in highly corrosive or flammable situations a perfluoropolyether fluid is used. The hould be of the viscosity recommended by the manufacturer; lower-viscosity oil normally results in the pump oisier, while higher-viscosity oil can give difficulty in starting at low ambient temperature and occasionally le

eizure.. Hydrocarbon Oils : The general fluid used in most applications is a highly refined mineral based oil; it normalapor pressure around 106 mbar at room temperature. Some oils have additives to help reduce the corrosive effny vapors being pumped, but their addition results in a higher ultimate total pressure. They are also graduallyeutralized, so their effective life is limited. Hydrocarbon oils are slightly hygroscopic, so the pump should be om





bottle or can which has only recently been opened. If the pump is not used for a lengthy period, it is advisable to gas ballast for a while oil of any dissolved water vapor.

Synthetic Organic-Type Fluids : These are used on heavy-duty applications because certain types have improved resistance to oxidationgh pump temperature associated with these applications.

Fluorinated Fluids [5]: These are rotary pump grades which are used in applications where their corrosion-resistant properties andemical inertness result in greatly increased operational times between pump maintenance. The basic properties of perfluoropolyether

d their advantages for use in vacuum systems are as follows:hemical inertness. Ideal for pumping aggressive materials, particularly in semiconductor processing.oninflammable. No fire risk.igh thermal No residual "tars" formed by overheating.sistance. Eventually reduced to gaseous products.xygen-compatible. Allows safe pumping of oxygen. Refer to manufacturers literature for maximum recommende

service temperature and pressure with oxygen.mmiscible with most common solvents. Allows pumping of solvent in some cases without gas ballast.

he pump must have no traces of hydrocarbon oil when charged with perfluoro-polyether fluid; otherwise, some or all of the above adve adversely affected. With this type of fluid the ultimate vacuum of the pump is not normally as good as with the normal oils. This is x gases being dissolved in the fluid and evolving when the fluid reaches the high-vacuum stage of the pump. Note : Perfluropolyether fluidscompose at 250300°C, and the resultant products are toxic.

1.4l Suckback [6]

his occurs if the pump is stopped for a period of time under vacuum. Oil suckback is prevented by incorporating into the pump inlet linreturn valve. When this is an integral part of the pump, it is operated in a number of different ways. When this arrangement is used, rmal for the pump mechanism to be allowed to reach atmospheric pressure so that there is no chance of oil being sucked back due to aling of the valve. An alternative way is to keep the pump under vacuum and stop any oil entering the pump by an oil valve and a seatlet valve. The oil and outlet valves are designed so that only a small amount of oil can be sucked into the pump mechanism if the vaseal.

1.5wer Requirements and System Protection

he power to the pump rises at a maximum of 100300 mbar and then falls to a low level. It is mainly caused by friction within the pumotor losses, when the pump reaches 10 mbar and below.





ontamination of the system occurs at low gas flows toward the pump, normally when the inlet pressure is belombar. This is due to condensation of both the oil vapor from the pump and its breakdown products in the system

at a lower temperature than the pump. Therefore, it is inadvisable to leave a rotary pump on a system at or neltimate vacuum for a prolonged period without a trap or another type of pump between it and the system. Thesed contain either an activated alumina or a molecular sieve trapping medium. Both these materials absorb waapor, and it is therefore best to bypass them during pumpdown because otherwise it becomes difficult to achieood ultimate vacuum.

.1.6Accessories [7]

esides the inlet trap mentioned above, there is a wide range of accessories mainly aimed at preventing dust froetting into the pump mechanism, decontaminating the pump oil, and preventing oil from being lost from the pnlet filters are often used on dusty systems, but these reduce the pumping speed considerably especially at the ressures. The filter element is normally removable and of a pleated construction to give a high conductance. Ipplications where dust that is too fine to be readily stopped by inlet filters or is being continuously formed at tnlet, an oil circulation system is fitted to the pump oil box. This system includes an oil filter and a circulating osometimes an integral part of the vacuum pump). An oil pressure gauge or switch gives an indication of when

lement has to be changed.On a system where large quantities of vapor are to be pumped, it is normal to use an inlet condenser. The coolimedium of this condenser is normally water, but it can be cooled down to as low as 80°C depending on the app

or details see "Sorption Roughing Pumps," Section 5.20. Outlet mist filters are used to capture the extremely hat is evolved from a pump. Some pumps include a preliminary oil filter directly above the outlet valve, but toompletely eliminate mist under all operating conditions it is still necessary to fit an external filter. In smaller shis filter can also include a charcoal deodorizer. In cases where the pumps are running at reasonably high pressabout 10 mbar), it is possible to suck the collected oil back from the outlet filter into the inlet of the pump or thhe gas ballast connection; otherwise, it is necessary to periodically empty the oil from the filter and return it toump. If vapors are being pumped, neither of these systems is possible and the oil should not be returned to the





art IIquid Ring Pumps

elmut Bannwarth

2quid Ring Pumps

Capacities available: 1 m3/h to 27,000 m3/h vacuum pumps [8]Operating pressure range (minimum): 1013 to approximately 33 mbar total pressure extended to 5 mbar with gas ejector

2.1echanism

With regard to the arrangement of the impeller in the housing, it is necessary to distinguish between the concentrically mountedcentrically mounted vane-impeller. Machines with cylindrical housings are designated as single-acting or single-chamber liqu

umps. According to their method of operation, machines with oval-shaped or elliptical housing are designated as double-actinghamber liquid ring pumps. A further classification is made with regard to the direction of the gas inlet and outlet stream in relampeller. Usually, pump assemblies have axial or radial flow. Liquid ring vacuum pumps are, as a rule, of single-stage or two-st

sign. The functioning of a liquid ring machinefor example, a vacuum pump with eccentrically arranged impelleris described ahe liquid ring vacuum pump with eccentric impeller, arranged in a circular housing, belongs to the group of single-acting or sihamber liquid ring pumps. The housing must not be exactly cylindrical, but should have an elliptical profile. Through varying

the housing, it is possible to attain the optimal adjustment of the machine for the operating requirement. In these pumps, the drce from the impeller is transferred through the liquid ring to the pumped medium. The liquid ring will accelerate on the






Fig. 3.3Cross section of a one-stage liquid ring vacuum pump

with canned motor (Lederle-Hermetic GmbH).

uction side and, therefore, has augmented energy. On the discharge side, the ring liquid enters the impellerompartments, whereupon a portion of the kinetic energy is transformed into static energy of compression. On issipation of the static energy, the losses in the gas and liquid streams are overcome, so that the gas is compresected.

Assuming that the vane-impeller is arranged eccentrically in the properly adjusted housing, the moving impellempetus to the rotating liquid ring. Because of the eccentricity of the impeller to the housing, a crescent shapedormed between the impeller hub and the liquid ring as the impeller rotates. The impeller vanes split up this cav

many segments of differing volume. On rotation of the impeller, the segments increase in size in the region of tort (Fig. 3.3) and gas or gas vapor mixture is sucked in.

n the region of the discharge port opposite, the pumped medium in the segments (which are here becoming smompresses and is ejected. The intake and discharge ports are to be found with control plates on the side of axia

machines. Liquid ring pumps are rotary machines with the characteristics of piston pumps. The liquid ring assu

unction of the piston..2.2ingle-Stage Liquid Ring Vacuum Pumps [9]

With the single-stage liquid ring vacuum pump, it is possible to attain various pressure ratios through the designrrangement of ports. Liquid ring vacuum pumps with control plates and venting holes are operated economicaompression ratios of up to 1:7 for suction pressures between 1013 mbar and about 150 mbar





Fig. 3.4Cross section of a two-stage liquid ring vacuum pump (Sihi GmbH). 1, Shaft;2, impellers; 3, control plates; 4, middle section of housing; 5, end cover;

6, shaft seal; 7, shaft bearing; 8, suction port; 9, discharge port.

with water at 15°C as the ring liquid. The single-stage liquid ring vacuum pump can operate at compression ratreater than 1:7 but at considerably diminished capacities, provided that the discharge port is reduced, the ventre suitably arranged, and an automatic valve is provided. Disc valves are usually used. The compression ratio ccommodated by means of this valve, which is contiguous with the discharge opening in the control plate. Thlate in use covers or uncovers the venting holes automatically over the entire pressure range and preventsvercompression and back flow. Using water at 15°C as the ring liquid, inlet pressures in the range between 10nd about 33 mbar are achieved with a corresponding compression ratio between inlet and discharge pressure of other ring liquidsfor example, oilare used, inlet pressure is limited to between about 10 mbar and 30 mbar duutgassing.

.2.3wo-Stage Liquid Ring Vacuum Pumps [8,9]

or inlet pressures which lie in the region below 150 mbar, instead of using single-stage machines with flexibleischarge ports, it is possible to use a two-stage liquid ring vacuum pump (Fig. 3.4). This construction has gas penings without valves. The discharge from the first stage becomes the suction to the second stage. The partiaompression ratio per stage is variable in regard to the inlet pressure. Through







fixed outlet port, a compression ratio of less than 1:7 per stage is maintained. The overall compression ratio isroduct of the two partial compression ratios. With water at 15°C as the ring liquid, two-stage liquid ring vacuuumps may also be used to accommodate suction pressures in the range between 1013 mbar and 33 mbar.

.2.4he Operating Liquid

he operating liquid serves both to transfer energy and to seal the vane-impeller and spaces between the impellontrol plate, and housing, and it also absorbs and removes quantities of heat generated in the pump [10]. Wates other ring fluids, dependent upon the nature of the process, may be usedfor example, hydrocarbons, solventsynthetic light oils. In addition to the heat of compression, additional heating in liquid ring pumps may be geneondensation of vapors and absorption of gases, through chemical reactions occurring between process gas andquid or through the cooling of the principal gas at elevated temperatures.

.2.5Operating Ranges of Liquid Ring Gas Pumps

o obtain the lowest achievable pressure with the liquid ring vacuum pump, it is necessary to prevent boiling operating liquid. Using water at 15°C as the ring fluid, the lowest possible inlet pressure which is practical as wossible is approximately 33 mbar [11]. Lower inlet pressures may be reached through the use of a liquid havinigher boiling point. An improvement of the inlet pressure can also be attained through the use of an additionalump operating on a different principle connected on the inlet side of the liquid ring pump. Liquid ring vacuumre often used in combination with gas ejector pumps; and here it is possible, using water at 15°C as the ring liqccommodate inlet pressures in the range between 33 mbar and approximately 5 mbar. In the combination, the ector is placed directly at the intake of the vacuum pump (Fig. 3.5). The special curve over the operating rangacuum pump with gas ejector, using water at 15°C as the ring liquid, is shown in Fig. 3.6. As the driving medhe gas ejector, we may use atmospheric air, the process gas itself, or any suitable noncondensable gas at atmosressure.

he liquid ring vacuum pump can also be adapted for use at inlet pressures below 5 mbar. In these cases, one oacuum pumps utilizing a different pumping principle are placed at the inlet side of the liquid ring pump. The cacuum pumps is to be such that the pump combination will operate synchronously over the required suction pange. Since over wide pressure ranges there are changes in specific gas densities and types of flow (viscous, Knd molecular flow), different pumping principles are used for operation over wide pressure ranges. A condensften used in a vacuum pump combination for handling vapors and often improves the overall efficiency of thequipment [12].

.2.6avitation and Protection against Cavitation

he application range of the liquid ring vacuum pump for lower inlet pressures is limited by the vapor pressureperating liquid. If the physical properties of the





Fig. 3.5Liquid ring vacuum pump with gasejector. A, intake gas; B, atmospheric

air as motive gas; P 0, intake pressure; P , back pressure of the gas ejector =

intake pressure for the liquid ringvacuum pump; C, exit of theintake gas and motive gas.



Fig. 3.6Operating range of a liquid ring vacuum pump with gas ejector.





perating liquid are unsatisfactory, it will boil and the impeller vanes will fill up with vapor. The vapor transpoy the movement of the impeller vanes toward the pump outlet side results in collapse of the vapor bubbles. Thmplosion, known ascavitation , causes a banging noise and noticeable shaking of the pump. Cavitation will not he liquid ring vacuum pumps if the pump operation is always limited to a minimum inlet pressure and correspolumetric flow and noncondensable gases are handled. The pump can also be provided with gas from a liquidn the inlet side operating in conjunction with a regulating valve toward the inlet. If a gas ejector is used in a pombination and there is always a gas flow through the open driving gas inlet, cavitation will not occur [11]. Tavitation damage, a liquid ring vacuum pump can be provided with a built-in cavitation protection. This is in tf a gas ballast in the working space on the discharge side. This has only a small effect on the pumps operatingharacteristics.

.2.7ypes of Operation; Conveyance of Operating Liquid

hree principal methods of operation may be differentiated: operation without back flow of liquid (fresh liquidooling circuit); operation with back flow of liquid (combination operation, economical circuit); and closed liqirculation (return circulation, closed circulation) [12]. The principle of operation and disposal of the operating

will depend upon the process technology, the suction pressure, the available cooling medium and its temperatu

tuation with regard to corrosion of materials, and the nature of the process gas and operating liquid. The instahese machines and correspondingly optimized vacuum systems should be done in an economically favorable mhat environmental safety precautions are observed. Figure 3.7 shows the principal circuitry for operation with quid circulation.

n this method of operation, the operating liquid in the liquid separator is separated from gas as well as vapor aack into the pump through a heat exchanger wherein it is indirectly cooled. In the heat exchanger, the heat is rom the system. The special advantage of this method of operation is that the intake gases and

Fig. 3.7Principal circuit for operation withclosed liquid circulation.





apors as well as the operating liquid do not come into contact with the cooling medium. There is no problem oisposal from the cooling liquid side. By reason of the isothermal compression at low gas temperatures, the gasapors discharged into the atmosphere contain only small quantities of noxious materials.

he closed circulation method of operation is used in the chemical industry and in other situations wherein theequirement for freedom from leakage and protection of the environment exists. The contaminated operating liqequire special disposal procedures.

.2.8Materials of Construction

n the choice of materials of construction, resistance to corrosion normally plays the major role. In process techhe gases to be compressed are very often chemically active or process conditions require the use of alkaline orperating liquids. Liquid ring pumps are robust machines whose moving and fixed internal parts are not subjecailure. It is practical to use all materials in the construction of these pumps which are usual in machine buildinrocess technology. Liquid ring machines may be constructed using such materials as gray cast iron, spheroidaon, cast steel, chemically resistant chrome nickel steels, high nickel alloys, titanium bronze polypropylene, polastics, Noryl (polyphenylen oxide), Ryton (PPS), ceramics, and stoneware. Combinations of different materia

lso be used. Parts for these pumps may also be coated with hard rubber, plastics, enamel, or special lacquer to gainst corrosion and erosion.

.2.9ealing

n liquid ring vacuum pumps, one differentiates between static and dynamic sealing. Fluid seals based onolyvinylacetate, polyisobutylene, and epoxyresin are used as static seals for the housings. Nitrile rubber, fluorlastomers, polytetrafluorethylene, ethylenepropylene rubber and chloroprene rubber are used for O rings and faskets. Where dynamic sealing is required, such as for shafts, conventional seal elements such as stuffing boxngle- or double-acting mechanical seals are used. Stuffing boxes with double packing and lantern rings are usacuum technology the demand exists that there be zero leakage when machinery is operating and when it is stiquid ring machines in hermetic construction are presented as an alternative to vacuum pumps of the usual deynamic seals.

here exist two alternative types of hermetic machines: those using a drive with permanent magnet coupling anwith canned motors (Fig. 3.3). In choosing a drive system, the transfer of torque and the requirement for shaft sxist concurrently. The hermetically encapsulated construction is recommended in cases where an absolutely lend maintenance free operation is demanded. With machines of this type, a zero rate of leakage is achieved.

.2.10Drives

wo-, four-, or six-pole low-voltage asynchronous squirrel-cage motors are usually used as drives. For larger maving drive requirements above about 150 kW, high-voltage squirrel-cage motors are used. For large pumps o

t low speeds,





ear reducers of V-belt reducers may be placed between motor and pump, thus allowing for speed and adjustmhat specific operating conditions may be optimally met. Especially for large machines it is useful to place aydrodynamic coupling between the motor and pump in order to take care of starting resistance and frequency n start-up of induction motors.

Hermetic drive systems may be used as alternatives to conventional drives. The torque is transferred through eiermanent magnets or electromagnets. The complete leak tightness of these pumps is especially necessary whearcinogenic, or radioactive gases or vapors are handled and where no leakage of the operating liquid can be toiquid ring vacuum pumps with hermetic drive systems are presently in use in the process industries; these pum

maximum capacities of about 3000 m3/h and can be provided in special construction for higher capacities.

With canned motors, the noise emissions of a pump may be reduced by an average of 810 dB(A).

.2.11Accessories

A heat exchanger and liquid separator are needed for the operation of a liquid ring vacuum pump with closed cFig. 3.7). Dependent upon the operating conditions, various other accessories such as gas ejector, check valvemission cooler, control and surveillance instrumentation, and so on, may be required.





rt IIIy Vacuum Pumps

gel T. M. Dennis

y Vacuum Pumps

3.1oots Pump

oots Pump (mechanical booster) plus oil-sealed rotary forepump

apacities available: 75 to 30,000 m3/hperating pressure range: 10 to 103 mbar total pressure, inlet pressure is sensitive to fore pressure

ultistage Roots Pump

apacities available: 25 to 1000 m3/hperating pressure range: (4-stage) 1000 to 5 × 102 mbar total pressure

(5-stage) 1000 to 2 × 102 mbar total pressure(6-stage) 1000 to 103 mbar total pressure

typical Roots pump is illustrated in Fig. 3.8. It consists of two figure-of-eight-shaped rotors, although for higher pressure duty three-le sometimes used. These rotors are synchronized by external gears and rotate in opposite direction within the stator. The gears and rotarings are oil-lubricated; but they are external to the pumping chamber, so the swept volume of the pump is dry. A small clearance, gtween 0.05 and 0.25 mm, is maintained between the rotors and between each rotor and the stator wall. As the rotors run dry, back leacurs through these clearances at a rate dependent on the pressure difference across the pump and






Fig. 3.8Cross section through a Roots (mechanical booster)

pump and its operating cycle.

he gas being pumped. The pressure ratio generally achieved by this mechanism is shown in Fig. 3.11, indicatinompression at low pressures and a low compression at high pressure.

A mechanical booster is basically a Roots pump modified for high-vacuum applications. This generally involvemproved leak tightness, different stator/rotary seals, and the connection of the gear box to the outlet of the pumame pressure exists in the gear box as in the foreline.

As indicated in Fig. 3.11, the ultimate pressure achieved by a mechanical booster is very dependent on the ultimhe fore pump [13], and where a liquid ring pump [14] is used it is usually necessary to use two mechanical booeries to obtain pressure below 1 mbar.

Rotational speeds vary between 500 and 3440 rev/min and depend on the size of pump; the upper limit is depehe supply frequency.

orepump speed is normally between one-fourth and one-tenth the displacement of the mechanical booster so arelatively small pressure differential across the pump.






Fig. 3.9Speed curve and power consumption of a 100-m3 · h1multistage Roots pump at 50 Hz. The ultimate vacuum

improves when the pump is run at 60 Hz, and thespeed curve increases by about 20%. The speed

and power curves are without gas purge.

an flow back into the pump because there is no exhaust valve; it then undergoes further compression and heathis normally only becomes a problem when the inlet pressure is held between 2 and 40 mbar for long periods

arger-size pumps, an after cooler consisting of a water-cooled finned tube is inserted in the outlet as close as phe rotor. Because the forepump is generally much smaller, start-up of the mechanical booster is normally at ab

mbar, but with the use of a spring/gravity loaded bypass valve or a fluid coupling [16] it is possible to start themechanical booster at atmospheric pressure. In the case of a fluid coupling which varies the rotational speed ofotors, assistance is given during the roughing cycle and no overheating occurs when pumping a large volume tmospheric pressure.

ystem contamination is still possible from either the forepump or the gear box oil which is pumped via the oumechanical booster [17]. This latter source of contamination is often overlooked. If an oil-free forepump is used

mechanical booster, then to largely eliminate system contamination the gear box should be pumped separatel

he mechanical booster with a forepump provides a group capable of high pumping speed in the range 5 to 102n conjunction with a water ring pump it can handle fine powders, although coarse powders can cause wear.

Multistage roots pumps normally have three, four, or five stages of Roots mechanisms in series and are driven ame shaft. In the case of three-stage pumps it is normal to back them with a further three-stage pump, thereby x in total.

Rotational speed is normally that of a two-pole electric motorthat is, 2850 rev/min (50 Hz) or 3440 rev/min (60

tage ratios are important to ensure efficient running at the normal inlet pressures. The inlet stage is the largestutlet stage the smallest. A typical speed curve for a five-stage pump is shown in Fig. 3.9 with the typical poweequirements. The power starts low and then reaches a level which remains constant as the pressure drops.





Overheating is a potential problem in the high-pressure stages when the pump is working at low pressure, and feason the higher pressure stages are frequently fitted with water-cooled heat exchanges in their outlet port. Gar purging is often used on a number of the stages to ensure that vapors being pumped do not condense. Frequehere are gas purges at the shaft seals to keep them clean so as to improve their reliability.

ystem contamination is minimal because the gear box, which is at atmospheric pressure, is adjacent to the outump, or in the case of six-stage pumps it is at least three stages from the pump inlet. The bearings at the inlet he pump are normally the only source of contamination and are generally packed with a very-low-pressureerfluoropolyether grease.

Dry pumping group controls often include thermocouples placed at critical points, outlet pressure and motor cumonitor, water flow switch, and so on. Frequently all these functions are monitored via a computer-compatibleontroller so that a large number of units may be run on one in-house computer.

Dry pump outlet management [18] is an important factor in systems where aggressive toxic or explosive gases umped. The use of water scrubbers on their own is not generally advisable because water vapor and water canump and, by combining with the pumped gases, can cause extensive damage. With the many gases used in themiconductor industry [e.g., halogen compounds (i.e., fluorine, chlorine, and bromine)], it is now becoming m

ommon to react and inert the pumped gases by the use of a number of different technologies, some of which aelow:

urning/Oxidation : This needs to be combined with an absorber or wet scrubber to remove the by-products. It sot be used for chlorinated materials due to risk of the formation of toxic by-products (e.g., dioxins).

dsorption/Chemisorption : Possible explosive risk from adsorbed gases and hazardous waste disposal issues.

ot Bed Reactors : Gases are passed into a heated granular bed, forming solid by-products, or are catalytically cy the bed into other gases or solids. By-products are nonhazardous or totally recyclable.

pplication : Pumping of highly chemically active gases and the handling of fine dustthat is, semiconductor manlus where system contamination is a concern.

.3.2law Pump

Multistage Claw

apacities Available: 25 to 500 m3/h (also including pumps with inlet Roots stage increasing to 1200 m3/h whwith a mechanical booster)

Operating Pressure Range: 1000 to 104 mbar

With Additional Mechanical Booster: 1000 to 7 × 104 mbar

A typical claw mechanism is illustrated in Fig. 3.10. It consists of two claw-shaped rotors. These are synchronixternal gears and rotate in opposite directions





Fig. 3.10

The claw mechanism and its operating cycle.within the stator. The gears and rotor bearings are oil-lubricated but are external to the pumping chamber, so tholume is dry. The clearance between the rotors and the stator wall is normally 0.1 to 0.2 mm. As the rotors runack leakage occurs through these clearances. The shape of the rotors and of the inlet and outlet ports is designs a valve, thereby almost eliminating back flow. This results in a much higher compression ratio at high pressuan be achieved with a Roots pump mechanism as indicated in Fig. 3.11. A further advantage is that the heat geetween stages and at the outlet is much smaller than with the Roots-type mechanism, and interstage cooling oigher pressure stages is not required. The power consumption is also lower when the pump is operating at lowressures.



Multistage claw pumps [19, 20] normally have three or four claw stages, although in some cases the inlet stageRoots design. The advantage of using a Roots





Fig. 3.11Attainable pressure ratio (for air) with a single claw and a single Roots

mechanism as a function of outlet pressure with no gas throughput.

let stage is that the inlet to a claw pump is more restrictive at low pressure than a Roots stage, so the use of the latterlet stage improves the speed of the pump at low pressures where the compression ratio of the Roots stage is somewhan that of a claw-type stage.

otational speed is normally that of a two-pole motorthat is, 2850 (50 Hz) or 3440 (60 Hz).

typical speed curve of a multistage claw pump is shown in Fig. 3.12, along with a curve of its power consumption.

s with most other dry pumps, system contamination is minimal because the drive gears and oil box are at the atmospf the pump [21].

or gas ballast, system contamination, pumping group controls, pump outlet management, and applications, see previoection.

3.3crew Pump

Capacities Available: 24 to 2700 m3/hOperating Pressure Range: 1000 to 5 × 103 mbar

he mechanism of a screw pump consists of two intermeshing screw rotors enclosed in a close-fitting stator. There is mall clearance between the screw form of the two rotors, the rotors, and the stator wall; the stator has specially shapee inlet and outlet. The rotors are normally coated to improve resistance to chemical attack and also to reduce the cleithin the pumps to a minimum.

wo forms of screw are currently used; one type is of a rectangular form (see Fig. 3.13) and runs at about 10,000 rev/me other type is illustrated in Fig. 3.14 and runs at two-pole motor speed. Figure 3.15 shows a trapped volume of gas aansfer from the inlet to the outlet which is at atmospheric pressure. A typical speed curve is shown in Fig. 3.16 whichdicates the power requirements.





Fig. 3.12Speed curve and power consumption of a four-stage

claw pump at 50 Hz. The ultimate vacuum improves whenthe pump is run at 60 Hz and speed curve increases

by about 20%. The speed and powercurves are without gas purge.

Fig. 3.13Screw pump with a square thread form.

his type of pump is particularly suitable for applications where slugs of liquid from the process vessel are likeeach the pump.



or gas ballast (or purging), system contamination, pumping group controls, pump outlet management, and appee Section 3.3.1 on the Roots pump.





Fig. 3.14Alternative screw profile which is normally run at two-pole motor speed.



Fig. 3.15Transport of gas by the square thread mechanism.





Fig. 3.16Speed curve and power consumption of a typical pump using ascrew form similar to that in Fig. 3.13 and without gas purge.

Obtainable pressure of pump type with the different screw form(Fig. 3.14) and using two pole motor is about one decade higher.

3.4croll Pump

Capacities Available: 20 to 50 m3/h

Operating Pressure Range: 1000 to 102 mbar

he two main components of this type of pump is a stationary scroll and an identical moving scroll. The moving scmounted on a spigot, or spigots, so that the rotation of the shaft produces an orbital motion of this member. The mocroll is constrained from rotating by an arrangement which ensures that it maintains the same angular position durrbiting motion. Such an arrangement is shown in Fig. 3.17, which indicates how gas is taken in at the inlet and trao the outlet. The main problem in achieving a good vacuum is leakage across the edge of the moving scroll and thationary scroll. A spring-loaded gasket is normally fitted to ensure good sealing along the moving scroll to overcroblem [22]. However, this gasket can lead to the formation of a small amount of dust. So it is important to ensurnot at any stage blown back into the system.

typical speed curve and power consumption of a pump is shown in Fig. 3.18.

his pump is generally not suitable for severe or chemically active gas pumping applications but gives almost noontamination when pumping clean systems or if it is used as a forepump (e.g., with a turbomolecular pump).

special version of the pump has been used for many years, mainly in the nuclear industry. In this version the conhe motion is made completely external to the system by the use of metal bellows. This ensures that there are no oromponents in the system that could be contaminated by the radioactive materials being pumped. Pumps of this tyvailable in capacities ranging from 15 to 600 m3/h and with ultimate vacuum of 5 × 102 to 103 mbar.





Fig. 3.17Transport of gas in a scroll mechanism.



Fig. 3.18Speed curve and power consumption of a 30-m3 · h1

scroll pump without gas purge.





.3.5iston and Diaphragm Pumps

Multistage Piston PumpsCapacities Available: 12 m3/hOperating Pressure Range: 1000 to 3 × 102 mbar

Fig. 3.19Three-stage piston pump.

Two-Stage Diaphragm PumpsCapacities Available: 0.8 to 5 m3/hOperating Pressure Range: 1000 to 2 × 102 mbar



Fig. 3.20Speed curve of a two-stage diaphragm pump.





hese two types of pump are basically of similar design. In the case of the diaphragm pump the diaphragm is ueal the piston while the piston in the piston pump either is a close fit in the piston housing or uses piston ringsesults in the diaphragm design being more applicable to small capacities while the normal piston is used for thzes.

n vacuum applications the piston sealing is often obtained by a long path with a close clearance. The inlet valvot in the cylinder wall opened by the piston and the outlet valve is pushed open by the piston [23]. A three-sta

24] is shown in Fig. 3.19. Three or four stages are used to achieve a vacuum of less than 0.1 mbar.

he diaphragm pump used in vacuum is normally a two-stage pump. The inlet and outlet valve are opened andy the diaphragm. The use of a molded diaphragm with strengthening ribs has greatly improved the reliability omponent.

Gas ballast, pumping group controls, and pump outlet arrangements are not normally required. The main appliche piston pump is for use on reasonably clean systems or as a forepump for a turbo pump. The diaphragm pumecoming more widely used, outside its normal laboratory application, as a forepump for a turbomolecular dra

A typical speed curve for a two-stage pump is shown in Fig. 3.20.

References

. F. A. Flecken, Gaede's influence on the development of mechanical vacuum pumps.Vacuum 13, 583 (1963).

. W. Gaede, Gas Ballast Pumpen. Z. Naturforsch A . 2A, 233 (1947).

. B. D. Power and R. A. Kenna, Vapour pumping characteristics of gas ballast pumps.Vacuum 5, 35 (1955).

. L. Laurenson, Technology and application of pumping fluids. J. Vac. Sci. Technol . 20(4), 989 (1982).

. L. Laurenson and G. Caporiccio, PerfluoropolyethersUniversal vacuum fluid. Proc. Int. Vac. Congr., 7th , 1977, V, p. 263 (1977).. N. S. Harris and L. Budgen, Design and manufacture of modern mechanical vacuum pumps.Vacuum 26(12), 5251976).

. D. Balfour, L. Budgen, P. Connock and D. Phillips, Pumping systems for corrosive and dirty duties.Vacuum 34, 71984).

. U. Segebrecht, Liquid Ring Vacuum Pumps and Liquid Ring Compressors , 1st ed. Expert-Verlag, Renningen-Malmsheim, 1994.

. H. Bannwarth, Liquid Ring Vacuum Pumps, Compressors and Installations , 2nd ed. VCH-Verlagsges., Weinheim

0. H. E. Adams,Thermodynamic Characteristics of Nash Compressors . Nash Engineering Company, South NorwT, 1953.

1. M. Wutz, H. Adam and W. Walcher,Theory and Practice of Vacuum Technology . Vieweg Verlagsges.,raunschweig, 1989.

2. J. L. Ryans and D. L. Roper, Process Vacuum System Design and Operation . McGraw-Hill, New York, 1986.

3. M. Bussard, La Technologie des pompes à vide système roots. Le Vide 12, 425 (1957).







4. W. Armbatruster and A. Lorenz, Die Kombination Roots PumpeWasserring Pumpe.Vak. Tech . 7(2), 85 (1958).

5. C. M. Van Atta, Theory and performance characteristics of a positive displacement rotary compressor as amechanical booster pump.Trans. Natl. Symp. Vac . 3, 62 (1957).

6. H. Wycliffe and A. Salmon, The application of hydrokentic drives to high vacuum mechanical boosters (Roumps).Vacuum 21, 223 (1971).

7. N. T. M. Dennis, L. J. Budgen and L. Laurenson, Mechanical boosters on clean and corrosive applications. J. Vacci. Technol . 18, 1030 (1981).

8. P. Mawle, Exhaust management. Eur. Semicond . May, p. 17 (1995).

9. H. Wycliffe, U.S. Pat. 4,504,201 (1985).

0. H. Wycliffe, Mechanical high vacuum pumps with an oil-free swept volume. J. Vac. Sci. Technol. A 5, 2608 (19

1. W. Wong, L. Laurenson, R. G. Livesey and A. P. Troup, An evaluation of the composition of the residualtmosphere above a commercial dry pump. J. Vac. Sci. Technol. A 6, 1183 (1988).2. D. Arthur, Little Inc., U.S. Pat. 1,507,254 (1976).

3. M. H. Hablanian, E. Bez and J. L. Farrant, Elimination of backstreaming from mechanical vacuum pumps. J. Vacci. Technol. A 5(4), 2612 (1987).

4. E. Bez, A compact oil-free rough vacuum pump.Solid State Technol ., February (1995).

General References

. Cummings, Liquid ring vacuum pumps optimise power generation.World pumps , January pp. 1415 (1987).

Duval, Will tomorrow's high vacuum pumps be universal or highly specialized. J. Vac. Sci. Technol. A 5(4), 25481987).

R. G. P. Kusay, Vacuum equipment for chemical processes. Br. Chem. Eng . 16, 29 (1971).

F. Lennon, Vacuum process in drying of power transformer insulation. J. Vac. Sci. Technol ., 19, April (1982); Proatl. Symp. of Am. Vac. Soc ., Pt. 2, p. 1039 (1981).

A. O'Neill, Industrial Compressors: Theory & Equipment . Butterworth-Heinemann, London, 1993.

. D. Power, High Vacuum Pumping Equipment . Chapman & Hall, London, 1966.

W. F. Ravette, Paper machine vacuum systems.TAPPI Wet End Oper., Semin. Notes , Seattle, WA, 1980, p. 97, TAress, Atlanta, GA, 1980.

G. F. Smith, Machine vacuum systemhow to get the most out of this versatile papermaker's tool.TAPPI Eng. Conf.,ap ., Houston, TX.,1976 , Book 1, p. 243, TAPPI Press, Atlanta, GA, 1976.

A. P. Troup and N. T. M. Dennis, Six years of dry pumpinga review of experiences and issues. J. Vac. Sci. Technol. A3), 20482052 (1991).

M. Wutz, H. Adam and W. Walcher,Theory & Practice of Vacuum Technology . Vieweg Verlagsges., Braunschwe989.






Kinetic Vacuum Pumps

A kinetic vacuum pump is a pump that imparts momentum to the gas being pumped in such a way that the gas ansferredcontinuously from the inlet of the pump to the outlet. This distinguishes it from the positive displacemacuum pumps described in Chapter 3 in which a volume filled with the gas being pumped is cyclically isolatehe pump inlet and then transferred to the outlet. In the capture vacuum pumps described in Chapter 5 the gas meing pumped are trapped on internal surfaces within the pump by sorption or condensation.

n the kinetic vacuum, pump momentum may be transferred to the gas being pumped in the direction of the pumy mechanical moving parts or by entrainment in a high-speed vapor stream. Both types of pumps are describehapter.






art IDiffusion and Diffusion-Ejector Pumps

enjamin B. Dayton

When a liquid such as water, mercury, or petroleum fluid is vaporized in a boiler and the vapor is conducted thiverging nozzle exiting into an evacuated chamber, the vapor expands through the nozzle and continues to expeyond the nozzle exit, acquiring a high forward mass velocity as the random molecular motion is converted inirected stream of molecules known as a vapor jet. If some gas is present in the chamber, the expansion beyondozzle exit is limited to a certain extent and a boundary region is formed where gas mixes with the vapor streamoundary region may take the form of a turbulent layer of mixed gas and vapor when the pressure is high enouower pressures it may be a diffuse layer of vapor mixed with penetrating gas molecules moving in laminar flowither case the entrained gas is moved forward in the direction of the vapor jet; and if some means can be foundeparate the gas and vapor without allowing the gas to find its way back into the region near the nozzle, then a ction has occurred.

One means of separating the entrained gas from the vapor stream is to design the pump housing or chamber wahe cross section narrows gradually to a throat in front of the vapor jet and then expands rapidly beyond this thrstructure is called a Venturi tube or ''diffuser," although no gas diffusion is necessarily involved. If the cross-srea of the throat of the diffuser is about equal to the exit area of the nozzle and the gas pressure beyond the dif

he region known as the "fore-vacuum" is not too high, the vapor stream will converge and accelerate through tiffuser throat at such a density and mass velocity that gas molecules cannot






eadily penetrate back through the diffuser throat. The vapor expanding beyond the throat is cooled and condenhereby releasing the entrained gas which must then be discharged into another (backing) pump or into the atmhis is the principle of action of vapor-jet ejector pumps. While multistage steam-jet ejector pumping systems [een used in the past to produce pressure as low as 7 Pa while discharging the gas directly into the atmosphereeldom used today because of the availability of mechanical booster or blower pumps of various sizes.

Another method of separating the entrained gas from the vapor stream which can be employed when the gas prhe fore-vacuum is sufficiently low and the vapor is readily condensable, as in the case of mercury or oil vapor,ool the pump housing walls in the region where the main vapor stream encounters the wall. The cross section ump at this point does not necessarily have to be about equal to the nozzle exit area since at low pressures thexpands freely and fills the pump cross section at the level where condensation occurs. Since the vapor must mertain distance along the pump axis before it is entirely condensed, a vapor barrier is formed by forward-movi

molecules through which only a few gas molecules can diffuse back from the fore-vacuum. This back diffusionlways negligible and may limit the performance of the pump when the gas molecules have a low molecular wollision cross section, as for hydrogen and helium. Vapor pumps employing a cooled casing and low-vapor-pre

working fluids are termed "diffusion" or "condensation" pumps. They require backing pumps or ''forepumps" the necessary fore-vacuum and can only operate when the gas pressure in the chamber to be pumped has alreadeduced to less than about 70 Pa.

jector pumps will not be considered here, but some hybrid pumps are still in use which combine oilvapor ejecages with diffusion pumping stages. The latter are known as "diffusion-ejector" or "vapor booster" pumps andescribed briefly in Section 4.2.

1iffusion Pumps

.1.1History of Development

he invention of the diffusion pump arose out of studies made by W. Gaede [2] in Germany in 1913 on the couf mercury vapor and air in a vacuum system pumped by his rotary mercury-sealed mechanical pump with a coondense mercury vapor. During this study to determine the lowest partial pressure of gas that could be produceyond the trap, he discovered the effect of the counterdiffusion of air and mercury vapor on the reading of a Mauge and conceived of the pumping effect which might be obtained by allowing gas to diffuse through a narronto a rapidly moving stream of mercury vapor. Figure 4.1 shows his first embodiment of this concept. Note thaegion is surrounded by a water-cooling jacket to condense mercury vapor escaping through the slit.

n 1916 Irving Langmuir [3] showed that the slit or diffusion diaphragm through which the gas was pumped in Gaede pump [4] could be widened if the mercury vapor was directed away from the slit by a suitable nozzle as

ig. 4.2. He emphasized the importance of adequate condensation of the mercury vapor and referred to his pumondensation pumps. The pumping speed was thereby greatly increased, and Langmuir was granted U.S. Paten,393,550 in 1921.







Fig. 4.1Gaede's slit-jet mercury vapor pump. a, returntube; b, steel cylinder with slit e; c, condenser;

d, mercury-filled gutter; f, gas inlet; f1, connectionto roughing pump; g, connection to fore-pump;

h, thermometer; V, mercury cut-off valve; Q, boiler.

n 1916 Langmuir also applied for a patent on the inverted or "mushroom cap" nozzle design which was issueds U.S. Patent 1,320,874 as shown in Fig. 4.3.

he detailed history of the development of mercury diffusion pumps is given in earlier editions and will not be ere. Mercury vapor pumps became widely





Fig. 4.2Langmuir's mercury condensation pump with cylindrical nozzle.

sed in the electronic tube industry in the United States from 1920 to 1940, but they required the use of refrigeaps to keep the vapor out of the tubes (except for mercury rectifier tubes). In 1928 in connection with experimhe vacuum impregnation of pressboard with transformer oils to improve the dielectric strength of insulators, Curch [5] at Metropolitan-Vickers in England became interested in high-vacuum distillation at moderate tempenown as "molecular distillation." He succeeded in obtaining some very-low-vapor-pressure fractions from theetroleum oil used in rotary mechanical pumps. It then occurred to him to try these oil fractions as the pump fliffusion pump in place of mercury. He was able to obtain a pressure reading on an ionization gauge of 104 Pacold trap and thus began a revolution in the application of diffusion pumps (British patent, 303,078).

After visiting England, Dr. Kenneth Mees, Research Director of the Eastman Kodak Laboratories, brought the wurch to the attention of Dr. K. C. D. Hickman, who had been working with low-vapor-pressure synthetic orga

n place of mercury in special manometers for measuring the pressure in apparatus for







Fig. 4.3Langmuir's metal condensation pump

with umbrella nozzle.

he drying of photographic film where mercury vapor was harmful. In 1929 Dr. Hickman found that these esterood results when used as the pump fluid in small glass diffusion pumps of simplified design which he construimself [6]. He applied for a patent on the use of butyl phthalate, and similar esters, in place of mercury in thesU.S. patent 1,857,506 issued in 1932). Many articles were published in the period from 1932 to 1940 on the cof mercury vapor pumps to oil diffusion pumps and the use of baffles and charcoal traps to reduce oil vaporontamination.

During the period from 1929 to 1937 the factors involved in designing diffusion pumps for use with the new syils were studied by Dr. Hickman and his co-workers in the Research Laboratories of the Eastman Kodak Comesulting in the development of multiboiler "self-fractionating" oil diffusion pumps [7] which extended the lowressure attainable without cold traps from 103 Pa to about 5 × 106 Pa. Figure 4.4 shows a water-cooled three-actionating pump constructed of Pyrex glass with coiled nichrome heater wire in each of the boilers which in overed with glass-wool-lined insulation bags. The total length is 25 in. Two alembic heads, or catchment loberovided in the tubing leading to the forepump connection for the purpose of retaining the most volatile fluids om the boiler.







Fig. 4.4Hickman's three-stage glass oil fractionating diffusion pump.



Fig. 4.5Vertical multistage oil fractionating

pump design of Malter and Markuvitz [8].





n 1937 L. Malter [8] of the Radio Corporation of America applied for a patent on an all-metal vertical multistaiffusion pump, as shown in Fig. 4.5, which incorporated the Hickman self-fractionating principle by having seoiler compartments feeding vapor through concentric cylindrical tubes to the various nozzles with small openetween compartments at the bottom of the cylinders so that returning condensed oil first enters the outer compeeding vapor to the lowest stage where the more volatile components are removed and the purged oil then enteext compartment, where more of the volatile constituents are removed, and finally passes to the innermostompartment feeding vapor to the nozzle nearest the pump inlet, so that the oil condensed on the walls near thiage has a lower vapor pressure than the original unpurified oil mixture. An alembic head is also shown in the

o catch the more volatile components of the pump fluid.

Much of the history of diffusion pumps involves investigation of various synthetic oils for use as diffusion pumnd attempts to minimize the backstreaming of the vapor of these oils from the first stage into the vacuum cham

.1.2Diffusion Pump Design

he first practical diffusion pumps were single-stage with a boiler at the bottom and a vapor conduit leading to ylindrical or expanding conical nozzle, or an inverted (umbrella-type) nozzle to form a high-speed vapor jet. I

umps the vapor jet was directed vertically upward into a condensing region with an alembic at the bottom to cistilled mercury or oil and return the fluid to the boiler. Later designs employed nozzles which directed the jetownward, or vertically downward, so that the condensed pump fluid ran down the pump wall and returned to hrough a connecting tube or through a narrow passage between the pump wall and a skirt on the vapor conduithe head of oil prevented the escape of vapor from inside the conduit. Single-stage pumps with parallel multipl

were tried and gave improved speed and required less power input, but multiple nozzle designs are not practicamultistage pumps.

Multiple in-line stages were introduced when it was realized that the compression ratio between forepressure anmaximum inlet pressure before jet breakdown had to be limited for each stage of an oil diffusion pump becauseecomposition of organic pump fluids at elevated temperatures and pressures. Since the pumping speed of any epends on the nozzle clearance area (the annular gap between the rim of the nozzle exit and the wall of the puousing) while the forepressure at which the jet breaks down depends on the boiler pressure (or temperature) aatio of the nozzle throat area (narrowest cross section) to the "body clearance area" (the annular gap between tf the pump housing and the vapor conduit leading from the boiler to the nozzle), by arranging a series of nozzcommon axis with stepped increases in the nozzle clearance area and body clearance area from the stage nearrimary pump to the stage nearest the vessel to be pumped, the overall speed of the pump could be maximized ill maintaining operation against relatively high forepressures as produced by the primary pump without requxcessively high boiler temperature.

he design of the first stage (nearest the pump inlet) was particularly important since some vapor from this stagcatters backward into the high vacuum and influences the speed and ultimate pressure obtainable. In 1937, Em0] applied





Fig. 4.6Design of Embree jet (b) compared with straight-sided jet (a) [10].

or a patent on a streamlined inverted nozzle design (as shown in Fig. 4.6b) which greatly improved the pumpiver prior designs of the type shown in Fig. 4.6a.

ince for multistage pumps the speed depends on the nozzle clearance area of the first stage (nearest the inlet), method of increasing the speed without changing the size of the flange connection to the vacuum chamber or thength is to widen the pump housing in the neighborhood of the first- and second-stage nozzles (as shown in Fipump designed by Hablanian and Maliakal [11]. Also shown in Fig. 4.7 is a cowl or cap, cooled by conductio

hrough the supports mounted on the water-cooled pump casing, placed over the first-stage umbrella nozzle wherves to intercept and condense vapor scattered backwards from the outer edge of the jet or evaporating from the hot umbrella nozzle. This "cold cap," which may also be cooled directly by a loop of water-cooled copper tnvented by Power [12] of the Edwards High Vacuum Ltd., greatly reduces the back-streaming of pump fluid inigh-vacuum region.

A similar design, including a built-in butterfly valve at the inlet, is shown in Fig. 4.8. Both Figs. 4.7 and 4.8 shoiler filler and drain pipe at the side of the boiler and last-stage nozzle directing the vapor jet into a water coorm in the form of an ejector diffuser. Water cooling of metal pumps is preferably through copper tubing wrappround the casing and brazed to the wall since double-wall cooling jackets as shown in Fig. 4.5 are less efficienubject to corrosion. Coiled tubing may also be





Fig. 4.7Metal multistage pump with enlarged nozzle clearancearea and cold cap [Varian Vacuum Products].

laced around the boiler region through which water can be circulated during the cool-down of a pump on a sywithout a high-vacuum valve.

roper design of the pump boiler region involves several details, such as (1) the size and spacing of boilerompartments for fractionating pumps, (2) having a "skirt" at the lower end of the outer vapor conduit close to

wall and of sufficient height to maintain a head of pump fluid (from the condensed fluid returning down the waalance the vapor pressure inside the boiler, and (3) the method of conducting heat from the electric heating unil in the boiler in such a manner that superheating and "bumping" is reduced.

2iffusion-Ejector Pumps

efore the development of efficient mechanical booster (rotary blower) pumps with adequate pumping speed d0 Pa, there was a problem in providing an adequate fore-vacuum for the diffusion pumps used on large molec

K. C. D. Hickman decided to develop a booster pump for the 5-Pa to 200-Pa pumping range based on the desigeam ejectors but using a stable hydrocarbon oil at high boiler pressures instead of steam. This resulted in theroduction of an oilvapor ejector or 'kerosene booster" pump which was then used on the molecular stills and i





Fig. 4.8Cross section of three-stage oil-vapor diffusion pump

with integral water cooled baffle and high-vacuumvalve [Edwards High Vacuum International].



rying of frozen foods and blood plasma. Hickman was unable to obtain a patent on the basic idea of an oil-ejeecause of a prior invention by W. K. Lewis of an oil-ejector pump for the petroleum industry. However, U.S. p,279,436 was issued to K. C. D. Hickman and G. Kuipers for an improved oil-ejector design, and a series of sage and multistage oil-ejector pumps was developed and applied to use in the vacuum metallurgy industry. Thevelopment of mechanical boosters (of the RootsConnersville blower type with rotating lobes) eventually obveed for these oil-ejector pumps. However, hybrid ejector-diffusion pumps with the high-pressure stage in the fn oil-ejector were developed in the United States and in England and found use in various industrial applicatiohe gas load involved relatively high pressures in the fore-vacuum produced by mechanical pumps.





Fig. 4.9Diffusion-ejector pump [Edwards

High Vacuum International].

igure 4.9 is a diagram of such a diffusion-ejector pump [13] with a 38.7-cm-i.d. inlet which can operate againa backing pressure and which has a maximum pumping speed of 4000 liter·s1 at inlet pressures up to 1 Pa usi

Apiezon A201 booster pump fluid and 6.0-kW heater input. The boiler pressure can be as high as 4000 Pa.

heoretical and experimental studies of the ejector stages of vapor pumps were performed by Jaeckel, Nöller, aKutscher [14], by Kutscher [15], and by Bulgakova et al. [16].

3erformance of Vapor-Jet Pumps

.3.1umping Speed

he rate at which gas flows across the inlet of a vapor-jet pump can be expressed in at least four ways: (1) the nf molecules crossing the inlet in unit time, (2) the mass of gas in grams per unit time flowing across the inlet, olume of gas in volumetric units (liters, m3, cubic feet, etc.) flowing through the inlet in unit time at the prevaressure and temperature at the inlet, and (4) the throughput (usually







Fig. 4.10Typical speedpressure curve of diffusion pump

as measured with a total pressure gauge.

epresented by the letterQ) of gas across the inlet area in pressurevolume units per unit time at the prevailing gaemperature. Historically, the precedent set by W. Gaede was to express pump performance in terms of the voluow rate or ''pumping speed" (usually represented by the letterS ). The flow rates (1) and (2) are almost impossibl

measure directly. Flow rates (3) and (4) can easily be measured by procedures given in the next section, but difrise in the method of measuring the pressure (represented in the following by the letter p) depending on the type oacuum gauge used, the location and orientation of the gauge tubulation relative to the pump inlet, and the metonnecting the pump to the test system. In any case, the speed at the cross section where the pressure is measurefined by

or a given gas at the specified temperature.

he equation of continuity for gas flow through the diffusion pump into the forepump is

whereC is the "capacity" or volumetric speed of the forepump at the prevailing forepressure F .

Measurements of the speed of diffusion pumps using the test dome recommended by the American Vacuum So17] (or by the equivalent ISO standard), along with a total pressure gauge, show that the speed varies with the ressure as shown in Fig. 4.10. The speedpressure curve can be divided into three regions or zones of pressureeclining speed in the "jet breakdown region," or forepressure breakdown region , from the breakdown value of the

ntake pressure, pb , (corresponding to a forepressure F equal to the limiting forepressure, or breakdown forepressb ), to the crossover pressure, pc , where the inlet pressure equals the forepressure Fc , (2) the region of nearly constantmaximum speed, Sm , from pb to pd , the lower limit of pressure at which the speed is nearSm, and (3) the decliningpeed in theultimate pressure region from pd to the ultimate pressure, pu , at which the speedS becomes zero due toack migration of pump fluid vapor and fragments of decomposed pump fluid, and back-diffusion of gas in theacuum through the vapor jets.





When the forepressure is maintained at a sufficiently low value to eliminate appreciable back-diffusion of gas forevacuum and the outgassing of the measuring dome is negligible, the ultimate pressure, pu , is determined mainlyhe vapor pressure of the pump fluid on the walls near the pump inlet or on a cooled baffle or trap between the nd the test dome. In the region from pb to pu the pump speed is given approximately by

with apparent deviations from this formula during measurement being due to the varying response of the pressuusually a tubulated ionization gauge) to the changing mixture of air and pump fluid vapor and the change in thutgassing rate of the ion gauge itself.

n the region from pc to pb , when no gas is leaked into the fore-vacuum while the intake pressure p is increased bydmitting gas to the test dome, the pump speed is given approximately by

whereC is the volumetric speed of the forepump at the prevailing forepressure and can be assumed to be nearlyonstant over the forepressures prevailing during jet breakdown.

.3.2imiting Forepressure for Maximum Speed

he limiting forepressure for maximum speed depends on the amount of gas admitted through the pump inlet apeed of the forepump. It is convenient to distinguish between (a) static breakdown , which occurs when the forepreas been raised by throttling the forepump at a given gas load or by admitting gas to the fore-vacuum until the ressure (high vacuum) has risen by about 2 × 102 Pa, and (b)dynamic breakdown , which occurs when gas is admnly through the pump inlet until the forepressure maintained by a given forepump has risen to the limiting val Fb

marked by a noticeable decrease in the pump speed (knee of the pump speed curve).

When the forepressure, F , is increased by opening an adjustable leak in the fore-vacuum while the high-vacuumressure, p, is held constant by adjusting the rate of air admitted through a leak into the test dome, the variations a function of forepressure for a fixed value of p can be obtained and plotted for different heater inputs. For a gieater input the speed remains constant until the forepressure reaches the limiting value and then decreases rap

maximum speed varies with heater input because of the vapor-backstreaming factorα and the fore-vacuum gas baciffusion factorβ as explained in Section 4.4.

When the heater input is constant and the throughput is also maintained constant by controlling the leak into thome and reading the intake pressure, p, while the forepressure, F , is slowly raised by admitting gas into the fore-acuum, a curve of inlet pressure versus forepressure at constant throughput is obtained. Two extreme values





Fig. 4.11High vacuum versus forepressure with constant

throughput and constant heater input.

f throughput are of special interest: the no-load value, orQ = 0, and the maximum load value,Q = Qm. Figure 4.11

hows such curves for a two-stage pump.or a single-stage oil-vapor diffusion pump, as explained later, it can be shown that as an approximation, when

eaked into the fore-vacuum while gas is admitted to the pump inlet until p = pb at which dynamic jet breakdownegins, then

where At is the nozzle throat area, B is the body clearance area (the open cross section of the pump casing in fronorward-directed nozzles, or area between the inside wall of the pump casing and the outside wall of the vapor eading to an inverted or "umbrella"-type nozzle), Kn is a constant with value in the range from 0.5 to 1.1 dependhe design of the nozzle as explained later, and Pc is the vapor pressure inside the vapor conduit leading to the no

which is approximately equal to the vapor pressure in the boiler. Since, as shown in Section 4.3.6, the boiler prncreases more or less linearly with the watt input to the heater, we note that pc, Fc, pb , and the limiting forepressub , all increase linearly with the watt input. The knee of the speed versus intake-pressure curve for a single stagan be moved to higher pressures, pb , by increasing the speedC of the forepump.

he static forepressure breakdown of single-stage pumps is given by



where Kn is nearly independent of the gas load (throughput) and Pc is approximately equal to the boiler pressure, bor multistage pumps the static limiting forepressure depends on the gas load. When curves of p versus F for a two-sump are plotted





Fig. 4.12Intake pressure versus forepressure for each stage in

two-stage pump and combined stages at no load.

ogether with the corresponding curves for each stage separately, as in Fig. 4.12, using the fact that the forepreshe first (top) stage, F 1, is the same as the intake pressure, p2, for the second stage while the inlet pressure, p, equals

can be seen from the figure that the no-load static limiting forepressure for a two-stage pump is given approxy

where F 1b is the no-load limiting forepressure for the first stage alone, while F 2b is the no-load limiting forepressund F 2c is the crossover forepressure for the second stage alone. At the upper end of the forepressure breakdowor any individual stage the crossover pressure is given by

where At/Ae is the ratio of nozzle throat area to nozzle exit area. Hence, from Eqs. (4.6) and (4.8) we obtain







where A2e/ B2 is the ratio of nozzle throat area to the body clearance area for the second stage. Usually, for the searest the forepump, Ae/B = 0.3 0.5. Thus, for a two-stage pump, Eq. (4.7) gives Fb = 0.6 F 1b + F 2b.

imilarly, it can be shown that for a three-stage pump the no-load static limiting forepressure is

where F 3b is the static limiting forepressure and F 3c is the crossover forepressure for the third stage (nearest theorepump) alone. Again, F 3b/ F 3c = A3e/ B3, the ratio of nozzle throat area to body clearance area for the third sta

he compression ratio of a single pumping stage is defined as the ratio of forepressure to inlet pressure when puas that is not absorbed within the pump. This ratio is a variable quantity which depends on the ratio of the pumpeed of a given stage to the net speed of the next stage in series. However, for a given throughput there is a limompression ratio which can be maintained at a given power input. At maximum throughput of air the limitingompression ratio for single-stage ejector pumps is about 10, and for the individual stages of multistage diffusi

he limiting ratio is about 4. Thus a four-stage diffusion pump can compress air from 0.2 Pa to 51 Pa, corresponotal compression ratio of 44 or 256. For a single-stage diffusion pump the limiting compression ratio as obtainq. (4.5) will be

.3.3nfluence of Nozzle and Entrance Chamber Design on Speed

n order to simulate the gas flow pattern into the pump from a pipe connecting the pump to the vessel to be evaump speed is always measured using a test dome over the inlet with an inside diameter either equal to the inleiameter of the pump housing or else equal to the inside diameter of the pipe fitting which is normally used to he pump to the vessel. The American Vacuum Society has established recommended configurations for the tes17] as described in Chapter 12. The location and orientation of the tubulation of the total pressure gauge instalhe dome influence the measured speed [1820]. The nozzle design of the first stage of pumping (nearest the higacuum inlet) determines the pump speed. For this stage the exit of the nozzle should not be beveled to deflectet toward the pump wall, but rather should direct the jet along the axis of the pump as much as possible by alloome inward expansion as in the Embree nozzle design. The "nozzle clearance area," Anc, between the rim of the vozzle exit (or the rim of a cold cap over an umbrella nozzle) and the inside wall of the pump housing in the enhamber region is the limiting factor determining pump speed. The theoretical maximum speed across this areaonsidered as an opening in a thin plate would be





where fn is the "effusion law" factor in liter · s1 · cm2 as given by

n which R0 is the molar gas constant,T is the absolute temperature, and Mn is the molecular weight of the gas.However, because the nozzle clearance area is the exit of a tube or chamber of varying cross section consistingwalls of the pump casing and the nozzle assembly between the nozzle clearance area, Anc , and the pump inlet area, Aas does not cross the area Anc according to the cosine law but is beamed forward across this area by scattering fhe walls of this entrance chamber. If gas at pressure p (in Pa) were to enter the pump inlet from a large chamberirectly connected to the pump so that the molecules crossed the inlet area with a cosine law distribution, then

would be a transition probabilityw less than 1 that a molecule crossing the pump inlet would also cross the nozzlearance area into the vapor jet. The forward flow in Pa · liter · s1 across the pump inlet would then bewfnApp. Fort a partial pressure pj scattered back from the vapor jet and crossing the nozzle clearance area (with an approxiosine law distribution) and continuing on out of the pump inlet, the backward flow in Pa · liter · s1 out of the p

would bewfnAncpj . When the back-diffusion of gas from the fore-vacuum is negligible, the pump speed as meahe large chamber would then be

heoretically,w could be calculated from the known geometry of the entrance chamber by applying various forue to Clausing [21], Oatley [22], Harries [23], and others, orw could be calculated by Monte Carlo methods, but pj

would not be known. However, it is not necessary to knoww and pj exactly, but merely to recognize that the entrahamber impedance, Rc (in seconds per liter), to gas flow should be made as small as possible while the nozzlelearance area of the first-stage nozzle should be as large as practical to obtain maximum speed. The maximum

measured speed,Sm, can then be expressed as

where H is the "speed factor" or "Ho coefficient" which has been defined by T. L. Ho [24] as

whereα is Gaede's factor for the fraction of the gas molecules from the high vacuum that succeed in diffusing the back-scattered vapor and reaching the nozzle clearance area which depends on the ratio of the mean free pa

molecules through the back-scattered vapor in the nozzle clearance area and the width of the nozzle clearance, he fraction of the gas molecules which reach the nozzle clearance area and pass on to be carried away by the vnd 1γ is the fraction which return through the nozzle clearance area. It should be noted that for mercury vaporhe vapor pressure of mercury in the entrance chamber is not negligible,







Gallium and fusible metal alloys have been suggested as pump fluids, but are not considered practical. P. Alexa] found glycerol as the pump fluid to give advantages over mercury vapor pumps, but glycerol has a vapor prebout 102 Pa at room temperature.

able 4.1 gives vapor-pressure data for oils used as pump fluids as obtained by various authors using tensimetehe pressure range from 0.1 to 1000 Pa. Since most commercially available pump fluids are mixtures of organic

molecules having a range of molecular weights and isomeric forms, the measurement of the vapor pressure isomplicated by the tendency of fractionation to occur during the measuring process. Therefore it is not surprisinifferent methods give slightly different results and that the data reported by different authors for the same matot in close agreement as shown by this table. Parameters A and B are those of the vapor-pressure relation

where P is the vapor pressure in Pa andTc is the temperature in °C. This equation is a good approximation to moapor-pressure curves over the range of temperatures involved in diffusion pumps, but plots of log10(7.5 × 103 P )ersus the reciprocal of the absolute temperature obtained by actual measurements usually are not perfectly stranes but show a slight downward curvature. Vapor pressure measurements in the range from 1 to 103 Pa by mo

eam [27] and dew-point [28] methods give higher values of B. The latent heat of vaporization of the liquid in kcamole as calculated from

listed in the last column. The values of temperature listed under the vapor pressure equal to 67 Pa are of espenterest since this vapor pressure is about the optimum value for the boiler pressure in oil diffusion pumps. Theressure of fractionating pumps will be about the same as the pressure listed in the column labeled P (Pa), 25°C, buroved experimentally by Blears [29], the reading of a tubulated ionization gauge may be somewhat lower thanapor pressure as measured by a nude gauge because of clean-up or sorption of the vapor inside the envelope oubulated gauge, resulting in a pressure drop across the tubulation. In interpreting ultimate pressure readings byonization gauges using the "nitrogen equivalent" calibration factor, it must be borne in mind that the equivalen

itrogen pressures of organic vapors may be 5 to 10 times higher than the true vapor pressure depending on theonization probability for the molecules of the vapor and its decomposition products within the gauge.

Octoil® is vacuum-distilled commercial grade di-ethyl-hexyl phthalate (molecular weight 390.3). Octoil-S® isistilled commercial grade di-ethyl-hexyl-sebacate (molecular weight 426.3). Apiezon B and Apiezon C are mistilled petroleum fractions. DC 704 and DC 705 are silicone fluids. Chemically, DC 705 is a pentaphenyl trimisiloxane with molecular weight 546 g/mol [30]. DC 704 is a tetraphenyl tetramethyl trisiloxane with molecul84 g/mol [31]. Convalex-10® is a vacuum-distilled polyphenylether of average molecular weight 454 g/mol. is a mixed penta-phenyl ether of average molecular weight 447.




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Table 4.1. Vapor-Pressure Data for Diffusion Pump Oils

Degrees C for P in Pa P (Pa) 25°C ∆ H (k cal/mol) Name Ref. A B 133 66.7 13.3 1.33 0.133 0.013Octoil 1

12.125590 188 177 153 123

97 744.1 × 105 25.6

210.31

4808 193 180 152 11788 63

2.0 × 104 22.0

411.62

5540 204 192 166 134106 82

1.5 × 105 25.3

Octoil-S 311.26

5514 215 204 177 142114 89

2.7 × 106 25.2

2

10.02

4878 214 199 169 133

102 75

6.1 × 105 22.3

411.90

5780 213 201 175 143115 90

4.4 × 106 26.4

Convoil-20 79.94

4800 210 196 166 12998 71

9.2 × 105 22.0

Convalex-10 29.97

5525 281 265 230 188156 122

3.6 × 107 25.3

Santovac 5 69.68

5450 290 273 237 193157 125

3.3 × 107 24.9

Lion A 210.24

4950 210 196 167 131101 74

5.7 × 105 22.6

DC 704 211.02

5376 215 202 174 140110 85

1.3 × 105 24.6

511.49

5700 223 210 183 149149 94

3.2 × 106 26.1

DC 705 211.65

6098 250 237 209 174143 116

2.1 × 107 27.9

512.31

6490 254 241 214 180151 125

4.7 × 108 29.7

Apiezon B 29.91

4831 214 200 170 132101 74

6.8 × 105 22.1

Apiezon C 29.27

4808 246 229 195 153119 89

1.9 × 105 22.0

Cellulube 211.61

5780 225 212 185 152122 97

1.7 × 106 26.4

References

1. K. Hickman, N. Embree and J. Hecker, Ind. Eng. Chem., Anal. Ed . 9, 264 (1937).

2. K. Nakayama, J. Vac. Soc. Jpn . 8, 333337 (1965).3. Metropolitan-Vickers, S. Dushman, personal communication (1946).4. E. Perry and W. Weber, J. Am. Chem. Soc . 7, 3726 (1949).5. D. Crawley, E. Tolmie and A. Huntress,Trans. 9th Natl. Vac. Symp . 9, 399, Macmillan (1962).6. K. Hickman,Trans. 8th Natl. Vac. Symp., 2nd Intern. Congr ., 1961, Vol. 1, p. 307, Pergamon (1962).



7. B. Dayton, calculated from vapor pressure data of CVC.





he application of polyphenyl ethers as diffusion pump fluids was introduced by K. C. D. Hickman [32]. Cellu a triarylphosphate. Lion A is an alkylnapthalene oil. Convoil-20 is a vacuum-distilled petroleum fraction andverage molecular weight 388 g/mol.

he stability of the various pump fluids against exposure while hot to air at atmospheric pressure has been invey several authors [30, 31, 3336]. In general, the silicone fluids are more resistant to thermal decomposition anxidation than the phthalate and sebacate esters and the paraffin hydrocarbon oils, but have the disadvantage thlicone vapor migrating back into a vacuum system can decompose on hot filaments and electrodes bombardeharged particles to form silica-like insulating deposits which disturb the operation of electrical devices. The pothers have much higher thermal stability than the ester fluids in addition to being resistant to damage by radiat

he open-cup flash point of the ester pump fluids is about 200°C, and thermal decomposition results in formatirystals of the acid anhydride and tarry deposits on the nozzle assembly whereas the nozzle assemblies remain lean when silicone fluid is employed. If the exposure time is brief, fractionating pumps can usually recover inme of normal operation, so that the speed and ultimate pressure are not seriously affected. However, dark dep

he nozzle assembly increase the radiation loss to the water-cooled walls and require an increase in heater inputmaintain the normal boiler temperature. Jaeckel [34] found that thermal dissociation of organic oils is favored burfaces, so that all-glass pumps tend to give lower ultimate pressures than metal pumps. In any case, it is recom

hat for ester and hydrocarbon pump fluids the oil in the boiler be allowed to cool below 100°Cand for polyphethers, to below 150°Cbefore exposure to the atmosphere.

erfluoropolyether has been investigated as a diffusion pump fluid and has the advantage of comparable or greability but the disadvantage of somewhat lower speeds as compared to polyphenyl ether and silicone pump fl8]. It has been used under the trade name Fomblin as the fluid in rotary mechanical pumps [39].

.3.5ackstreaming and Back Migration of Pump Fluid

Vapor molecules, originating from the pump fluid and its decomposition products, can escape back through thenlet cross section into the components of the vacuum system attached to the inlet. In 1957 Ruf and Winkler [4lso Power and Crawley [41] showed that these vapor molecules can have four sources: (1) back migration duevaporation of fluid condensed on the pump wall or on any baffles in the region between the first-stage nozzle rea and the pump inlet; (2) backstreaming due to backward curving streamlines and scattered vapor moleculesapor jet between the rim of the nozzle exit and the pump wall; (3) backstreaming due to evaporation from hotump fluid clinging to the outside of the first stage nozzle; (4) backstreaming due to leaks around the nut holdiop (umbrella) cap to the nozzle assembly. The invention of the cold cap by B. Power [12] greatly reduced theackstreaming from sources (3) and (4). Examples of a cold cap installed over the top nozzle are shown in Figsnd 4.9. In general, it is common practice to place water-cooled baffles and refrigerated or liquid-nitrogen-cool





etween the diffusion pump and the vacuum chamber to reduce the backstreaming and back migration to an acevel.

When the backstreaming rate is high, it can be measured during pump speed measurements with a test dome byhe top of the dome dished convex or sloping slightly to one side so that condensed oil runs down the side wallutter at the bottom of the dome from which the oil can drain into a burette as described in the AVS Standardsommittee document T.S. 4.5 (1963). When the rate is very small, other techniques must be used, such as weigil collected on a thin metal foil clamped to a liquid-nitrogen-cooled plate above the pump and any baffles emp42]. Measurements of the backstreaming rate, B, (in cm3/h of oil) obtained by the author on the MC series of thrage vertical metal diffusion pumps having a top-stage nozzle with 3-mm throat width (without cold cap) at noeater input and ultimate pressure with either Octoil or Convoil-20 for casing diameters 12, 14, 16, 20, 32, and

When plotted as a loglog graph gave a straight line corresponding to

where D is the inside diameter (in inches) of the straight cylindrical pump casing. The specific gravity of Convo.90, so that 1.0 cm3/h = 15 mg/min. For the 12-in. pump we obtain B = 0.52 cm3/h, which corresponds to 0.011 m

m2 · min1. Power and Crawley [41] obtained a rate of 8.2 × 103 mg · cm2 · min1 on a 6-in. pump with Apiezo cold cap, while addition of the cold cap reduced this rate by a factor of 10. Duval [43] measured the backstrom various source points within a 600-mm-i.d. pump and showed that 99.8% came from the lip of the top nozlso showed that the reduction in backstreaming produced by a cold cap depended on the position of the lower old cap relative to the lip of the top umbrella nozzle. Baker [44] has described a cooled quartz crystal microba

method for measuring backstreaming and showed that the peak backstreaming rate is as much as ten times the unning rate during warmup of the pump and approximately four times as high during cooldown. These high rauring start-up and shut-down can be largely avoided by using the gas purge technique [45, 46]. Hablanian, usioil and liquid-nitrogen-cooled plate technique, obtained 1.6 × 103 mg · cm2 · min1 for a 6-in. pump with DC-ump fluid and a water-cooled cold cap. Addition of a liquid-nitrogen-cooled trap with no creep barrier above educed the rate to about 6 × 106 mg · cm2 · min1. Interposing a water-cooled baffle between the pump and theitrogen baffle gave a rate of 2.8 × 107 mg · cm2 · min1, and adding a creep barrier to this combination reduceo about 1 × 107 mg · cm2 · min1.

esign of Baffles and Traps to Condense Backstreaming Vapor. When a baffle or trap is installed directly over theozzle assembly in a water-cooled pump casing, the baffle plates can be cooled by conduction through copper, luminum support fixtures making thermal contact with the pump wall. However, such baffles must be removahat the nozzle assembly can be inserted and removed for cleaning. External baffles and traps are to be preferrehey can be cooled independently of the pump casing to any desired low temperature.





When backstreaming is relatively high, it is important that most of the pump fluid condensed on the first bafflehe pump inlet drain back into the diffusion pump. This baffle is therefore usually air- or water-cooled, and the fitted to the diffusion pump in a manner that allows the condensed fluid to return. A second refrigerated baffl

hen be installed beyond the first baffle and operated at a temperature so low that the condensate does not drainxcept when this baffle trap is warmed again. The design of an effective baffle or refrigerated trap requires thato line of sight through the baffle plates or the cold-trap reservoirs and housing (which is usually not refrigerat

while the conductance for air should be as large as possible consistent with the ''optically tight" requirement. Hven optically tight baffles or traps may be a source of vapor contamination since condensed pump oil tends tolong the inner surface of the baffle or trap housing and may reach regions at warmer temperatures where the oeevaporate directly into the vacuum chamber. Thus, anticreep barriers are sometimes incorporated [47, 48].

he efficiency, Be, of a baffle in condensing backstreaming vapor depends on the number of collisions,n, made by apor molecule on the cooled baffle plates and the condensation coefficient,αc, according to the equation

where for baffles with short passages between bends in the plates or between entrance and exit cross sections thverage number of hits with the wall for molecules passing through can be estimated from

n which L is the length (in cm) of the shortest passage from entrance to exit along a path equidistant from adjacaffle surfaces,b is the number of bends (usually right angle) in the passage, and Re is the equivalent radius (in cmraight cylindrical tube of length L having the same probability of transmission for noncondensing molecules asaffle. For long straight cylindrical tubes of length L and radius R, the number of collisions with the wall in free

molecular flow is [49]

nd the transmission probability is [21]

or mercury vapor molecules colliding with water-cooled steel or aluminum baffle plates the condensation coec, is less than 0.5, but for the large molecules of organic or silicone pump fluidsαc will be nearly unity, and most

molecules will be condensed within the baffle. The effectiveness of the baffle then depends on the rate of reevaom the baffle surfacethat is, on the sorption lifetime,ta , on the surface. Assumingta constant for the whole baffle

urface, the mean transit time through the baffle for vapor molecules will be





where

n which R0 is the molar gas constant, andTn is the mean absolute temperature of the vapor in transit which depehe temperature in the entrance chamber, the thermal accommodation coefficient, the temperature of the baffle nd the number of hits with the wall after entering the baffle. For oil molecules at the usual baffle temperatures

When the vacuum system is operated for times longer thantn, the flow of vapor molecules through affle will reach a steady state and the baffle has no effect. The quantity of vapor passing through the baffle wiqual to the backstreaming flux from the pump into the baffle times the probability of passage for any moleculewithout regard to the time spent in the condensed state) in molecular flow. For long narrow passages the time the steady state can be several hours, which is the principle of the Alpert copper-foil trap for oil vapor [50].

onductance of Baffles and Cold Traps. The conductance of a baffle or cold trap can be measured directly by adas from a throughput meter into a test dome, similar to that used for measuring diffusion pump speed, over the

which will be furthest from the diffusion pump and placing a short pipe section (collar) with inside diameter eqhat of the exit of the baffle, and having a gauge attached to a tube joining the pipe at right angles to the axis so

measure static pressure between the baffle and a diffusion pump. If the maximum speed,Sd , of the diffusion pump lready been measured without the baffle over a wide pressure range, the pipe collar can be omitted and the netn, of pump and baffle measured over a wide pressure range with the standard test dome, the baffle conductancU ,hen being obtained from the net speed formula

he conductance may be calculated with or without entrance and exit corrections. The conductance with theseorrections corresponds to the throughput divided by the difference in pressure between two very large vacuumhambers placed over the entrance and exit of the baffle, as measured in the interior of the chamber far from thntrance and exit. Since baffles are seldom used in this configuration, it is the conductance without entrance anorrections, corresponding to measurement of the static pressure exactly at the entrance and exit cross sections,

more relevant. Because of the location of the gauge in the AVS or ISO standard test domes, an entrance correctncluded in the measurement of pump speed or net speed of pump and baffle. As an approximation, this correcto the impedance can be assumed to cancel out when using Eq. (4.27), so thatU is the conductance without entrancxit corrections. The entrance correction to a straight pipe section is about equal to one-half the impedance of ahin plate of the same area and cross section as the entrance to the pipe as measured between two large chambectual calculation is complicated by beaming of gas from one pipe section across the entrance to an adjacent sehe scattering of gas from any baffle plates or right angle bends [18, 51].





Among the various types of baffle design which have been tried are (1) circular disk sandwiched between two nnular rings or located at the center of a cylindrical housing of about twice the diameter of the disk, (2) straighhevrons, (3) concentric circular chevrons, (4) stepped flat annular rings, (5) stepped concentric circular chevrolternating semicircular plates inside cylindrical housing, and (7) split-chevron or louvre baffles. When backstr high, some alteration in the design of the baffle plates is needed to avoid condensed pump fluid dripping off late on to the top of the hot nozzle assembly in the diffusion pump. Zinsmeister [52] has treated very thoroughharacteristic properties of various baffle designs, including cold caps over the top nozzle. He defines a specifionductivity as the total conductivity of the baffle divided by the area of the cross section of the baffle housingnd obtains 3.6 liter · s1 · cm2 for typical single-chevron baffles. The specific conductivity of optically tight baelatively independent of the diameter of the baffle housing. Davis, Levenson, and Milleron [53] have investigaptimum dihedral angle for the chevrons in a straight chevron baffle for maximum conductance both by experiy Monte-Carlo calculation. Their results indicate an optimum angle of 120°.

.3.6hroughput

n vacuum engineering calculations the quantity of gas flowing through the pumping system is usually expresshroughput (symbolQ), defined as the product of pumping speed,S , and the static pressure, p, at the prevailing gas

emperature at a specified cross section. It is recommended that speed be expressed in either liters per second (lr cubic meters per second (m3·s1). The ISO unit of pressure is the Pascal (abbreviated Pa); but current practicellows use of the millibar (abbreviated mbar), which equals 100 Pa. The unit Torr is no longer recommended. O

millibar equals 0.75 Torr. Suitable units of throughput are mbar·liter·s1, Pa·liter·s1, or Pa·m3·s1 at a specifiedemperature (such as 23°C).

As pointed out by Lewin [54] and by Ehrlich [55], the above definition of throughput leads to complications was temperature is not the same in all parts of the vacuum system. However, by correcting all measurements to andard room temperature of 23°C and using the continuity relations,

whereU 12 is the conductance of the flow path between the points 1 and 2 at which the static pressure is measuacuum system calculations are simplified. The conductance,U 12, in the molecular flow region is independent of

wall temperature [49, 56, 57]; but the entrance and exit pressures, p1 and p2, depend on the gas temperature and, wmeasured by hot-filament ionization gauges, also depend on the wall temperature of the gauge [58, 59].

ach stage of a multistage vapor-stream pump has a maximum throughput which can be handled without jet bretermined by the heater input and the speed of the next pumping stage in series. From Eq. (4.5) the maximumhroughput is





where the subscriptn refers to the number of the stage (the first stage being nearest the pump inlet and the last searest the forepump connection). For the last stage of the vapor-stream pump, the next pumping stage is that oorepump; andSm(n + 1) =C , the speed of the forepump. When the nozzle assembly has optimum design, the vam for a given boiler pressure, P 0, should be approximately the same for each stage in series. The required speeC

he forepump then depends on the characteristics of the last stage of the vapor pump as given by Eq. (4.5). Whpeed of the forepump is sufficiently high, the limiting forepressure, Fmb , at this maximum throughput can beetermined by measuring the forepressure, F , as gas is admitted to the forevacuum region until jet breakdown bendicated by a rapid rise in the high-vacuum pressure, p, when the leak rate of gas on the high-vacuum side is

maintained constant at a series of increasing values.

eater Input and Water Cooling. Since according to Eq. (4.29) the maximum throughput is proportional to the bressure, it is of interest to determine the dependence of the boiler pressure on the watt input to the pump heateeat carried away by the cooling water, and the radiation and conduction losses from the pump casing. The heaway by the cooling water per second (in watts) can be estimated from

where we have used Eq. (4.53) below and

n which P 0 is the vapor pressure (in Pa) andT 0 the absolute temperature in the boiler, M is the mean molecular wef the pump fluid, R0 = 8.314 × 107 erg · K1 · mol1,Σ Ant is the sum of all the nozzle throat areas in ann-stage pumv is the latent heat of vaporization per gram of pump fluid, s is the specific heat of the liquid pump fluid,T 0 is theagnation temperature of the vapor from the nozzles,Tw is the lowest temperature reached by the cooled condens

n its way back to the boiler, D is the casing diameter (in cm), Lbw is the distance (in cm) between the level of fluhe boiler and the lowest turn of the cooling coil,kc is the thermal conductivity of the casing material, andt is thehickness of the casing wall (in cm),Wr is the rate of heat transfer (in watts) by radiation from the hot nozzle asseo the cooled casing in the region of the cooling coils, Aj is the area (in cm2) of the outside surface of the hot nozzssembly directly exposed to the casing in the region of the cooling coils,ej is the emissivity andTj is the averageemperature (in K) of this surface which will be slightly less than the vapor temperature,T 0, in the boiler, andTac isverage temperature (in K) of the inside of the pump casing in the region of the cooling coils which will be somigher thanTw and Wc is the rate of heat transfer by conduction along the casing wall from the boiler to the lowf the cooling coil. Heat transfer from the ambient air to the cooling coil is neglected. The





eat exchange between the casing wall and the returning pump fluid over the distance Lbw is also neglected.

or organic pump oils, Lv is in the neighborhood of 6070 cal·g1 and s is about 0.2 cal·g1·deg1. A more exact treatwould use the emissivity factors for concentric cylinders and consider the heat conduction through the film of p

uid on the casing wall; but since emissivity of the pump fluid is nearly equal to 1 and the film is thin, the abovquation is sufficient for a rough estimate. The value ofej will vary from about 0.2 to 1.0, depending on the degreiscoloration of the surface of the nozzles assembly. It has been found that the radiation loss is somewhat less tf the heater input when the nozzle assembly is clean.

inally, the required heater input to the boiler will be

whereWb is the rate of heat loss by radiation and air convection to the surroundings of the boiler region up to thooling coil. The boiler region in some pumps is thermally insulated with fireproof insulating material. The eleeating units may be installed as hot plates in direct contact with the flat bottom of the boiler or may take the foartridge units inserted in cavities which extend into the pump fluid. The latter arrangement reduces the "bump

which sometimes occurs as the oil becomes superheated and flashes into vapor. This bumping can cause vibratwhich create problems in apparatus attached to the pump, such as electron microscopes.

he heat transferred to the cooling water has been measured to be between 55% and 75% of the heater inputW forxternal heaters and between 65% and 80% ofW for immersion heaters. The rate of flow of cooling water througoils should be adjusted so that the discharge temperature is 3545°C to maintain a relatively warm temperatureescending along the wall from the last coil turn to the boiler. This helps to prevent condensation and return to oiler of light ends of the pump fluid which normally undergoes some decomposition during pump operation. Af-thumb, for pumps with external heaters the cooling water should circulate through the coils from the high-vaoward the fore-vacuum side at a rate (in cm3/min) about equal to the heater input in watts.

While the vapor pressure, P 0, during operation of diffusion pumps may vary over the range from about 10 to 10epending on the heater input,W , the absolute temperature,T 0, of the vapor in the boiler varies only from about 4

80 K for typical pump oils as shown by Table 4.1. The variation in in Eq. (4.30) is therefore only from 1.9, and for all practical purposes it can be assumed that the boiler pressure, P 0, is a linear function of the heater i

W . This is confirmed by the experimental data.

o ensure a supply of vapor to the nozzles at a pressure near that in the boiler and to avoid overheating the fluioiler, the area of the free surface of the pump fluid in the boiler should be at least five times the total nozzle threa, Σ Ant . In the forepressure breakdown region from pb to pc the vapor jet is deformed and cooling is less efficihat the boiler temperature tends to rise to dangerous levels. Also, the deformation of the first-stage vapor jet wncrease the backstreaming rate. Oil





iffusion pumps should not be allowed to operate in the forepressure breakdown region for any length of time, he heater power should be turned off.

4heory of Pump Performance

he theoretical analysis of the pumping action of diffusion and ejector pumps has engaged the attention of manuthors. Kinetic theory can be applied to analyze the counterdiffusion of gas from the high-vacuum side and vapreading sideward and backward from the nozzle exit as well as the counterdiffusion of gas from the fore-vacuapor discharged in the forward direction from the nozzle. Hydrodynamic theory, as developed in connection weam turbines, can be applied to the expansion of the vapor through the nozzle and beyond the nozzle exit. Thquations have been derived for the following aspects of pump performance: speed, limiting forepressure, ultimressure, and backstreaming.

.4.1peed

n 1915 Gaede derived a theoretical equation for the speed of a diffusion pump by analyzing the counterdiffusin a mercury-vapor stream as follows. First, he considered the case of a stream of mercury vapor flowing in theirection ( x-axis) through a cylindrical tube of radiusa with average velocityv and a density high enough to be in tiscous flow region so that entrapped gas molecules diffusing countercurrent to the vapor stream tend to be carlong by the vapor stream. In the steady state the concentrationn of gas molecules at x varies linearly from a very salue n0 at x = 0 to a maximumnm at x = L because of a reservoir of gas beyond L from which gas molecules canenetrate into the vapor stream and diffuse counter to the stream velocity with diffusion coefficient D . For L/a < 10 elocityu will be approximately constant over any cross section of the tube. Sincen is proportional to the pressure phe gas and D varies inversely with the pressure P (in mmHg) of the mercury vapor, Gaede obtains

where D is the diffusion coefficient at 760 mmHg (101,308 Pa), anddp/dx is the pressure gradient of gas along thewhich is equal and opposite to the pressure gradient,dP/dx , in the vapor. Integrating Eq. (4.33) from p = p0 to p = pmives

he counterdiffusion of gas and vapor results in an actual pressure drop in the gas from x = L to x = 0 given by





As Gaede pointed out, this introduces an error in the reading of gas pressure with a McLeod gauge. For a mercream of sufficiently high pressure P and velocityu the gas pressure at x = 0 can be reduced to a very low value, p0pm.

Gaede then considered the case of mercury vapor flowing past a small hole of diameterd in a thin wall separating tmain body of vapor from a region containing gas at the pressure p. From kinetic theory the number of vapor molecrossing a small surface elementσ normal to the radius from the hole and located at the angleϕ with the normal to lane of the hole will be

where N is the number of vapor molecules per unit volume in the vapor stream near the hole coming from the sde andua is the average molecular velocity at the temperatureT . Since the emerging vapor molecules do not actart at a point at the center of the hole, Gaede introduces a spherical surface of radius x0 at which the concentration. Since the total number of vapor molecules crossing the hemisphere of radius x0 per second will be equal to theumber Z crossing the hole of diameterd , it follows that the concentration N will be equal to Z divided by the volum

or

o that The number of vapor molecules per unit volume, N ( x, ϕ), at σ will be

he mean free path,λ( x, ϕ), of the gas molecules through the vapor at x andϕ can be assumed to be inverselyroportional to the concentration N ( x, ϕ) of the vapor molecules since the gas pressure is small compared to the vressure, or

whereλ0 is the mean free path of a gas molecule through the vapor at the hole, where x = x0. Gas molecules diffusehrough this mercury vapor toward the orifice and are scattered so that only a fraction,α , of the molecules finally rehe orifice depending on the mean free path,λ( x, ϕ), for the gas molecules through the vapor as given by

y integrating over all angles, Gaede obtains

or λ0 = d , this givesα = 0.793.





hen Gaede's complete formula for the speed at the entrance slit is

where A is the slit area, andβ is the back-diffusion coefficient for gas from the fore-vacuum at the forepressure F whenetrates back through the vapor jet by counterdiffusion and generates a partial pressure

f this gas at the entrance slit area, whileα is the fraction of the gas molecules from the high-vacuum side that pehrough the backstreaming vapor and reach the slit area as given by Gaede's Eq. (4.41), andγ (using Ho'sγ notation lace of Gaede'sk ) is the fraction of the gas molecules which have reached the slit area that actually pass througre carried away by the vapor stream. The coefficientβ is given by Eq. (4.34) when P, v , and L are constant, but forapor jets diverging from a nozzle in modern pumps these parameters are not constant and integration must beerformed over a path through the vapor jet from the fore-vacuum to the high-vacuum side. Experimentally,β orresponds to the slope of the p versus F curve for no load in Fig. 4.11.

As explained below, Molthan [60] modified Gaede's equation forα by taking account of the effect of the streamelocity, v, of the vapor molecules on the pattern of flow of vapor molecules emerging through the hole, or slit.

.4.2imiting Forepressure

As the forepressure is increased by admitting a gas leak into the fore-vacuum with a constant gas throughput onde, a shock boundary is formed between the supersonic vapor jet and the gas in the fore-vacuum. Increasing tressure further pushes this shock boundary back toward the nozzle exit as shown by Dayton [61] in 1948 inxperiments with a glass diffusion pump using pump fluid colored with a red dye and observing a glow discharas and vapor in front of the nozzle. When the shock boundary is pushed back to the point at which the jet no l

makes contact with the cooled pump casing, the vapor jet again shoots forward as a narrow beam into the fore-ut has a side boundary with the gas at the elevated pressure and eventually bends to one side to condense on t

wall.

his behavior is also shown for the case of a metal pump by the isobar diagrams obtained by a pressure probe mnd down through the jet of a mercury vapor pump by P. Alexander [62] (see Fig. 4.13) and by the glow dischahotographs and line drawings in a 1955 article by Kutscher [15]. Similar diagrams were prepared in 1960 by Nlorescu [63].

he gas density distribution around the upper stage of a 6-in. vertical metal pump at an inlet pressure of 5.3 × 1was explored by Hablanian and Landfors [64, 65] using an ionization gauge probe. They also measured the disf vapor arriving at the wall from the top nozzle (both with and without a cold cap) by using a series of gutters ubes.





Fig. 4.13Isobars of air pressure in mercury vapor pump [62].



.4.3Vapor-Jet Flow Pattern

When the average stream velocity is parallel to the nozzle axis and both the throat area, At , and the exit area, Ae, arerthogonal to this axis and no condensation occurs





Fig. 4.14Expanding conical nozzle showing various

defined cross sections.

n the nozzle, then the mass of vapor discharged by an expanding conical nozzle is given (in cgs units) by

whereρt is the vapor density, Pt is the static vapor pressure in dyne·cm2,vt is the stream velocity in cm/s,Tt is thebsolute vapor temperature at the nozzle throat of cross-sectional area At , and the subscripte indicates theorresponding quantities at the nozzle exit (see Fig. 4.14). It is known that for adiabaticisentropic expansion ofhrough the nozzle when the forepressure is below the limiting value, the velocityvt at the throat equals the acoustielocity,

wherek is the ratio of specific heats. Since any change in downstream pressure cannot influence the throat preswhen the flow is supersonic, the discharge rate is a maximum.

n passing adiabatically from the cross-sectional area Ac of the vapor conduit from the boiler to the throat area At theapor density and pressure changes according to

whereρc is the density of the vapor in the conduit from the boiler. For sufficiently large Ac relative to the throat aret , it can be assumed that Pc is approximately equal to the boiler pressure, P 0, andρc is approximately equal to theapor density,ρ0, in the boiler.

When the forepressure is below the limiting value, the discharge rate is a maximum and the static vapor pressurhroat cannot be increased beyond the critical value,



where Ptc will be in Pa if P 0 is in Pa.





ombining the above equations gives for the maximum discharge rate (in cgs units) of short nozzles

or adiabaticisentropic expansion through a short nozzle the static pressure, Px , the vapor density,ρ x, and the absolapor temperature,Tx, at any cross section x are related to the initial pressure Pc , densityρc, and temperatureTc in tapor conduit by

here are no experimental data on the value ofk for the high-molecular-weight organic and silicone molecules ofypical diffusion pump fluids, but from the equipartition theorem as modified by quantum mechanics it can be hat for all temperatures above 300 K the specific heat ratio can be estimated from

where Nv is the number of vibrational degrees of freedom which are fully excited at the temperature of the vapooiler [66]. A study of the available data on the value ofk for large organic molecules reveals that in the temperatange 30°C to 300°C the value ofk will be about 1.5 times the number of atoms in the molecule [67]. The theore

maximum value is 3n 6, wheren is the number of atoms in a molecule (withn > 3), but this value cannot be reachexcept at extremely high temperatures where in most cases the molecule decomposes. The pump fluid Octoil (dhthalate) contains 66 atoms, so that Nv = 99 andk = 1.019. For typical hydrocarbon pump fluids with molecularbout 390, the molecules have about 28 carbon atoms and 54 hydrogen atoms and Eq. (4.50) using the 1.5 fact

1.015. It can be assumed, as an approximation, thatk = 1.02 for organic pump fluids. The specific heat ratio formercury vapor isk = 1.666.

he above equations involve the assumption that the initial stream velocity,vc, in the conduit of cross-section area Aractically zero. This will be true when but for some diffusion pump designs Ac is less than 5 At and a fac

hould be included in Eq. (4.48). Neglecting this correction factor for the initial velocity and assuming that P 0 at theozzle entrance is about equal to the boiler pressure and usingk = 1.02, Eq. (4.47) gives the critical throat pressure P0.60 P 0 and Eq. (4.48) gives





or oil diffusion pumps with forepressure below the limiting value corresponding to a maximum discharge rate.he vapor density,ρ0 (in cgs units), is not measured directly but calculated from

where M is the average molecular weight of the pump fluid, R0 is the molar gas constant, andT 0 is the absoluteemperature of the vapor in the boiler region, a more convenient form of Eq. (4.51) is

As the vapor passes from the throat to the nozzle exit of area Ae > At , it expands and acquires supersonic streamelocities. When the forepressure is below the limiting value and the initial velocity,v0, is negligible,diabaticisentropic flow through a short expanding conical nozzle results in an average stream velocity (paralleozzle axis) at the nozzle exit given by

where Pe is the static vapor pressure at the exit. For organic pump fluids with values ofk approaching 1, it can behown by an application of L'Hôpital's Rule [67] that the nozzle discharge rate is given by

DifferentiatingG with respect to Ptc and setting the result equal to zero gives the critical pressure at whichG is amaximum,

which is approximately the value found above. Substituting in Eq. (4.55) then gives

which is the same as Eq. (4.53). Similarly, applying L'Hôpital's Rule to Eq. (4.54) ask → 1, we obtain

hen, using Eq. (4.45) and Eq. (4.63) below withk = 1, the ratio of exit to throat velocity is





ombining Eq. (4.44), Eq. (4.56) and Eq. (4.59) using gives

ince this equation cannot be solved explicitly for Pe , but Pe / P 0 < 1, then by successive approximations we obtaihe static vapor pressure at the exit of a short expanding conical nozzle:

where e is the base of the natural logarithms and the last P 0/ Pe has been replaced by as an approximation. Fylindrical nozzle, At = Ae and the static pressure at the exit is

where Pt is the throat pressure as given by Eq. (4.56). In this case the exit velocity,ve, equalsvt as given by Eq. (4.

When the forepressure is below the limiting value, the vapor temperature at the throat is

nd for organic vapors withk = 1.02 one can assumeTt = T 0, the boiler temperature, so that the acoustic velocity,vshe throat is essentially the same as the acoustic velocity at the boiler temperature,

When the forepressure is below the limiting value, the vapor diverges from the nozzle exit at supersonic velocientral portion of the vapor jet can be assumed to follow the hydrodynamic equations for streamline flow develrandtl and others for steam jets [68]. However, the outer regions of the vapor jet expand to such low pressuresontinuum physics cannot be applied, and the vapor expands freely according to the laws of kinetic theory so thattern in the outer fringe region can be estimated by superimposing a downward stream velocity on the randomirection and thermal velocity distribution according to Maxwell's equation.

igure 4.15 is a modification of a diagram first presented by Molthan [60] which shows that a hemispherical suadiusu, corresponding to some fixed value of the thermal molecular velocity for molecules escaping through an a wall between the vapor source and a high vacuum with zero initial stream velocity, becomes displaced in tirection of a superimposed vapor stream velocity,v, of the vapor on the other side of the wall. Choosing, as Gaecircular hole with





Fig. 4.15Displacement of vapor stream pattern

diverging from slit c for fixed thermal velocity,u, by superimposing a stream velocity,v.

iameterd , then when the mean free path of a vapor molecule in the vapor at the hole is less than 10 times the d

Molthan assumed that the vapor does not emerge from the hole according to the cosine law but rather emergqual probability in all directions so that the density of molecules at any point on the hemispherical surface of rwill be a constant.

he magnitude of the thermal velocity,u, varies from 0 to∞ with the probability,w(u), that the velocity lies betweend u + du being given by Maxwell's distribution law:

where the unit of the velocityu is chosen as the most probable velocity

As a result of the translation of the surface of a given radiusu in the directionv, the flux per unit solid angle in diffirections is no longer the same. Let a line (which will be termed the x-axis) be drawn on the surface of the wall thhe center of the hole and parallel to the stream velocityv, then any plane through this line cuts out two semicirclehe two hemispheres as shown in Fig. 4.15. The intersection of this plane (which will be called the ''diagram pla

with a plane through the center of the hole and perpendicular to the stream direction determines the line . T

alculate the new density distribution on the displaced hemisphere, consider a small arc on the initial sem

which is displaced to the position of equal arc length, on the displaced semicircle. A plane passed throug

ne orthogonal to the diagram plane will determine a dihedral angleθ with the plane through perpendicuhe stream direction, and a plane passed through orthogonal to the diagram plane will form the dihedral anθ

with the plane through . Now let the arc represent a small surface element, AB, cut from the hemisphere blanes forming the dihedral angle and planes through x-axis. The solid angle determined by the surface element AB wow be greater than the solid angle atc determined by the surface element A'B' of area equal to that of AB. As showhe diagram, let the latter solid angle also determine the surface elementab on the hemisphere of radiusu. The vapo





ream flux per unit solid angle will then be greater in the direction of A'B' (or ab ) than in the direction of AB by theatio A'B' : ab . To find this ratio, form the intersection of all the rays within the solid angle A'B' and a sphere of radi

which cuts the ray at B" . Then the spherical surface element of area A'B" determines the solid angle

while the element AB determines the solid angle AB/u2 which is numerically equal to A'B'/u 2. For infinitesimal surflements we have

whereψ is the dihedral angle B'A'B" which is numerically equal to the dihedral angle AcA' = θ ' θ, where angles to thght ofcB are considered positive and angles to the left are considered negative. Then

or surface elements on the portion of the displaced hemisphere to the left of the plane through , this ratio wess than unity corresponding to reduced flux per unit solid angle in directions with x-components opposite to the st

elocity vector. Forθ' = 0, corresponding to a surface element of the displaced hemisphere intersecting the line ux is unchanged becauseab = AB. The probability that a molecule has the velocityu now depends on the directioight, θ', so that Eq. (4.65) must be replaced by

n whichβ = θ + π/2 is the angle betweenv and u, and

Only those molecules having a backward component of thermal velocity greater than the downward stream vele able to travel back through the nozzle clearance area. For a cylindrical nozzle the vapor velocity at the centeozzle exit will be near the acoustic velocity, which for mercury is only 0.8 times the mean thermal velocity, soonsiderable fraction of the vapor molecules will be scattered back through the clearance area. For these molecegative. To





etermine this fraction it is necessary to find the value of the integral

whereθ' has been eliminated using Eq. (4.72).

or vapor molecules with positiveθ' the lower limit of integration is replaced by

ecause then molecules with thermal velocities,u, smaller than the stream velocity,v, contribute to the flow, depenn θ'.

Molthan evaluates the integral equations for Z (θ) by a series expansion of the integrand in different quadrants andse of the Error Function when appropriate. He then uses the relation

o convert the distribution Z (θ) to a function ofθ', which can be denoted D(θ'), and which Molthan presents in tabuorm. For a stream velocityv = vs, the velocity of sound in the vapor, his calculated values are given in Table 4.2

Neglecting friction at the nozzle wall, Molthan obtains the vapor jet pattern shown in Fig. 4.16.

he outer curved dashed line is orthogonal to all streamlines. Along this dashed line the distance between tworeamlines is proportional to the mean free path of gas through the vapor. In the regiona where vapor travels backom the edge of the nozzle exit, Molthan calculates that the mean free path is 4.742/0.063 = 75 times greater th

egionb in the center of the vapor jet. For mercury vapor at 133 Pa and 400 K the mean free path of nitrogen thhe vapor is about 7 × 103 cm, and if this vapor pressure and temperature occurs in the regionb, then the mean free

Table 4.2. Molthan Angular Distribution Function

θ ' D(θ') θ' D(θ')90° 0.063

0°10'0.422

73°20' 0.07015°50'

0.757

60°10' 0.08130°40'

1.309

44°40' 0.11145°40'

2.139

28°40' 0.16960°30'

3.177



16°20' 0.24790°

4.742





Fig. 4.16Scattering of mercury-vapor stream atthe exit of a cylindrical nozzle [60].

or nitrogen through the vapor in the regiona will be about 0.53 cm, which is comparable to the slit width in Lanylindrical nozzle pump.

Molthan did his work under Gaede's direction, and one purpose of his mathematical analysis was to confirm Gypothesis that the speed of all diffusion pumps, including Langmuir's pump, will become small when the meaath of gas through the vapor at the pumping annulus (nozzle clearance area) becomes smaller than the "slit

width" (distance from nozzle exit rim to pump wall). Alexander [62] applied an analysis similar to Molthan'sapparently without having read Molthan's papers) and came to the conclusion that Gaede's diffusion principle xplain the action of vapor-stream pumps. By using a mercury vapor pump with an expanding nozzle, he showhe vapor stream is mainly directed downward away from the nozzle clearance area and very little vapor is scatackward. Using a long vertical tube to probe the vapor jet, Alexander obtained the isobars of gas pressure shoig. 4.13. However, Jaeckel [69] considering the same problem disagrees with Alexander's conclusion. Also, A

Witty [70] showed that Alexander's criticism of Gaedes' theory was based on a misconception of Gaede's meanath rule.

Molthan obtained a corrected form of Gaede'sα factor by dividing the original hemispherical surface centered onole c into zones of area







However, one can also use differentials,

hen, instead of Gaede's Eq. (4.38), one now has for the vapor concentration atd σ,

where D(θ ') is Molthan's vapor dispersion factor. Molthan omits the factor cosϕ for simplicity since it is difficult tntegrate this factor over a zoneσ (or d σ). Gaede'sα formula is then modified to

where K is of the order of unity and depends on the method of correcting for the variation over the angleϕ with theormal to the plane of the hole. Since

he general effect of K is to introduce a factor of 1/2. Molthan's failure to account for the angleϕ leads him to thencorrect resultα = 2 whenλ0→∞ and hence a maximum flow of 734 cm3 · s1 through a hole whose area is 0.0m2.

Oyama [71] criticized Molthan's assumption of spherical symmetry for the velocity directions of the thermal m

he grounds that the gas is expanding after leaving the nozzle and not in thermal equilibrium and in fact may inondensation into liquid droplets. He also questioned Molthan's assumption that the cosine law did not apply toapor crossing the hole, although Molthan may have been justified in this assumption for the case that the meanath is less thand /10. However, the cosine factor should be included for the gas molecules crossing the hole sin

mean free path is greater thand , but Molthan omitted this factor. Oyama considered the problem in two dimensiopplied the PrandtlMeyer theory of the supersonic flow around the edge of a flat wall where the streamlines cuutward until the vapor is expanded to the point at which the mean free path was 1 mm, after which he consideapor to continue in the same direction in a straight line without further change in velocity. By integrating overossible values of the thermal velocityu he calculates the angular distribution of the molecular flux from aonexpanding (two-dimensional) nozzle as a function of the angleθv between the molecular velocityw and the streelocityv for mercury vapor withk = 5/3 and for a vapor withk = 20/19 = 1.053 for three different boiler pressure

he PrandtlMeyer formula [68] for the bending of the streamlines of a vapor expanding adiabatically with specatio k around the edge of a horizontal flat plate in two dimensions into a vacuum is





where r is the radial distance from the edge as a function ofϕ, the angle of turning measured from the starting rayhrough the edge to the initial point on the streamline at which the velocity component along the ray direction ihat the ray makes the angle 90° with the stream velocity. For a hypothetical nonexpanding nozzle with a rectanross section of widthd and length so great that the flow can be considered in two dimensions only, the vapor stelocity at the exit plane will equal the acoustic velocity and be directed parallel to the nozzle axis so that the romponent toward the nozzle edge is zero and no lateral expansion occurs until the vapor has crossed this exit hen for streamlines starting near one edge of this nozzle the angleϕ equals 0 for the ray lying in the exit plane an the vertical distance to the streamline as it crosses the exit. For mercury vapor,k = 5/3 and the expression in therackets becomes cos(ϕ/2); thus the maximum angle of turning is 180°, at whichr = ∞. For organic vapors, such as

Octoil,k = 1.02, and theoretically for hydrodynamic flow with adiabatic expansion the maximum angle of turni

would be so that the vapor streamline closest to the wall of the flat nozzle could curl right aroundnd flow backward on the underside. However, when the vapor has expanded to the point that the mean free paonger small compared to the width (of orderd ) of the vapor jet, the path of the molecules is no longer influencedradient in the vapor pressure but is determined by the local stream velocity and the random thermal motion at emperature as calculated by Molthan. A plot of Eq. (4.81) for the casek = 1.02 is shown in Fig. 4.17.

Fig. 4.17Two-dimensional streamline flow pattern around edge of

flat plate into vacuum for organic pump fluid vapor.





Fig. 4.18Expansion ratio fork = 1.02 as a function of the angle

of turning. Nozzle exit plane horizontal.

he static vapor pressure decreases along a streamline as the vapor expands, so that the pressure P at (r , ϕ) is a certaaction of the initial vapor pressure, P 0, before any expansion occurs as given by the PrandtlMeyer formula [68]

wherek is the specific heat ratio and P 0 can be considered to be the boiler pressure. A plot of this equation for th= 1.02 is given in Fig. 4.18, where P 0 is the boiler pressure and Pe = 0.602 P 0 is the static vapor pressure at the eepresented by the horizontal line), whereϕ = 0, of the above hypothetical flat rectangular nozzle or of an equivonexpanding annular nozzle formed by concentric cylinders of very large diameter. Atϕ = 180° the ratio is 3.6 ×

able 4.3 lists numerical values for the PrandtlMeyer ratiosr/r 0 and P/P 0 for Octoil (k = 1.02) and mercury (k = 5/3

y an application of L'Hôpital's rule for the evaluation of indeterminate forms it can be shown that for organic uids withk → 1, Eq. (4.81) reduces to the very simple form

which is equivalent to the isothermal solution of the problem of steady flow around a corner as given in Stodoloewenstein [68, p. 983]. Similarly, ask → 1, Eq. (4.82) reduces to







able 4.3. PrandtlMeyer Ratios

k = 1.02 k = 1.67 ϕ k = 1.02 k = 1.67

r/r 0 P/P 0 r/r 0 P/P 0 r/r 0 P/P 0 r/r 0 P/P 0

01.0039 0.602 1.0049 0.487

90 3.45070.170

4.000 0.086

51.0153 0.600 1.0154 0.485

100 4.62320.126

5.8582 0.053

101.0349 0.593 1.0350 0.478

110 6.38570.091

9.2421 0.030

151.0629 0.581 1.0632 0.467

120 9.11580.063

16.000 0.015

201.1000 0.567 1.1007 0.451

135 16.4770.0345

46.642 0.004

301.1471 0.523 1.1488 0.410

150 32.0310.0175

88.731 0.0006

401.2762 0.469 1.2824 0.357

180 151.153.6 × 103

∞ 0

501.4641 0.408 1.4821 0.298

195 367.31.5 × 103

601.7322 0.344 1.7778 0.237

210 9655.4 × 104

702.1128 0.281 2.2212 0.180

240 84505.9 × 105

802.6589 0.222 2.9036 0.129

270102800 4.7 × 106

d using Eq. (4.62) this becomes

here Pe is the static vapor pressure at the exit of a short cylindrical nozzle of large diameter or of a concentric cylinder nozzle of largedius so that the flow pattern is approximately two-dimensional. It is evident that the static pressure is assumed to be constant along anth fixed angleϕ. Combining Eqs. (4.83) and (4.85) gives

us for organic vapors issuing from the type of nozzle specified above, the static vapor pressure in the jet is inversely proportional to ththe ray from the edge of the nozzle to the intersection with the streamline starting atr 0. For concentric cylinder nozzles with finite mean

dius, one might expect the vapor pressure to decrease as some higher power of 1/r .

sing Eqs. (4.86) and (4.83) the mean free path of a vapor molecule through the vapor at (r , ϕ) will be given by

here T is the local vapor temperature,σv is the mean molecular diameter (in cm), and the pressure is expressed in Pa. As an example,nsider Octoil withσv = 1.2 × 107 cm at a local temperature of 160°C (433 K) and boiler pressure P 0 = 67 Pa, for whichλv = 2.33 × 103 ex2/2). If we assume that the boundary between hydrodynamic theory (continuum) flow and kinetic theory scattering occurs when the mee path is of the order of 0.1 cm, then the boundary angle will be





= 2.742 rad = 157.1°, which from Fig. 4.17 occurs in front of the nozzle so that kinetic theory must be used fapor molecules scattered back through the nozzle clearance area.

As the vapor expands the flow velocity,v(r , ϕ), becomes greater than the acoustic velocity,vs, and the Mach numbiven byv(r , ϕ)/vs. Stodola defines a Mach angle,ψ , by

wherevr is the component of the stream velocityv(r , ϕ) directed downward along the ray from the turning edge. Ahe starting ray we haveϕ = 0, ψ = 0, andvr = 0, so that no lateral expansion has begun and the ray is perpendicuhe streamline.

or Octoil withk = 1.02 this becomes

r for k → 1 by L'Hôpital's rule we have tanψ = ϕ.

he acute angle between a ray from the nozzle rim and the tangent line to a streamline is the complement of Mngle, orψ c = (π/2) ψ , as defined by Stodola, and this angle is constant for all streamlines cutting a given ray asn Fig. 4.19, which is adapted from Fig. 954 in Stodola and Loewenstein.



Fig. 4.19Prandtl's two-dimensional flow around a corner into gas at pressure p2 [68].





Nöller [72] has modified Oyama's approach by calculating the angular distribution function from the state of mapor at the discontinuity surface between the PrandtlMeyer expansion and molecular flow and by assuming thbserver moving with the preferred velocity will observe a normal Maxwellian velocity distribution at that poiniscontinuity surface the mean free path is not kept constant but rather the Knudsen numberλ/ x is kept constant, x bhe distance from the edge of the nozzle. He applies this approach to a nozzle for which the mercury vapor velohe exit is 2.2 times the acoustic velocity; thus from Eq. (4.88) the angleϕ in the Prandtl diagram increases from 0 arting ray inside the nozzle toϕ = 95.45° at the ray corresponding to Mach 2.2, as compared to the angleϕ = 53.13

or the Mach 1.0 case above. For an exit velocity of Mach 2.2 the Mach angle at the exit isψ = 65.56° as compared45° for the Mach 1.0 case. The starting ray for the Mach 2.2 case is thus rotated counterclockwise by about 2

espect to the starting ray for the Mach 1.0 case. This rotates the ray pattern for a nozzle with the acoustic velocxist counterclockwise by about 21°, so that the streamlines are less divergent.

n the above cases the normal to the exit plane of the nozzle was parallel to the axis of symmetry of the nozzle.However, many diffusion pump designs involve nozzles for which this normal makes an angle with the axis ofymmetry for which we use the termbeveled exit . Nozzles of this type are used in steam turbines, and Zerkowitz as analyzed the deflection of the jet pattern away from the nozzle axis. Applying his equations for the case of

with specific heat ratiok = 1.02, we [67] obtain for a nonexpanding nozzle with exit plane making the angleϕ = 65°with a plane orthogonal to the axis of symmetry a jet deflection of the middle streamline by 36° as shown in Fi

Fig. 4.20Oil-vapor jet deflection

from nonexpanding verticalnozzle with beveled exit.





n moving from the plane CD orthogonal to the nozzle axis at the outer rim to the exit plane CE the static vapoecreases from P 1 to P 2 and the vapor velocity increases. The ratio P 2/ P 1 will be a function of the angleϕ, anderkowitz assumes that this ratio will be given by the PrandtlMeyer equation [Eq. (4.82)]. The velocity vector apor crossing the middle of the beveled exit CE can be shown to have the magnitude

wherevs is the acoustic velocity at the throat and makes the angle with the nozzle axis as given by

or a bevel angleϕ = 65° this givesv2 = 1.6vs and But there is a further deflection after leaving the elane CE as shown by Fig. 7 in the Zerkowitz article. As the vapor crosses the exit plane CE it is free to expan

des so that the pressure beyond the exit, P 3 is lower than P 2 and there is a driving pressure, P 2 P 3, acting in airection perpendicular to CE. The derivation of the equation [67] for this second deflection will not be given hhe result for oil vapor withk → 1 is the additional angleε as given by

When the throughput is small so that the inlet pressure and forepressure are low, one can assume P 3 small compare

2 so thatε = 16° and the total jet deflection along the middle streamline is as shown in Fig. 4.20iasova et al. [74] computed the vapor flow from the top-stage nozzle of a diffusion pump by a marching proce

he frames of parabolized NavierStokes equations. These authors also computed the gas flow through the pumpnd into the vapor stream by the Monte Carlo method and computed the net pumping speed to be expected for nlet chamber design and vapor stagnation density. Sadykov and Figurov [75] investigated the vapor flow insidozzles experimentally with the help of Pitot tubes and in the free jet beyond the nozzle exit by pressure and





emperature measuring instruments. They also calculated theoretically the vapor flow allowing for a boundary sing the equations of aerodynamics and rarefied gas dynamics. The mixing of the pumped gas with the vapor ackstreaming region and the forward pumping region was measured with pressure probes. Backstreaming ratenlet stage was measured by weighing. Heating the nozzle to 25 K higher than the vapor conduit decreased theackstreaming by 20%.

Attempts to explain the operation of diffusion pumps by kinetic theory considerations of the collisions of gas mnd vapor molecules were made by Riddiford and Coe [76], by Reichelt [77], by Florescu [63], and by Tóth [7

.4.4Ultimate Pressure

Many authors have discussed the ultimate pressure obtainable with diffusion pumps which depends mainly on factors: (1) the back-diffusion [61] of gas from the fore-vacuum through the vapor jets to the high-vacuum sideapor pressure of the pump fluid [7, 79, 80] condensed on the walls of the inlet chamber or on baffles over the he evolution from the oil in the boiler of dissolved gas and low-molecular-weight (cracking) fragments [33, 34ecomposition of the pump oil; and (4) the outgassing [81] of the vacuum system beyond the pump. In addition

migration of oil vapor from a mechanical forepump may contaminate the system when the diffusion pump is no

perating and no valves are closed. This source of contamination can be reduced by the use of a purge gas durihutdown [45].

ack-Diffusion of Gases from the Fore-Vacuum. Several authors have derived a first approximation to a more expheoretical value of the back-diffusion coefficientβ than that given by Gaede's simple Eq. (4.34). Matricon [82]ssumed that the vapor jet from a cylindrical nozzle in a single-stage mercury vapor pump could be simulated braight lines of flow originating at a point inside the nozzle exit at a distance from the exit plane of about one-

he exit diameter. However, to derive a formula for theβ factor, as a first approximation, he assumed that in the ref counterdiffusion of vapor and gas from the fore-vacuum the pressure gradient from the axis to the wall at anistance x along the axis from the nozzle exit was negligible and that no condensation of mercury vapor occurrehe distance x = 0 to x = L, where L is the useful length of the vapor jet when the forepressure is so low that the vream is not obstructed by the gas in the fore-vacuum. Then he obtains

where N is the concentration andv is the stream velocity of the vapor molecules independent of x, while D0 is the van cm1 · s1) of the gas-vapor diffusion coefficient at unit vapor concentration. Using the Meyer formula for theiffusion coefficient and the StefanMaxwell formula for the mean free path through a binary mixture, Matricon





able 4.4. Calculated Diffusion Coefficients at 101308 Pa and 160°C

nits σ(108 cm)

σ '(108 cm)

M (g) M ' (g) D0(1018 cm1·s1)

D760(cm2/s)

irmercury3.11 5.67 29 200.6 2.88 0.17

irmercury

3.72 4.50 29 200.6 3.30 0.19irOctoil

3.11 12 29 390 0.99 0.058

ydrogenmercury2.38 5.67 2 200.6 13.9 0.82

ydrogenmercury2.74 4.50 2 200.6 17.2 1.01

ydrogenOctoil2.38 12 2 390 4.35 0.257

eliummercury2.2 3.5 4 200.6 19.6 1.16

eliumOctoil2.2 12 4 390 3.2 0.19

euteriumOctoil2.38 12 4 390 3.1 0.18

760 = D0/ N 760 = 5.9 × 1020 D0 at 160°C

here σa = (σ + σ ')/2 is the mutual collision diameter for the gas and mercury molecules, M is the molecular weight of the gas, M ' is theolecular weight of the vapor, andT is the absolute temperature of the gas within the vapor stream. The diffusion coefficient D760 (in cm2 · 101,308 Pa (760 Torr) as used in Eq. (4.34) is obtained from

here N 760 is the concentration of vapor molecules at 101,308 Pa and the specified temperature.

lues of the diffusion coefficient D760 for various gas-vapor combinationsT = 160°C and 101,308 Pa as calculated by Dayton [61] fromatricon's formula are listed in Table 4.4 together with the values of D0. The mean diameterσ ' = 5.67 × 108 cm for mercury,σ = 3.11 × 108

m for air, andσ = 2.38 × 108 cm for hydrogen are the values used by Matricon. Texts on kinetic theory giveσ ' = 4.50 × 108 cm for mercury50°C),σ = 3.72 × 108 cm for air, andσ = 2.74 × 108 cm for hydrogen. The valueσ ' = 12 × 108 cm for Octoil was estimated by Jacobs anapff [83].

aede [2] measured an average value D760 = 0.18 cm2 · s1 for air through mercury vapor and an average value D760 = 0.66 cm2 · s1 fordrogen through mercury vapor at 140°C. It may be noted that D0 is proportional toT ½ while D760 is proportional toT 3/2.

ertenstein [84] and Jaeckel [69] also arrive at Eq. (4.96) but use Enskog's [85] formula for D0,

his equation gives values of D0 about 10% lower than those from Eq. (4.97) using the same constants. Jaeckel citesσ = 2.7 × 108 cm fordrogen and 3.68 × 108 cm





or air. The ratio of the diffusion coefficient for hydrogen through mercury to the coefficient for air through mebout 4.8, while the ratio for hydrogen to air for diffusion through an organic vapor such as Octoil is about 4.4.

or a cylindrical nozzle with no loss from throat to exit the stream velocity,ve, of Octoil at the exit is the acousticelocity as given by Eq. (4.64). The molecular concentration of vapor at the exit will be the same as at the thro

where Na is Avogadro's number and P 0 is the vapor pressure in dyne · cm2. When P 0 is expressed in Pa, one must

f we now assume that the nozzle clearance is small compared to the diameter of the nozzle exit, then, as the vaows from the cylindrical nozzle exit into a condenser with a cross section only slightly larger than the nozzle apor concentration will be only slightly decreased and the stream velocity only slightly increased, so that the pv will be approximately equal to Neve = Ntvt . Then for an organic vapor, such as Octoil, Eq. (4.96) with P 0 in Paecomes

with D0 in cgs units given by either Eq. (4.97) or Eq. (4.99) and assuming that the temperatureT of the gas in thesequations equals the vapor temperatureT 0 and that very little condensation of the vapor jet occurs within the distom the nozzle exit. As an example, at the relatively low temperature of 160°C orT 0 = 433 K the vapor pressure, P f Octoil is about 13.33 Pa; and using M ' = 390, R0 = 8.31 × 107, Na = 6.02 × 1023, D0 = 1018 cm1 · s1, and L = 5 q. (4.102) givesβ = 3.35 × 1029 for air through Octoil. Using D0 = 4.35 × 1018 cm1 · s1 for hydrogen through Oives β = 2.84 × 107, so that a forepressure of 1 Pa of hydrogen would limit the ultimate pressure to pu = 2.84 × 107

Actually, there is considerable condensation of vapor over the distance L which is determined by the position of thhock boundary created by the forepressure; and the ratio of nozzle throat area to body clearance area is about or the last stage (nearest the fore-vacuum), so that the static vapor pressure at the body clearance area is about /3 of the pressure at the throat, which in turn is about 0.6 times the boiler pressure P 0. Thus, even for the moreommon temperature 180°C and boiler pressure P 0 = 67 Pa, theβ coefficient for hydrogen through Octoil can be rder of 107 or greater.

heory of Pump Performance in the Forepressure Breakdown Region. A shock boundary is formed between the vet and the gas in the fore-vacuum when the forepressure rises above 1 Pa. The vapor expanding from the nozzavels with increasing supersonic velocity, and the static vapor pressure decreases as the jet expands and diver

oward the pump walls. Any obstruction, such as a Pitot tube which has a small opening at the tip of a tapered nlaced in the vapor stream





which permits the vapor to escape laterally will result in a compression shock in front of the obstruction as the elocity perpendicular to the obstruction is reduced to zero. The law of conservation of momentum requires tharessure is exerted on the obstruction when the latter is fixed in position. According to the definition in Stodolaoewenstein, [68, p. 85], this pressure, known as the ''impact pressure" or "dynamic pressure," is the reading of

manometer attached to the open channel in the Pitot tube. The magnitude of this pressure depends on the residumomentum in the vapor stream after lateral dispersion and on the heat transferred to the Pitot tube. It has been

öliger (and independently by Prandtl) that the impact pressure can be calculated by assuming that a compressollowed by an adiabatic compression takes place in front of the pointed end of the Pitot tube until the kinetic ehe flow is consumed. The shock arises from the sudden conversion of stream momentum into static pressure aapor at supersonic velocity impinges on vapor moving with subsonic velocity.

he method of computing the impact pressure given in Stodola and Loewenstein involves the tracing of the "cooci" on the entropy diagram [68, Fig. 51]. The condition change leads from the initial condition A1 along the Fnd Rayleigh curves to the shock point A2, and from there adiabatically to the impact pressure Pi . The Fanno line isiven by combining the total energy per unit mass equation

where P 1 is the initial static pressure and P 2 is the final static pressure while E 1 and E 2 are the initial and final intenergies per unit mass due to molecular rotation and vibration, with the equation of continuity

where a1 and a2 are cross sections in a tube of flow. For adiabatic expansion [86] we obtain

he Rayleigh line is obtained by combining the equation of continuity with the impulse-momentum equation

ince compression shock occurs in a very thin zone over the shock boundary,a1 and a2 will be approximately equor perfect gases the algebraic solution for the intersection of the Fanno and Rayleigh lines is easily obtained, g

he static pressure after the compression shock the following equation:





r for organic vapors withk → 1 we obtain

which is the total flux of stream momentum per unit area before the shock. Prandtl's solution for the stream velfter the shock is

or organic vapors withk → 1 we obtain

wherevs1 is the value of the acoustic velocity under the initial conditions. There can be no shock unless the iniream velocityv1 exceeds the acoustic velocityvs1 for the initial state. From Eq. (4.110) it is obvious that if the iream velocity is much larger than the acoustic velocity, the final velocityv2 after the shock will be a small fractio

he acoustic velocity. After the shock the vapor is compressed adiabatically and the stream velocity falls fromv2 to zwhile the static pressure rises to the final maximum value which represents the impact pressure, Pi .

When measuring the impact pressure at the throat of a nozzle, there is no compression shock, but the process odiabatic expansion is suddenly reversed to one of adiabatic compression. Then in Eq. (4.110) bothv2 and v1 equal coustic velocity,vs, at the throat and P 2 = P 1 = Pt . The measured impact pressure at the throat then equals the bressure, P 0, for which the vapor stream velocity is zero. All streamlines are parallel at the throat and remain pahe nozzle axis when the nozzle is cylindrical and short so that no energy is lost at the walls, but in expanding cozzles of the DeLaval type the streamlines diverge and the impact pressure at the exit is less than the boiler pr

However, in an expanding nozzle with walls curved in a certain way, the Prandtl nozzle, all the streamlines at t

an be made parallel to the nozzle axis and to each other. However, for most diffusion pumps the expanding noave straight walls and the vapor acquires some momentum in directions perpendicular to the axis in passing frhroat to the exit. In expanding from the acoustic velocity at the throat to supersonic velocity at the exit of a Deozzle, some of the energy of random motion is converted into a flux of forward momentum parallel to the noznd the impact pressure at the exit is difficult to calculate. As shown by Fig. 49 in Stodola and Loewenstein [68xpansion of steam through a DeLaval nozzle, the measured impact pressure at the exit is given approximately

where At/Ae is the ratio of throat area to exit area andC is somewhat greater than 1.0.

y application of the definitions [87] of pressure in terms of momentum flux with respect to a specified surfacempact pressure can be related to the dynamic pressure as given by





wheren is the number of molecules in unit volume,m is the mass of each molecule,

the average molecular velocity, andv is the stream velocity perpendicular to the surface. The impact pressure ibtained by omitting the last term on the right since molecules moving with velocityua v in the negative direction wespect to the surface normal will never strike the surface of the shock boundary. Since the vapor velocity at th

ne can substitute

roceeding in this manner the author [67] obtained the following as an approximate formula for the coefficientC :

or example, for steam through the nozzle studied by Löliger [68, p. 85, Fig. 49] we have At/Ae = 0.238,k = 1.3, Pe/0.05, Pt = 0.546 P 0, andC = 1.402, giving a computed impact pressure Pie = 0.33 P 0 close to the experimental va

.34 P 0 obtained by Löliger. For oil vapor withk = 1.02, and assumingTe = Tt , the same nozzle givesve/vt = 2.31830 = 0.0615, Pt/P 0 = 0.602,C = 1.502, and Pie = 0.36 P 0. When Ae = At and k = 1.02, Eqs. (4.117) and (4.119) givt = 1.1 and Eq. (4.116) givesC = 0.96 corresponding to Pie = 0.96 P 0.







Fig. 4.21Shock boundary near forepressure breakdown [15].

After the vapor leaves the nozzle the vapor diverges rapidly and the impact pressure for direct compression shoepend on a narrow bundle of streamlines intercepted at the shock boundary and the distance traveled from thexit. For cylindrical or expanding conical nozzles it has been found experimentally that as a good approximatioe assumed that the vapor diverges in straight lines from a point source located inside the nozzle on the axis at istance depending on the vapor velocity at the exit. For oil vapor through cylindrical nozzles with velocity aboo the acoustic velocity at the exit, this distance appears to be about one-half the diameter of the nozzle exit, soom the source point passing through the rim of the nozzle exit makes an angle of 45° with the nozzle axis and

wall of the pump casing. From Table 4.3 it can be seen that the static vapor pressure along this ray (ϕ = 135°) is abo.035 times the boiler pressure, or 2.3 Pa when P 0 = 67 Pa. For vapor diverging from a virtual point source the (dhock boundary can be expected to form on a spherical surface perpendicular to each ray from the source. Thatctually occurs in pumps with cylindrical or conical nozzles is shown by glow discharge experiments reported b

Dayton [61] and by Kutscher [15]. The curved shock boundary shape is particularly noticeable just at the pointorepressure breakdown as shown by Fig. 10 in Dayton [61] and by Fig. 4.21 adapted from Kutscher's article (wncludes some regions of oblique shock).

ince Eq. (4.111) indicates that the impact pressure is roughly inversely proportional to the ratio Ae/At of exit area throat area, as an approximation it can be assumed that the impact pressure at the wall of a pump with cylindric inversely proportional to the square of the radiusr from the hypothetical point source, wherer is greater than the

adius to the rim of the nozzle exit. Then from Fig. 4.22,r 2 = R2 + ( x + xs)2, where R is the radius of the pump casnd xs is the distance between the point source and the exit plane. The impact pressure at x will then be given by





Fig. 4.22Distance x of shock boundary at wall from plane of nozzle

exit with hypothetical point source of vapor flow.

where rn is the radius of the cylindrical nozzle and Pie is the impact pressure at the rim of the nozzle exit.

Assuming that at every point on the shock boundary before jet breakdown the impact pressure Pix equals theorepressure F and that the impact pressure at the nozzle exit, Pie , is given by Eq. (4.111), then using xs = rn we obt

where rt is the radius of the nozzle throat. From Fig. 4.22 the forepressure breakdown, F = Fb , occurs when the shooundary has been pushed back to x = x0 = R rn . Then for cylindrical nozzles we obtain

where B = π R2 is the body-clearance area and At is the nozzle throat area.

or most metal diffusion pumps the nozzle is constructed of concentric cylinders or cones so that the throat andross sections are annular with a width small compared to the mean radius. Then, as an approximation we can hat the vapor disperses in straight lines from a line source (circle of large radius) orthogonal to the plane throuump axis and located within the nozzle at a short distance from the exit of the order of one-half the width of thhown in Fig. 4.23.

he dashed line ti = R rB is the width of the body clearance area, B, and the angleφ gives the deflection of theenterline of the jet caused by the presence of the streamliner (or apron)hj. For each stage, the breakdown forepresb , at which the outer edge of the shock boundary is close to the pointt , is determined by the ratio of the nozzle threa, Ae, to the body clearance area and the amount of the jet deflectionφ. Then, as an approximation, the impactressure at a point on the pump casing wall located at the distance x from the plane of the nozzle exit will be given







Fig. 4.23Dispersion characteristics of inverted annular nozzle.

where Pie is the impact pressure at the nozzle exit, xs is the distance of the source from the plane of the nozzle exrhe distance of the source from the pump axis, R is the radius of the pump casing,θ + φ is the angle between the vene through the source and the ray from the source which passes through the rim of the nozzle exit, andn is an inde

which equals 1 for annular nozzles in which the throat widthw and the body clearance ti are small compared to thasing radius R, but which approaches the value 2 asrs → 0 corresponding to the previous case of a cylindrical noom which the vapor is assumed to issue from a point source. In general, the impact pressure at the casing walmaximum and forepressure breakdown will occur when the shock boundary reaches the pointt where x = x0. At thoint, F = Fb = P 1 and

o that the breakdown forepressure is







can be seen from the similar triangles in Fig. 4.23 that

o that, using Eq. (4.111) withC replaced by the empirical constant Kn, we obtain

which is equivalent to Eq. (4.122) whenn = 2 andrs = 0. Whenn = 1 and R rn is small compared torn , the ratio (rn R rm) will be approximately equal to the ratio of nozzle exit area, Ae, to the body clearance area, B. Then from Eqs4.126) and (4.127) whenn = 1 the general formula for the limiting forepressure is

xperimental data on various pumping stages has shown that the limiting forepressure is given by Eq. (4.128) w Kalues which in general range from 0.5 to 1.1.

o calculate theβ coefficient it is necessary to compute the rate of diffusion of gas from the fore-vacuum througapor jet from the boundaryuu ' at the forepressure F to the boundary te with the high vacuum pressure p. The lengthhe vertical diffusion path, Lj, between these boundaries can be calculated from the given geometry, and integrate performed over the upper boundary. However, it is obvious that most of the back-diffusion will occur where Lj ismallest, or close to the casing wall through a barrier of thicknessut = x x0, where from the above equations we ob

rom Fig. 4.23 we have

hen the thickness of the diffusion barrier at the casing wall is

ubstituting this for L in Eq. (4.34) together with mean values for the static vapor pressure P and the vertical compo

f the streamline velocity,v, at the casing wall obtained by extrapolating Eqs. (4.117) and (4.119) in terms of thexpansion ratio Ae/B to the region x x0 would then give an approximate formula forβ as a function of the forepress. A more exact relationship could be obtained by extrapolating these equations from the nozzle exit to the crot x to obtain the vertical component of stream velocity near the wall,vx( x), as a function of the distance x and the stapor pressure near the wall, P ( x), as a function of x and then substituting





hese functions in place ofv and P in Eq. (4.33), integrating from x x0 to x, and then using Eqs. (4.129) and (4.130

apor Pressure of Fluid Condensed in the Inlet Chamber or on Baffles. The vapor pressure of the fluid condensedwalls near the inlet of the pump (and baffle) can be reduced by proper design of fractionating pumps and baffles the use of cold traps. For fractionating pumps with water-cooled baffles the ultimate pressure limit due to puapor will be slightly less than the vapor pressure in Pa at 25°C as given in the next-to-the-last column in Tablehe given pump oil. Use of the more stable fluids, such as Convalex-10, Santovac-5, or DC-705 with the additiold trap cooled to below 40°C will usually allow ultimate pressures below 1 × 108 Pa when the forepressure iufficiently low. It has been reported [88,89] that using a system with an alumina or zeolite trap and gas purgerovisions to reduce contamination from the oil in mechanical forepumps and using a fractionating diffusion puolyphenyl ether pump fluid, a cold cap, a cryotrap chilled with liquid nitrogen or simply by circulating metha, and a high-vacuum gate valve with proper operating procedures can produce clean vacua as free of hydrocaO as those produced with conventional (hydrocarbon lubricated) turbopumps.





art IIMolecular Drag and Turbomolecular Pumps

örgen Henning

5Molecular Drag Pumps

A molecular drag pump is a vacuum pump in which gases are pumped by momentum transfer from a rapidly roolid surface to the gas molecules. The rotor impulse is transmitted to the particles by superposition of the thermelocity of the colliding particles with the velocity component of the moving rotor surface (Fig. 4.24). The non

motion of the particles is changed to a directed motion in the pumping process. When the mean free path of theetween the collisions with other particles is larger than the spacing between the rotating and the stationary surmolecular flow range, typically < 0.1 Pa), particles collide primarily with the rotor, resulting in an efficient pumrocess, and there is no interacting influence of the different gases.

n the laminar flow range (typically > 0.1 Pa) the action of the rotor surface is restricted by the frequent collisioetween particles. Therefore, a molecular drag pump is not capable of pumping gases against atmospheric pres

must be backed by an adequate roughing pump.

he first pump of this type was introduced in 1913 by Gaede [90], when he presented his "Molecular Drag Pummultistage cylindrical rotor design, with parallel slots around the circumference of the rotor, into which projecxtensions from the outer casing.






Fig. 4.24Principle of operation ofmolecular drag pump.

A modified form of the molecular drag pump, designed by F. Holweck [91] in 1923, used a smooth cylindricaldrum) inside a housing with spiral channels, decreasing in depth toward the exhaust side. The intake was in th

f the housing and the gas was dragged to both ends of the housing, making use of twice the pumping speed.n 1940 Siegbahn [92] described his disc-type molecular drag pump using a disc-rotor. A circular disc rotates inontainer consisting of two side plates with spiral grooves. These grooves are deeper at the periphery (inlet) anradually decrease in depth toward the center (exhaust).

Up to the 1970s, only few researchers were interested in these "early" molecular drag pumps because of their reow pumping speed and their questionable reliability; furthermore, in those days there was no real demand for tumps. In order to attain low ultimate pressures with these pumps the clearances between rotating and stationa

were made a few hundreths of a millimeter only. Therefore, any change in temperature or intruding solid particesult in a failure of the pump, caused by a ceased rotor. However, recently, the basic ideas of Holweck (drum)slotted rotor), and Siegbahn (disc) were picked up again successfully in the design of modern pumps (moleculumps and combined molecular drag and turbomolecular pumps), in order to attain extremely low pressures an

make use of simple dry roughing pumps..5.1heoretical Considerations and Performance Data

he principal design of the pumping stage of a molecular drag pump is shown in Fig. 4.25. It does not make anifference if the pumping channel is located in the rotating or the stationary part of the pumping stage. Differen

methods have been developed to describe the pump performance of molecular drag and turbomolecular pumpsontinuum methods [93], and methods using statistical calculations [94] agree in the basic results concerning therformances. The values depend on the transmission probabilities ( P ) of the particles moving in and against theumping direction. For the molecular flow, these probabilities depend on the ratiov/u of the rotor speedv and the mhermal velocityu of the gas particle, but not on the pressure.

or a pumping channel, in the range of free molecular flow, the compression and the net flow rate (pumping spe calculated from the law of conservation of molecules by assuming that the velocity distribution function of oth sides





Fig. 4.25Principle design of a molecular

pumping stage:l , channellength;h, channel height;b,channel width; s, gap between

rotor and housing; FA , entrancearea; FB , exit area.

f the channel is Maxwellian. For steady-state flow, the net flow rateW (Ho-coefficient) from side A to side B canerived from

where PAB and PBA are the probabilities that a molecule incidenting from side A or B will be transmitted throug

hannel to side B or A, and FA and FB are the entrance area of side A and the exit area of side B, respectively. K = nA is the compression (n is the number of molecules) [95].

n order to calculate the performance of a molecular pumping stage, two extremes, the maximum compression K maxero flow) and the maximum pumping speedS max (for equal pressure on both sides of the pumping stage) must bnown.

rom Eq. (4.132) the following relations can be derived:

or maximum compression, no gas flow (W = 0):



he important problem to solve remains the calculation of PAB and PBA, which, for example, was solved by Krugnd Shapiro [94] using Monte Carlo techniques. As a result it was found, in agreement with calculations using

methods [93], that K max of a molecular drag pump is exponentially dependent on the rotor speedv,





pump-specific factor g (rotor and stator geometry), and the square root of the molecular weight M of the particlesumped:

or maximum pumping speed ( K = 1):

max is proportional to the product of a specific pump factorG (rotor and stator geometry) and the rotor speedv; it dot depend on the pressure and the kind of gas pumped, because the molecular arrival rate at the inlet is proporhe thermal velocity of the gas:

An operating pumping stage works in the region between these two extremes. For real pumping conditions (gashroughputQ = Spinlet) and different pressures on both sides of the pumping stage ( K = poutlet/ pinlet) the followinelation exists between compression K and real pumping speedS of a single pumping stage:

herefore, the pumping speed of a molecular drag pump depends on the compression and the pumping speedSv of tacking pump, as given in Eq. (4.138). From there it can be derived that if K max for any gas is small, the pumpingpeed for this gas is a function of the ratioS/Sv. For practical purposes a molecular drag pump with low K max for Heeds a larger backing pump to pump H2 effectively (lowS/Sv ratio).

Due to the inlet conductance of the pumping channel, there is a limitation ofS max and the actual pumping speedS omolecular drag pump becomes a function of the ratiov/u and therefore it will depend on the molecular weight of t

umped.

More exact calculations take into account the losses through gaps between the rotating and the stationary parts.However, the main relation, Eq. (4.138), remains the same.As for any vacuum pump, the ultimate pressure pf , that a molecular drag pump can attain can be calculated from

ressure pv at the outlet side of the pump by dividing it by the maximum compression K max:





Fig. 4.26Principle of multistage molecular

drag pump (Balzers Pfeiffer).

he increase of K max with the molecular weight M means that heavy molecules are highly compressed and have ackflow probability; this is the reason for the ''clean" vacuum without contamination by oil vapors and hydroc

.5.2Design Considerations

tand-alone molecular drag pumps are designed on the basis of the Holweck principle [91]. These pumps in genclude two different sections: (1) an entrance section with a row of turbomolecular pump blades for maximumonductance to ensure a high pumping speed and (2) subsequent molecular pumping stages (up to 5) having in drum design with a multiribbed structure to ensure efficiency and high compression (Fig. 4.26). These pumpsvailable with mechanical rotor bearings or a combination of mechanical and magnetic bearings. The lubricanthe mechanical bearings is either grease or oil. More details of the design of molecular drag pumps are given in.6.2.

.5.3ypical Performance Data of Commercial Pumps

he working range for molecular drag pumps is, depending on the manufacturer, between 103 and 103 Pa. Dueigh admissible foreline pressure, molecular drag pumps can use small, simple, dry, and inexpensive fore-vacuumps (e.g., membrane pumps) with an ultimate pressure of <103 Pa.





5.3.1ompression

Depending on the manufacturer's design, molecular drag pumps have the following compression values: H2, 2 × 103; He, 1 × 103 to 2 × 104; N2, 1 × 107 to 1 × 109.

5.3.2umping Speed

Molecular drag pumps are available in a pumping speed range from 7 to 300 liter · s1.

ype designations of molecular drag pumps often use the pumping speed for nitrogen. Therefore the pumping N2 is used as the 100% value. This value is compared to the pumping speed data for H2 and He. From the cataifferent manufacturers: H2, 40% to 56%; He, 53% to 67%.

5.3.3ltimate Pressure

Depending on how many molecular pumping stages are used in series, the attainable ultimate pressure is in the05 to 103 Pa.

6urbomolecular Pumps

he turbomolecular pump invented by Becker [96] in 1957 (Fig. 4.27) became commercially available in 1958hen it has become very popular in every field of high- and ultrahigh-vacuum technique, due to a clean, consistredictable vacuum created, the easy operation, and the advanced degree of operating reliability. The turbomolump is the only mechanical vacuum pump which, together with a roughing pump, can attain ultimate pressureange below 108 Pa. It is a bladed molecular turbine that compresses gases by momentum transfer from the rapotating blades of the rotor wheels to the gas molecules. It is working on the same principle as the molecular dr

When the mean free path of the particles is larger than the spacing between rotor and stator (molecular flow ranurbomolecular pump, typically <101 Pa), particles collide primarily with the rotor, resulting in an efficient pumrocess, and there is no interacting influence of the different gases. In the laminar flow range (typically in aurbomolecular pump > 101 Pa) the action of the rotor is restricted



Fig. 4.27Principle design of turbomolecular pump [96].





y frequent collisions between the particles. Therefore, a turbomolecular pump is not capable of pumping gasetmospheric pressure and must be backed by an adequate roughing pump.

he Becker design avoided the obvious disadvantages of the "early" molecular drag pumps (relative low pumppeed, questionable reliability): The turbomolecular pump is composed of a series of wheels with coaxial bladelternately fixed and moving. In each wheel the sides of the blades are inclined with respect to the axis, in one or the blades of the moving wheels and in the other for the blades of the fixed wheel. The moving wheels haveotational speed so that the peripheral speed of the blades (up to 500 m/s) is of the same order of magnitude as f the molecules of the pumped gas.

he distances between these wheels were in the range from several tenths to a few millimeters. The channels bhe inclined blades of the wheels act like elementary molecular drag pumps, similar to the Gaede molecular dra

All channels (~2050) on one wheel are connected in parallel and together can yield a high pumping speed up tohousand liters per second.

.6.1heoretical Considerations and Performance Data

A milestone for the understanding of turbomolecular pumps was the work published by Kruger and Shapiro in 94] on blading geometry of axial-flow molecular turbines in the molecular flow range. However, most lateralculations of the pumping speed characteristics made by several authors [93, 94, 97] included complicated st

mathematics or, from the user's standpoint, unknown geometrical factors with different formulas for light and hases. In 1983, simple pumping speed calculations were published for gases with molecular weights between 298].

he main vacuum data of a turbomolecular pump, the compression, and the pumping speed can be calculated fata of single rotor and stator wheels. A rotating wheel with blades pumps molecules from one side to the otherome particles move opposite to the primary flow direction through the blades. The structure of most commonurbomolecular pumps is shown in Fig. 4.28. In order to calculate the performance of a single wheel, the sameonsiderations as with the molecular drag pump can be used, by replacing the wording "molecular pumping stasingle wheel." Again two extremes, the maximum compression K max (at zero flow) and the maximum pumping max (for equal pressure on both sides of the wheel), must be known. For a turbomolecular pump the transmissrobabilities in the molecular flow depend on the ratiov/u of the blade speedv and the mean thermal velocityu of thas particle, and additionally on the blade angleα , but not on the pressure. For K max of a turbomolecular pump Eq4.134) applies and is exponentially dependent on the blade speedv, a specific pump factor g (rotor and statoreometry), and the square root of the molecular weight M of the particles pumped.

n agreement with Eq. (4.136),S max is proportional to the product of a specific pump factorG (rotor and statoreometry) and the blade speedv, and it does not depend on the pressure and the kind of gas pumped:

An operating wheel works in the region between these two extremes. For real pumping conditions (gas throughQpinlet) and different pressures on both sides of the wheel ( K = poutlet/ pinlet) the relation given in Eq. (4.138) app

More exact calculation takes into account the gap between the rotating wheel's outer diameter





Fig. 4.28Structure of turbomolecular blades [98]:α , blade angle;d , blade thickness;

h, distance between blades.

nd the inner diameter of the stator housing and the variation of the blade geometry with the radius. However, t

q. (4.138) remains the same.A turbomolecular pump is assembled from several wheels in series with different blade geometries. Each wheeegarded as a separate pump. If the pumping speedSv of the next wheel downstream is known and the throughputonstant, K in Eq. (4.138) can be replaced byS/Sv; and beginning with the pumping speedSv of the backing pump asing the valuesS max and K max for the first wheel at the forevacuum side, the real pumping speed of this wheealculated. The formula can be used as a recurrence formula to calculate step by step the pumping speed of theump in the molecular flow range.

hen the pumping speed of a turbomolecular pump depends on the compression and the pumping speedSv of theacking pump, as given in Eq. (4.138). From there it can be derived that if K max for any gas is small, the pumpingpeed for this gas is a function of the ratioS/Sv. For practical purposes a turbomolecular pump with low K max for Heeds a larger backing pump to pump H2 effectively (lowS/Sv ratio).

Due to the inlet conductance of the blade area of the wheel, there is a limitation ofS max and the actual pumping spf a turbopump becomes a function of the ratiov/u [98], and therefore it will depend on the molecular weight of tumped:

where F is the pumping area of the wheel,α is the blade angle,ds is the blade thickness,h is the blade distance, andhe trapping probability≈1 [98]. The pumping speed







nd the compression of a turbomolecular pump decrease at pressures of above 101 Pa, caused by the interactioarticles with one another, as the mean free path is no longer larger than the blade distance and the blades of th

wheels no longer are in the molecular flow range. This value corresponds to a foreline pressure of 110 Pa.

Again, as for any vacuum pump, the ultimate pressure pf a turbomolecular pump can attain can be calculated fromressure pv at the outlet side of the pump by dividing it by the maximum compression K max using Eq. (4.139). Thencrease of K max with the molecular weight M means that heavy molecules are highly compressed and have a lowackflow probability; this is the reason for the "clean" vacuum without contamination by oil vapors and hydroche smaller compression for light gases is the reason that the residual gas atmosphere of a turbomolecular pumonsists mainly of H2. This, however, holds true only for a "clean" system with metallic flange seals. In the casiton or rubber seals the ultimate pressure and the residual gas look differently [99].

.6.2Design Considerations

6.2.1otor and Stator Geometry

he pumping speed and the compression of a turbomolecular pump depend strongly on the rotor geometry andtarting from the 1958 original geometry of the rotor and stator wheels, new wheel geometries have been devehese geometries together with increased rotor speeds allowed much smaller and lighter rotors for the supercritpeed range.

he rotor and stator stages nearest the high-vacuum inlet are designed to serve a purpose different from those nutlet. The flow through each stage is constant, or, stated another way, the product of pressure times pumping sonstant. The blades nearest to the inlet of a turbomolecular pump are designed to have as high a pumping speeossible, whereas the blades nearest to the foreline port are designed for high compression. The opening angleslades are decreased from the high-vacuum side of the fore-vacuum side with the aim of optimizing the comprnd the pumping speed. For economic reasons it would be impractical to make each stage different from its neiompromise results in groups of two to four types of blades, in which each is designed for a particular speed anompression ratio.

he methods of manufacturing the rotors and stators have an influence on the pumping speed and compressionan be made of individually machined wheels which are heat shrunk to the rotor shaft, by machining complete

wheels from a single block of material or by manufacturing the rotors using spark erosion. The individually mawheels offer the advantage of making them "optically opaque", maximizing them for the compression. The othmethods of rotor production yield wheels with less opaqueness and lower compression, maximizing them for ppeed.

he stators are either manufactured from individually machined wheels or from stampings.

Meanwhile the first commercial turbomolecular pumps were dual-flow ("horizontal") pumps [96] having a dounded rotor, pumping the particles from a central inlet toward both sides and reuniting the gas flow in a commo

oreline; single-flow ("vertical") turbomolecular pumps, using single-ended rotors, became available in





969 [100]. The double-ended rotor design allows a more stable bearing design which is advantageous for easyalancing and lower vibration levels. The single-flow design has little conductance losses between the inlet flahe rotor, whereas the dual-flow design suffers losses from the inlet to both sides.

oday only a few models of commercial turbomolecular pumps still use the dual-flow design.

6.2.2otor Suspension

he development of the turbomolecular pump was quite spectacular concerning the reduction in size. This wasue to (a) an increase of the circumferential (tip) speed from 150 m/s in 1958 to approximately 500 m/s today ahanges of the rotor geometry. These high tip speeds relate to high rotational speeds of the rotors exerting highhe rotor's suspension.

oday most of the commercial turbomolecular pumps are equipped with lubricated mechanical rotor bearings, ombination of permanent magnet bearings at the high-vacuum side and a lubricated mechanical bearing at theacuum side. Depending on the wheel diameter the rotational speed of the rotor goes up to 90,000 rpm. These ave become possible because of the advances in bearing and balancing technology, without sacrificing the higeliability of the turbomolecular pump. Today, high-precision ball bearings are available, which, when speciallyo a certain turbomolecular pump rotor at comparable radial and axial loads, even at much higher rpm, have a sfetime compared to bearings of older design.

Ceramic" bearings (ceramic balls) are widely used today. The ceramic balls exert lower centrifugal forces andress on the races than metal balls, are harder and more temperature-stable, and, therefore, have a stable spherind minimal wear on balls and race. Their surface is smoother, leading to less friction, and the pairing of differ

materials (ceramic balls/steel races) avoids micropitting. Therefore these bearings are more reliable even underubrication-starved conditions.

6.2.3ubrication of Mechanical Bearings

hree main requirements have to be fullfilled by the lubricant used for the mechanical rotor bearings: (1) The las to cool the rotor bearings since these are running under fore-vacuum conditions, and a heat transfer from thhe outer race is possible only by the lubricant; (2) a low vapor pressure is required; and (3) good lubrication prt high speed are necessary. Today most of the lubricants used have a synthetic base.

ven at low rotor weights a minimum fluid flow through the bearings for heat transfer is necessary. Many smalurbomolecular pumps use a wick lubrication system or, together with "ceramic" bearings, a grease lubrication

while most larger turbomolecular pumps have pump systems circulating the oil.

6.2.4Magnetic Rotor Suspension

After some unsuccessful experiences with commercial "gas bearing" turbomolecular pumps [101], today commmagnetic bearing turbomolecular pumps are available in which one, two, three, or all of the necessary five degeedom of the rotor are actively controlled either by an analog or by a digital electronic system. The position o

otor spindle is monitored by sensors, and the electronics corrects the spindle position to the data supplied by thensors. There is no mechanical friction and hence no wear. The price of these magnetic pumps is still considerigher as compared to standard ball-bearing turbomolecular pumps, limiting their general use.





6.2.5alancing and Vibration

he dynamic balancing of the rotor of a turbomolecular pump is of great importance to minimize vibration andevels, which are related to the mechanical bearing lifetime. Due to the high rotational speed of turbomolecularotors, the centrifugal forces associated with the residual unbalance (material inhomogeneities, radial bearing peometrical imperfections) attain considerable values and transmit vibrations to the body of the pump.

he balancing process modifies the mass distribution of the rotor by adding or taking off material in order to brotational axis as close as possible to the principal axis of inertia. To further reduce the influence of the residuanbalance, the mechanical rotor bearings within a turbomolecular pump are held in elastic "antivibration" ringsffectively dampen the residual unbalanced forces.

Dynamic multifrequency balancing of the rotor is generally done in several balancing planes. This relative comrocedure in the last few years has become simplified by the use of computers and dedicated software. Modernurbomolecular pumps have very low residual vibration amplitudes, below 0.02 µm. These low values are necehe use of a turbomolecular pump with vibration-sensitive instruments, such as mass spectrometers and electron

microscopes.

6.2.6otor Materials

Most of the commercial turbomolecular pumps use high-strength Al alloys as rotor material. Compared to otherength materials, such as Ti and steel alloys, these Al alloys are lighter, are much easier to machine, and have

ufficient thermal stability for the operational temperatures even at the typical turbomolecular pump bakeout cyhe use of ceramics (Si3N4) has been reported for the use of turbomolecular pumps in very strong magnetic fie

102]. A typical maximum stress in the root of the rotor blades of a high-speed turbomolecular pump rotor at oonditions is in the range between 50 and 150 N/mm2, well below the 0.2% elongation limits of adequate Al a103].

6.2.7rive Systems

he drive rotor of a turbomolecular pump is an integral part of the turbomolecular pump rotor and together witrive stator can be located in the fore vacuum area. Today three different motor systems are used: DC motor, And hysteresis motor. The somewhat more expensive DC motor has lower energy consumption and energy losshe other motors. The motors are driven by solid-state frequency converters. Some of these converters can operurbomolecular pump at variable rotor speeds.

or special application (e.g., radiation) motor-driven frequency converters are used.

.6.3Applicational Considerations

6.3.1enting

After a power shutdown a turbomolecular pump should be vented; otherwise it will be contaminated by oil vapesult of pressure equalization between exhaust and inlet. By venting with a dry gas to atmospheric pressure, than be suppressed and a contamination of the vacuum system avoided. Most of the turbomolecular pumps, withxception of the larger pumps, can be vented at the high-vacuum side at full rotor speed. The venting air burstihe pumps puts a force of 1 kg on every cm2 of blade surface, which for larger areas represents a high load to thuspension. If the vacuum system cannot be vented







irectly, it is advisable to vent the turbomolecular pump by means of a special vent port which opens into theompression stages. Venting a turbomolecular pump from the contaminated foreline should be avoided, by all m

6.3.2aking

n order to attain low ultimate pressures in the high-vacuum and ultrahigh-vacuum range, the internal surfaces urbomolecular pump (rotor, stator, housing) can be baked out. Due to the temperature sensitivity of the Al alloor the rotors, there is a limit to the maximum value of the baking temperature. This maximum has to be well britical temperature for the rotor alloy with respect to its strength. Typical baking temperatures are in the range 00140°C, using the bake-out systems supplied by the pump's manufacturer.

6.3.3ooling

n order to dissipate the frictional heat from the bearing areas, the motor, and the heating by gas throughputs at ressures, the bearing areas of turbomolecular pumps have to be cooled. Meanwhile, for small pumps, convectooling is sufficient, whereas larger pumps are equipped with fans for cooling. For many pumps, water coolingommon.6.3.4peration in Magnetic Fields

urbomolecular pumps with their metallic rotors in the presence of magnetic fields experience induction of eddurrents which, due to heating, can cause serious problems concerning the material strength and the tolerances otating and stationary parts in the turbomolecular pump [104]. The eddy-current loss∆ P , is the amount of energyansformed by the eddy current into heat, and can be represented by the Eq. (4.141):

he eddy-current loss∆ P is proportional to the square of the magnetic flux B, proportional to the square of the rotootational frequency f , and inversely proportional to the resistivityδ of the rotor material. In addition∆ P is dependenhe shape of the rotor. Since in actual turbomolecular pumps the length of the rotor greatly exceeds its diameter

maximum heating of the rotor results from the component of the magnetic field in a radial direction.

herefore, turbomolecular pumps with metallic rotors can be used in magnetic fields only if certain maximum vhe magnetic flux density will not be exceeded. These maximum values are specified by the manufacturers andatic magnetic fields perpendicular to the axis of rotation, typically are in the range of 1030 mT. With pulsed melds, higher maximum values of Bmax are admissable. If the magnetic field is applied for a timet 1 and off for a tim

2 and since the heating of the rotor is proportional to the square of B, the following relation for Bmax(pulse) for pumagnetic fields applies:

n case of higher flux densities the turbomolecular pump will have to be shielded magnetically, which, howevereate problems with the distribution of the magnetic field itself. An experimental turbomolecular pump with a otor has been reported which has been tested with a magnetic flux density of 460 mT [102].





n this context it has to be kept in mind that the electronic drive systems and the control systems (magnetic suspf turbomolecular pumps create magnetic stray fields in their vicinity. These stray fields can influence other elend magnetic systems. Depending on the position relative to the turbomolecular pump, typical values for theseeld are in the range of 150 µT.

6.3.5umping Corrosive Gases

Modern manufacturing techniques require pumping processes where the ultimate system pressure has to be in tacuum range and corrosive gases have to be handled (e.g., below 101 Pa). At these pressures the rotor materiae attacked by the corrosives. However, the higher gas density at the fore-vacuum side in the rotor bearing areahe use of special lubricants (Fomblin®, Krytox®, etc.) which are corrosion-resistant.

n the semiconductor industry, Si and Al are etched in plasma etch machines (e.g., at pressures above 101 Pa). tching and corrosion of the turbomolecular pump's Al rotor and other parts, all internal parts of the turbomoleump having contact with the corrosives (e.g., Cl2, BCl3, CCl4) are either made of corrosion-resistant materiapecially coated (e.g., Ni-plated). Such coatings of the rotor can reduce the attainable ultimate pressure of aurbomolecular pump to 5 × 106 Pa. Besides using special lubricants, for further protection the turbomolecular

for plasma etching) are equipped with a purge gas system which admits inert gas (N2, Ar, typically 30 sccm) dnto the bearing area of the turbomolecular pump, where it creates a directed flow to the exhaust side of the pumow prevents the corrosive gases from entering the bearing area.

n some processes the reactive molecules of the etch gas from AlCl3 which is pumped off with the etch gas, anemperatures of 69°C solidifies inside the pump. To avoid this, the pumps will be heated to keep the temperaturbove this temperature. The use of turbomolecular pumps with magnetically suspended rotor will reduce the ab

mentioned problems.

6.3.6umping Toxic or Radioactive Gases

An additional range of problems has to be solved in the case of a turbomolecular pump pumping toxic or radioases (e.g., tritium in plasma fusion installations). Due to the safety hazards involved, the turbomolecular pumpe extremely tight. With a "tritium" turbomolecular pump, all seals to the atmosphere are made of metal. The ieak rate is below 107 Pa · liter · s1.

6.3.7urbomolecular Pumps in Combination with Other Pumps

n order to increase the pumping speed of a turbomolecular pump for hydrogen or water vapor and make use oonstant throughput and pumping speed, turbomolecular pumps have been combined with Ti sublimation pumpr, recently, with cryopumps [105] (see Chapter 9).

.6.4

erformance Data of Commercial Pumpshe variations in the performance of turbomolecular pump by different manufacturers depend on their actual d

blade design, rotor staging, etc.).





6.4.1ompression

igure 4.29 shows typical values for the maximum compression K max of a turbomolecular pump for different gasunction of the foreline pressure.

Depending on the manufacturer, turbomolecular pumps have the following compression values: H2, 1 × 102 toHe, 5 × 102 to 1 × 107; N2, 5 × 106 to 1 × 1010.

6.4.2umping Speed

igure 4.30 shows the pumping speed of a turbomolecular pump for different gases as a function of the inlet pre

urbomolecular pumps are available in a pumping speed range from 35 to 25,000 liter · s1.

ype designations of turbomolecular pumps often use the pumping speed for nitrogen; therefore the pumping sN2 is used as the 100% value. This value is



Fig. 4.29Maximum compression of turbomolecular

pump as a function of the foreline pressure (Balzers Pfeiffer).





Fig. 4.30Pumping speed of turbomolecular pump as a function

of the inlet pressure (Balzers Pfeiffer).

ompared to the pumping speed data for H2 and He from the catalogues of different manufacturers: H2, 341330133%.


he ultimate pressure of a commercial turbomolecular pump is generally between 108 and 107 Pa, using metaleals and a two-stage rotary backing pump.

7ombined Molecular Drag and Turbomolecular Pumps

n the past several years, different kinds of combined molecular drag and turbomolecular pumps have been devmprove the high-pressure performance of the turbomolecular pump and to attain very low ultimate pressures.ombinations of a turbomolecular and a molecular drag pump basically work on the same principle. Momentuansferred from a rapidly moving rotor surface to the particles to be pumped. Therefore the theoretical considere the same.

n 1975, Schittko and Schmidt [106] tried to combine a Holweck molecular drag pump with a turbomolecular prder to raise the compression for light gases. In 1973, Sawada and Tanigushi [107] proposed the concept of co

molecular drag pumps and turbomolecular pumps in which a turbomolecular pump and a drag pump stage are mn series on a single shaft (''Compound Molecular Pump") for the purpose of expanding the working pressure toressure range. Maurice [101] developed in 1974 such a pump ("Hybrid turbomolecular pump"). However, in tttempts the gaps between rotary and stationary parts were still extremely narrow, causing poor reliability at higotation.

With the progress in semiconductor manufacturing there has been an increasing demand for "clean" vacuum puwith high throughputs and capable of being used in the process range of 1103 Pa. This demand led to the develf combined turbomolecular pumps and molecular drag pumps in the 1980s. This combination has two effects: ompression is increased from typically 103 to 105, allowing ultimate pressures of below 108 Pa to be obtained

more significantly, allowing the







ressure in the backing line to rise above, for example, 103 Pa and higher, thereby enabling it to be backed with a dryembrane pump. In comparison, turbomolecular pumps, without the molecular drag pump have to be backed by a two

otary pump to ensure that the compression stages do not operate under laminar flow conditions.

With an integral molecular drag pump, oil is still present in the turbomolecular pump bearings and in the drive mechane diaphragm pump (separated from the high-vacuum space), but the elimination of the oil-sealed rotary pump is a su

mprovement.7.1esign Considerations

his pump design combines the advantages of a multistaged turbomolecular pumps and molecular drag pumps: Therbomolecular pump section provides a high pumping speed and low ultimate pressures, and the molecular drag pum

rovides a high compression and extends the fore-vacuum tolerance up to 102 to 5 × 103 Pa. These capabilities allowmple small, dry, and inexpensive backing pumps (e.g., membrane pumps) and therefore allow a dry evacuation frommospheric pressure down to 109 Pa.

hese pump combinations are available in several different design configurations:

MP stages + multistage MDP (disc type, derived from Gaede [90])

MP stages + multistage MDP (drum type, derived from Holweck [91])

MP + multistage MDP (drum type, derived from Holweck [91])

MP stages + multistage MDP (disc type, derived from Siegbahn [92]).

7.2ypical Performance Data for Commercial Combined Molecular Drag and Turbomolecular Pumps

7.2.1ompression

H2, 2 × 103 to 2 × 107; He, 7 × 103 to 2 × 109; N2, 5 × 107 to 1 × 1012

7.2.2umping Speed

N2, 100%; H2, 24133%; He, 42133%


epending on how many turbomolecular pump and molecular drag pump stages are used in series, the attainable ultimressure is in the range of 5 × 109 to 1 × 107 Pa.

8acking Pumps

ecause all of the above-mentioned turbomolecular pumps and molecular drag pumps and combination of these pumpacking pump, it is worthwhile to look at the existing types of backing pumps, in order to be able to evaluate which





Table 4.5. Typical Backing Pump DataType Ultimate pressure (Pa) Quality of VacuumMembrane

< 103Absolutely dry

Rotary vane < 101 Oil vapors

Piston< 1

Technically dry

Multiroots< 10

Technically dry

Claw roots< 10

Technically dry

acking pump should be used together with the high-vacuum pump (see Chapter 9). In principle, the selection dequate backing pump depends on its pumping speed, its pressure range, the quality of the fore-vacuum produrice, and its size. Typical backing pump data are shown in Table 4.5.

acking pumps producing an "absolutely dry" vacuum do not have any oil or grease in possible contact with thumping area. "Technically dry" pumps do not have any oil or grease in the pumping area; however, they haveil (e.g, in the bearing or feed-through area) that is kept away from the pumping area by dynamic seals, becausre labyrinths, and so on.

ogether with magnetically levitated combined turbomolecular pump and molecular drag pumps, even the mosemanding applicational requirements can be met.





art IIIRegenerative Drag Pumps

Nigel T. M. Dennis

9egenerative Drag Pumps

apacities available: 30540 m3 h1 (25150 liter·s1)

Operating pressure range: 1000 to less than 104 mbar

.9.1Mechanism

he regenerative pump is a high-speed single-shaft vacuum pump capable of delivering to atmospheric pressurynamic machine that relies on momentum transfer from fast moving blade rows that create the pumping actioame "regenerative" comes from the way the mechanism circulates the gas repeatedly through the same blade me "regenerating" the forward momentum. Other names are used: side channel, vortex, or peripheral flow pum

he advantage of this pump is that the high shaft speed results in small stage size, making the pump extremely he high rotational speed also allows other mechanisms such as a molecular drag stage (see Section 4.5) to beffectively used on the same shaft.

A single stage of the pump consists of a row of blades mounted on a rotor; these protrude into the flow channel.31). As the blades move around they generate a spiral vortex within the channel that circulates the gas througlades as it moves along the channel, thus creating a helical flow path. This ensures that

Foundations of Vacuum Science and Technology , Edited by James M. Lafferty.ISBN 0-471-17593-5© 1988John Wiley & Sons,Inc.





Fig. 4.31One stage of a regenerative peripheral flow pumpindicating direction of gas flow and where the flow

channel is interrupted by the "stripper."

igh-speed gas from the blades is continually fed into the channel, diffusing into the bulk flow to generate the pse. Within a single stage the gas may circulate many times through the blades, creating a high compression ratypical performances range from a compression of 2 to about 10, with the latter occurring in the very best mache blades are shaped to catch the incident gas with the minimum of turbulence, to deflect it, and to throw it fo

nto the bulk gas flow. The inlet and exhaust of a pump channel are separated by a restrictive section through wnly the blades may pass. This is generally known as the stripper . Pockets of gas between the blades are also carrihrough the stripper; these form a carry-over volume, limiting the efficiency and compression of the machine. Tze must, therefore, be small compared to the channel size. The amount of gas carried over to the inlet can be y allowing the closed pockets within the stripper to expand through a connection to an intermediate pressure p

within the stage.

ixsmith [108] revolutionized the understanding and design of these machines and showed that practical compnd vacuum pumps could be made. He developed many of the features described above and demonstrated a pro

machine with a maximum compression of 10 and a working flow of 250 m3·h1.

lade speeds are usually below Mach 1, and Mach 0.5 to 0.8 appears to be suitable. Speeds above Mach 1 resuhock wave problems.

he function of the blades is to impart momentum to the gas as efficiently as possible.







Fig. 4.32A typical pump with inlet drag stages.



Fig. 4.33Speed and power curve of a 240-m3·h1 regenerative

pump with two drag stages.

At the present stage of development, five or more stages of regenerative compressor are used with an inlet dragages based on the Holweck or Siegbahn principle. The regenerative stages are typically capable of reaching 1he drag stages extend the ultimate to pressures to as low as 1 × 104 mbar [109]. A typical pump





ross section is shown in Fig. 4.32. The speed curve obtained from a medium-size pump of this type is indicate.33.

he power requirement of a regenerative pump is high because of the poor efficiency of the mechanism which he slip required to generate a useful compression. A typical power curve is shown in Fig. 4.33.

umps of this type are susceptible to dust accumulation in their mechanism and, therefore, should generally belean duties. They are, however, the only single-shaft pumps to achieve this level of vacuum when working agtmospheric pressure.

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04. W. Becker and J. Henning, J. Vac. Sci. Technol . 15, 768 (1978).





05. J. E. de Rijke and W. A. Klages, Jr.,Solid State Technol ., April, p. 63 (1994).

06. F. J. von Schittko and C. Schmidt,Vak.-Tech . 24, 110 (1975).

07. T. Sawada and O. Taniguchi, Jpn. Pat. 68/1723 (1973).

08. H. Sixsmith and H. Altmann, J. Eng. Ind ., August, pp. 637647 (1977).

09. M. G. Mase, T. Nagaoka and M. Taniyama, J. Vac. Sci. Technol. A 6, 25182521 (1988).





apture Vacuum Pumps

A capture or entrapment vacuum pump is a pump usually located within the chamber being evacuated that remmolecules by sorption or condensation on its internal surfaces. Three types of capture pumps are described in thhapter; the getter pump, the sputter ion pump, and the cryopump.

Gas in the getter pump is retained principally by chemical combination with a getter material. The getter is usuhemically active metal or alloy, either in bulk or in the form of a freshly deposited thin film.

n the sputter ion pump the gas molecules are ionized and directed towards getter surfaces of the pump by electmagnetic fields. The getter surfaces are replenished in a continuous way by cathodic sputtering.

Gas molecules are condensed on refrigerated surfaces in a cryopump. These surfaces are cooled to a temperatunough to keep the vapor pressure of the condensate equal to or below the desired low pressue in the vacuum c

Foundations of Vacuum Science and Technology , Edited by James M. Lafferty.ISBN 0-471-17593-5© 1998John Wiley & Sons, Inc.





art IGetters and Getter Pumps

runo Ferrario

he use of getters in vacuum technology has gained an increasing interest during recent decades, and the develf this type of pump for new and advanced applications has required a deeper understanding of some basic scieoncepts. These concepts are particularly related to surface and bulk characteristics of metals and gassurface inhenomena. A review of some fundamental aspects of gettering will therefore be given before the description o

working and applicative characteristics of getters. A more complete description of the basic concepts of the gasnteractions and diffusion phenomena can be found in Chapter 10.

1ypes of Gas Surface Interactions

When gas molecules interact with a solid surface [1,2], several phenomena can take place. Among them, the fones shown in Fig. 5.1 are of particular interest for the subject here considered:adsorption (capture of molecules byurface),desorption (emission of molecules from the surface),backscattering (bouncing back of molecules impingn the surface),diffusion (penetration of adsorbed atoms from the surface into the solid bulk or movement of distoms from the solid bulk to the surface),displacement (displacement of an adsorbed molecule by another imping

molecule), and surface reactions (formation of new molecules at the surface from adsorbed molecules of differenpecies).

ome of these phenomena tend to remove molecules from the gaseous phase, while others tend to drive molecuhe gaseous phase. If the surface has suitable






Fig. 5.1Some types of gassurface interactions.

haracteristics, the adsorption phenomenon can, however, prevail (together with diffusion into the bulk, under conditions of temperature and pressure) in a vacuum system. As a consequence, there is a net removal of molecom the gaseous phase and, therefore, a decrease of the gas pressure. This phenomenon is usually known as gettering

nd the solid materials which exhibit this gettering capability are named getters . Usually the term ''getter" is adoptewhen the capture of gaseous molecules is due to relatively strong forces (i.e., chemical forces), and it refers to smetals both in pure or in alloy form. In this case, it is also common to say that "chemisorption" takes place, whxplains why getters are also called chemical pumps. Other materials such as molecular sieves, active charcoaln, exhibit adsorption of gas molecules or atoms; however, the forces involved are relatively weak and these mre therefore usually known as physical absorbers rather than getters. In this case, "physisorption" takes place.

Quantitatively, as will be seen in more detail later, the gettering capability is defined by a "gettering rate" and agettering capacity." The gettering rate represents the number of gaseous atoms or molecules which are removedhe gaseous phase by the getter per unit time. The gettering capacity is the number of atoms or molecules which captured by the getter before it stops sorbing gas.

hemical nature, crystal structure, and physical characteristics of pure metals or alloys used as getters are impospects to understand gettering; some discussion on these topics [35] is therefore presented for a better understahe characteristics of getters.

2asic Concepts of Getter Materials

he lattice structure (i.e., the "bulk" parameters) can influence the gettering properties of a metal in terms of dind solubility for gases [6]. The gettering properties are, however, first of all related to the surface characteristi

metals. The situation in the bulk of a metal, where each atom is completely surrounded by other metal atoms anaturated bonds, is quite different from that at the surface. In fact, the surface atoms have a smaller coordination comparison with the bulk atoms, since they are not completely surrounded by atoms; this surface coordinatioumber depends on the face of the crystal structure exposed at the surface. This means that the surface atoms h

nsaturated bonds which determine their reactivity versus the gas atoms or molecules colliding with the surfacedsorption of these molecules tends





o saturate the free bonds and to reestablish the symmetry of the force field to which the atoms would be submihey were in the bulk of the crystal. Typically the surface density of atoms is in the range of 1 × 1015 per cm2depending on the metal type and the exposed crystal plane).

n gettering, not only pure metals are used, but often also alloys [35] are of paramount importance to achieve sproperties. There are binary, ternary, multicomponent alloys, depending on the number of the components. Theomposition and the nature of the alloys depend on the type of the alloying elements and are characterized by tconstitutional diagram" (also called equilibrium or state or phase diagram) for the system of elements.

Most of the metals are completely miscible in the molten state, and the resulting alloys can be considered as sololutions. The solid solutions can be substitutional or interstitial. In the molten state, some metals can form stabhemical bonds; when this occurs, intermetallic compounds are formed.

Alloys can exhibit more than one phase and also show complex phase diagrams. The type of phases present in material can affect not only its chemical affinity, but also other properties such as solubility, diffusivity, hardneshermal conductivity, and so on. Also pure metals can exhibit more than one phase, depending on the temperatuonditions. For example [6], Ti has a hexagonal close-packed (hcp) structure (α -phase) below 885°C and a body-entered cubic (bcc) structure above 885°C. Fe exhibits anα -phase (bcc structure) below 910°C and between 140nd 1540°C; between 910°C and 1400°C, Fe exhibits aγ -phase [face-centered cubic (fcc) structure].

Metals and alloys are likely more frequently polycrystalline than monocrystalline. The grains consist of atoms n a lattice with a precise space orientation. Adjacent grains have the same crystallographic structure, typical oflement considered, but the orientation is different. Therefore, in the space between two adjacent grains, there iansition in the crystal orientation. This area, called grain boundary [5, 7], has an important influence on the metaroperties, also from the point of view of gettering. The grain boundary, in fact, is a zone of the metal where thower density and a smaller coordination number in comparison with the bulk. The grain boundary atoms can, e more prone to react with foreign atoms; diffusion can also take place more easily than in the crystal bulk.

Dimensions and shape of the grains can change during time, depending on temperature.

3dsorption and Desorption

As thoroughly discussed in Chapter 10, the experimental and theoretical studies of the gassurface interaction dietween two types of adsorption: physical adsorption or physisorption [8, 9] and chemical adsorption or chemi1013], which is normally involved in gettering.

is useful to keep in mind that chemisorption and therefore gettering can bedissociative , so that the individual atohe split molecules (such as O2, N2, CO, etc.) are actually bonded to the surface in the so-called adsorption siteventually diffuse into the bulk of the getter material if enough (usually thermal) energy is provided. The bond nvolved in chemisorption normally exceed 5eV, and the so-calledresidence time of the molecules on the capturingurface is so





ong that the process is practically irreversible in usual working conditions (apart from H2). In physisorption, oontrary, the process is nondissociative and reversible. In chemisorption, moreover, the adsorption characteristipecific as in all chemical reactions.

he number and position of the adsorption sites depend on the nature of the metal considered, the crystallograpructure, the orientation of crystal faces, the presence of impurities, and so on. The fraction of adsorption sitest the surface, occupied by the adsorbed atoms, usually called surface coverage (ϑ), is a useful concept to describedsorption phenomena and capacities of getters. The surface is completely saturated by the adsorbate whenϑ = 1 (a

monolayer is formed). During chemical adsorption (as well as during physical adsorption) there is heat generat, the process isexothermic . The heats of chemisorption depend on the gasmetal system and are reported in theterature [14].

During gettering there could be some increase of temperature which may be negligible or relevant, depending omount of gas adsorbed, its nature, the area of the gettering surface and its heat dissipation characteristics, the rdsorption, and so on.

n equilibrium conditions, the adsorption characteristics of a gasmetal system can be described by isotherms [1which are usually of five types as seen in Section 10.1.2. It is, however, important to notice that, besides thehermodynamic considerations, it is fundamental to describe the adsorption process and therefore the gettering lso from the kinetics standpoint (a process can be thermodynamically favored but too slow). Kinetically the adrocess can be described by the following general equation:

whereS is the rate of adsoption, P 1 is the probability that the particle colliding with the surface finds a free site, P 2 ihe probability that the particle has sufficient energy for the adsorption to take place (i.e., has the necessary actinergy), P 3 is the probability that when the two above conditions are fulfilled the particle is actually adsorbed, vhe collision frequency of the particle on the surface. The product s = P 1 P 2 P 3 is usually called sticking probability oicking coefficient and depends on the surface coverage, the size of the adsorbate, the dissociative or nondissocharacter of the adsorption, the activation energy (of the specific gas moleculemetal system), and so on. Considsual mathematical expression for the collision frequency, the adsorption rate per unit time and unit area can bey the following equation, which also represents the basic expression for the gettering speed:

where p is the pressure of the gas,m is the mass of the gas molecule,k is the Boltzmann constant, andT is theemperature in Kelvin. From the experimental data forS , it is then possible to derive the sticking probability valueicking probability parameter is often used in the field of getters to calculate the gettering characteristics of comettering structures when statistical methods are applied. The effectiveness in chemisorption of gases on metalselated to several factors: the electronic factor,





he geometric factor, and the effect of impurities and imperfections. Since chemisorption implies the formationovalent bond, the importance of the electronic factor is obvious. In this respect, the electronic properties of thed haracter metals are favorable to chemisorption for many gas molecules. As a matter of fact, getter materials arelected among metals withd characters (typically among metals of the IVB, VB, and VIB groups of the periodi

he possibility to accommodate molecules in the chemisorbed state also depends, however, on the geometricharacteristics of the metalthat is, on the relative distances of the surface metal atoms and the atom surface dens8]. Different exposed crystal planes of the same metal can exhibit different chemisorption capabilities. Impurimperfections may promote or inhibit chemisorption and are sometimes responsible for unexpected changes inhemisorption properties of the same metal.

After adsorption, molecules can be re-emitted, and this phenomenon depends on the energy imparted [810]. Thhysisorbed molecules can be easily desorbed, for example, by heating, since the bond energies involved are remall.

he release of chemisorbed (dissociated) molecules implies the preliminary recombination of the component athen the emission of the molecules. The energy involved in this process is large, and therefore desorption is genery difficult (apart for H2). Adsorption could be accompanied by desorption of gas molecules of different spe

ompared to the adsorbed molecules; this can be due to catalytic surface reactions [19] between the adsorbed,issociated molecules of different species simultaneously present on the surface or between the gas molecules aertain surface impurities.

4ulk Phenomena

.4.1Diffusion

Getter materials are not only characterized, as previously mentioned, by the phenomena taking place at the surfhemisorbed species can in fact diffuse [1922] from the surface into the bulk of the getter material, depending oature of the diffusing species and the physicochemical characteristics of the sorbing material. The component f the gas molecules chemisorbed at the surface have to break the chemical bonds with the adsorbing material nto the bulk. The driving force for the diffusion is then the concentration gradient of the considered element, phat enough energy is supplied (usually thermal energy is supplied to promote diffusion). In this situation the twrocesses of adsorption and diffusion proceed simultaneously. In the stationary state the diffusion rate of an elemenhrough the x-axis of a metal sheet can be expressed by Fick's first law and is characterized by the diffusion coe (cm2·s1) and by the concentration gradient at the considered plane from the surface. D depends on temperatureccording to the following equation:

where D0 is a diffusion constant depending on the diffusing element-metal system considered, E is the activation enor the diffusion process,T is the temperature in





able 5.1. Diffusion Coefficients for Various GasMetal Systems at Different Temperatures [22]

iffusion Species Metal Crystal Structure D0(cm2·s1) ∆ H (J/g·atom) D25°C

D400°C

D1000°C

α -Ti hcp 1.80 × 10251,900

1.42 × 1011 1.68 × 106

3.00 × 10261,500

4.92 × 1013 5.03 × 107

α -Zr hcp 7.00 × 10429,500

4.69 × 109 3.58 × 106

β-Ti bcc 2.00 × 10327,800

1.44 × 104

β-Zr bcc 5.30 × 10334,800

1.98 × 104

N α -Ti hcp 1.20 × 102189,300

7.60 × 1036 2.39 × 1017

N β-Ti bcc 3.50 × 102141,400

5.48 × 108

α -Zr hcp 2.00 × 101 171,600 1.61 × 1031 9.45 × 1015

β-Zr bcc 4.50 × 102118,000

6.44 × 107

and R is the gas constant. It is often observed that D is not independent of the concentration and of the concentration gradient, particugh concentration values. Typical values of D0 and E for some diffusing species-metal systems are shown in Table 5.1 [22].

he application of Fick's first law leads, for example, to the description of the permeation phenomena and can be used in first approxso to describe gettering when stationary diffusion is involved.

the description of gettering phenomena, the stationary state condition, however, is not always an appropriate approximation. Time-pendence of the phenomenon, as a matter of fact, is to be considered to better describe the process. In this case Fick's second law ap

e linear diffusion showing the variation of the concentration as a function of timet and position along the axis of diffusion. The applicais law for a semi-infinite slab represents a good approximation in describing gettering in some practical conditions; the derived Eq. Chapter 10 indicates that the rate of removal of molecules per unit area and time is proportional to the square root of the diffusion er time of sorption; the concentration of the diffused atoms at a certain distance from the surface is instead given by Eq. (10.126). Ts uptake per unit area after timet is calculated to be proportional to the square root of the diffusion coefficient multiplied by time [Eq0.128)] ; therefore for a given value of the diffusion coefficient (i.e., for a given getter material), the diffused quantity is expected tooportional to the square root of the diffusion time. By plotting the sorbed quantity as a function of the square root of time, one shound a straight line; this is often actually found even if deviations are observed, particularly at high concentration values.

or geometries such as spherical particles of radiusa , the solution of the diffusion equation can be expressed in the following form:

his is a relatively complicated equation, but can better describe the common situation where the getter material is in powder form anape of the particle is





ot too different from spherical. This equation can be used to derive the mass of gas diffused during timet as follow

where a is the radius of the sphere, M ∞ is the mass of the gas in saturated conditions, and Mt is the mass of the gas me t .

.4.2olubility

he mechanism associated with gas solution [6, 22] in a getter material is usually described as a three-step procissociation of the gas molecules at the gassurface interface; (b) sorption at the superficial, or near surface, siteissolution in the bulk of getter material, through diffusion mechanisms.

As well as in other gasmetal systems, a solid solution is formed with the sorbed gas species usually located at tnterstitial sites of the lattice of the host metal. The structural effects caused by gas dissolution are generally limome expansion of the lattice, with increase of the lattice parameter.

n the case of the dissolution of a di-atomic gas species, the formation of solid solution in a getter material can epresented by the following reaction:

where g and s denote gas phase and solid solution, respectively.

Once the thermodynamic equilibrium has been achieved, the pressure, P , is proportional to the square of the gas sponcentration in the material,q:

More precisely, the gas concentration is related to the gas pressure and to the getter temperature according to Saw [23], expressed by the following most common equation (for dilute gas solutions):

where A and B are constant parameters depending on the gas type and getter material, which can be determined

xperimentally.Although Eq. (5.8) is valid for any solute gas, it is used, in practice, only for hydrogen. In fact, hydrogen generorms a solid solution in metals with relatively low stability, enabling thereverse reaction to occur by a moderatencrease of the temperature.

he solid solution (α phase) is thermodynamically stable until the solubility limit is reached. Approaching thisoncentration, the interactions between the solute atoms tend to increase, nucleation and growth of solid phasesnd the isotherms





how a plateau, which depends on temperature, according to van't Hoff's law:

where P is the pressure,T is the getter temperature in K, and∆S and ∆ H are, respectively, the entropy and enthalpyormation of theβ phase. In the most common high-vacuum (HV) and ultrahigh-vacuum (UHV) applications of

materials, the amounts of gases involved in the sorption process are relatively small and therefore they typicallyilute solid solutions. The thermodynamics of hydrogen solution and hydride formation can be described byressurecomposition isotherms (Fig. 5.2).

5quilibrium Pressures

n order for a getter material to work properly, particularly in ultrahigh-vacuum conditions, the equilibrium prehe gettered gas should be as low as possible. The equilibrium pressures are the result of the balance between thdsorption and desorption processes, as previously illustrated. Due to the energy involved in chemisorption, it hlready been mentioned that the residence time of the adsorbate is extremely long and therefore the desorption negligible compared to the adsorption process; the equilibrium pressure of the adsorbates are therefore expecery low.

f the gettering process proceeds, for example, to the formation of certain stoichiometric oxides and nitrides of metals commonly used as getters, the corresponding equilibrium pressures can also be low or extremely low (e

elow 1020 bar [24]).

n the case of H2, the situation is different; as discussed in the previous section, in the range of concentrations onterest in gettering, Sieverts' law is found to be followed and the H2 equilibrium pressure may not be negligiblepending on the working conditions.

Fig. 5.2Typical pressurecompositiontemperature

curves for hydrogenmetal systems.





Of course, also the vapor pressure [25] of the getter material itself should be small or negligible compared to thperating pressure required in the considered vacuum applications.

6etter Materials

.6.1asic Characteristics of Getter Materials

he first basic characteristics for a getter material arechemical affinity with gases andbulk diffusivity ; the former isarticularly important in determining the chemisorption of the gas species to be removed in a vacuum system, atter allows the displacement of the adsorbate into the bulk of the getter material, thus increasing its capacity. Aasic characteristic is related to the possibility of achievinglarge surface areas . The development of suitable alloy

makes it possible, however, to modulate the various relevant properties for a getter material and achieve a usefuompromise. This explains why, in practice, getter materials are often made up of alloys rather than of pure me

here are other important parameters to be considered in developing and/or selecting a practical getter materialften requires a compromise with the above chemicophysical properties. As a matter of fact, getter materials ar

manufactured on an industrial scale and have to be handled in large quantities. For these reasons, workabilitypossibility to transform the original getter ingots into powder to ensure enough surface area), hardness, safety o possible toxicity, pyroforicity, and high exothermic reactions with ambient or process gases and materials), snder usual or specific storage conditions, availability, and cost all have to be taken into consideration.

.6.2orption Speed and Sorption Capacity

he net removal rate of molecules from the gaseous phase as a result of the various possible interactions with tmaterial (i.e., the gettering rate as already mentioned in Section 5.1) is also often defined as sorption speed of that gmaterial. This indicates that the removal of molecules can be due to adsorption combined or not with absorptioiffusion into the bulk of the material). The sorption speed can be expressed in m3·s1, liter·s1, or other conveninits. Multiplying the sorption speed by the pressure at which this speed is measured, one obtains the sorption

hroughput , which is therefore given in Pa·m3·s1, mbar·liter·s1, Torr·liter·s1 or other convenient units.

he gettering capacity is also called, more generically, sorption capacity . It is commonly measured in Pa·m3,mbar·liter, Torr·liter or other convenient units. Of course the maximum sorption capacity corresponds to the forf a stoichiometric compound. For example, in the case of O2 gettered by Ba to form BaO, the stoichiometric c 93 mbar·liter·g1.

he sorption characteristics of a getter are generally represented by the sorption speed as a function of the sorbuantity ; the typical trend of the curve is shown in Fig. 5.3.Q0 represents the total capacity at zero speed. This quorresponds to the amount of gas saturating the surface if there is practically no bulk diffusion, which





Fig. 5.3Typical sorption curve for a getter material.

ccurs when getters work at room temperature.Q0 corresponds to the maximum possible amount of gas sorbed ififfusion takes places and a stoichiometric compound forms. However, the corresponding sorption speed for a mount of gas sorbed can be too small and not acceptable for the application even at much smaller values thanQ0. Tseful capacity of the getter is then the amount of gas sorbed until the speed reaches the minimum acceptable vhe application. In Fig. 5.3 the capacity of the getter isQ1 if S 1 is the acceptable speed; it isQ2 if the acceptableorption speed isS 2. These values of the sorption capacity are therefore the so-called "practical capacities" and om situation to situation. ASTM F 798-82 defines aterminal gettering rate of a nonevaporable getter when the gas sorbed an amount of gas corresponding to a decrease of the sorption speed to 5% of its initial value; the ini defined as the value measured after 3 minutes from the start of the sorption test. In the case of evaporable get

etters) the terminal gettering rate corresponds to 1 liter·s1 and 0.1 liter·s1 for a Ba film in a large TV tube and eceiving tubes, respectively.

is common practice also to use the terms "specific sorption speed" and "specific sorption capacity"; they are nd capacity of the unit mass or volume or weight or area of the getter considered. For example, the specific sopeed can be measured in m3·s1·cm2 and the specific sorption capacity can be expressed in Pa·m3·g1.

he speed of a getter can decrease during time, depending on working temperature and pressure conditions. It more rapidly if sorption occurs at room temperature since bulk diffusion is not promoted (except for H2) and thapacity is basically surface-limited. If a getter is operating at high temperatures, its speed is generally increaseemains more constant as a function of time since the sorbed gases are diffused into the getter bulk. The behaviifferent for H2, however, because of the reversible character of its sorption. These situations are shown in Fig.5.

oncerning pressure-dependence, it is found that, usually, the initial speed of getters is practically independentressure in a very wide range: from 102104 mbar (depending on gas type) down to UHV conditions.





Fig. 5.4Typical sorption curves at different temperatures

for irreversible sorption.

Fig. 5.5Typical sorption curves at different temperatures

for reversible (H2) sorption.

.6.3rincipal Types of Getter Materials and Their General Working Conditions



A practice which has now become common identifies two different broad classes of getter materials:evaporable andonevaporable getters. Sometimes it is also common to sayevaporated and nonevaporated getters. In principle, alletters can be used either as evaporable or as nonevaporable; however, it is easier or more convenient to use ceetter materials in the evaporated mode and others in the nonevaporated mode. Nonevaporated getters are also bulk" or "volume" or "massive" getters.

n the case of evaporated getters, the getter material is heated to a sufficiently high temperature to evaporate anlm onto a surface inside the vacuum system.





his film is immediately ready to sorb gases. The geometric area and the real area of the film determine the speapacity of the getter.

n the case of nonevaporated getters, there is no evaporation or sublimation of the getter material; the gases reavailable surface of the material and, if sufficient energy is supplied, diffuse into the bulk.

ased on the considerations made in Section 5.1, the typical materials studied as practical getters are shown in

he alkaline-earth metals and particularly Ba are generally used as evaporable getters, whereas the metals of throup and particularly Zr and Ti, in pure or alloy form, are generally used as nonevoporable getters. Ti is also uvaporable getter in the so-called sublimation pumps. The Zr- and Ti-based alloys can be binary, ternary, or

multicomponent, comprising elements such as Ni, Fe, Al, Co, rare earths, and so on, to obtain specific getteringharacteristics and other required physicochemical features. Rare-earth metals are often used in alloy form contarious combinations of these elements. ''Mischmetal" is the common name of this type of alloy, rich particularerium and lanthanum. Thorium and uranium have also been found to be useable as getter materials; their radiond pyrophoricity (particularly for U), however, limit their applicability. Hafnium also exhibits some interestinettering capability, but availability, costs, and stability problems limit its use in real getters.

articularly in recent years, getters with high sorption capabilities for all the residual gases found in a vacuum ave been developed to cope with various specific requirements.

efore describing getter materials in more detail, however, the concept of "activation" has to be introduced as no understand the gettering behaviour of all these materials. The surface of the powder particles of any type of g

material is readily covered mainly by an oxide layer when exposed to air the first time after its manufacturing. ayer usually passivates the getter material thus preventing further pick-up of gas. The getter material, thereforemmediately active and ready to work when introduced in the vacuum environment. In order for the getter to bhemisorb gases, the passivating layer has to be removed. In the case of evaporated getters, this occurs automa

when the material is heated and evaporated because a new fresh metal surface is formed under vacuum, with oxnd carbon atoms being dissolved in the evaporated film mass. In the case of nonevaporated getters, the removassivating layer to get a clean, essentially metallic surface is usually necessary before the getter starts workingrocess is

Table 5.2. Typical Getter MaterialsEvaporable NonevaporablePhosphorus (red)

Zirconium

StrontiumTitanium

CalciumHafnium

Barium Thorium

TitaniumRare earths

Alloys based on Zr and Ti





alled activation [25, 26] and is generally performed by heating the material for sufficient time to promote the df the superficial oxygen and carbon atoms into the bulk of the material. The process is regulated by the diffusind can be performed using suitable combinations of temperature and time. Higher temperatures are more efficleaning the surface due to the exponential dependence of the diffusion coefficients on temperature; but in manractical applications, too-high temperatures are not acceptable and the time factor can be more conveniently en some cases, to overcome the problem of possible unacceptable heating of the surfaces surrounding the getterf pulsed activation is adopted; it consists in successively heating to a high temperature for short times, to avoidxcessive heating of the surroundings, until the temperaturetotal-time combination for activation is reached.

he activation process can be schematically represented as shown in Fig. 5.6.

When a practically completely metallic surface is obtained, the maximum number of available adsorption sites ccupied and the speed is maximum: full activation has been achieved. However, in practical conditions also partialctivations can be useful. The activation conditions depend on the getter material usedthat is, on the type of oxiormed (thickness, compactness) and its diffusivity characteristics. The activation of a getter requires that a reareliminary vacuum has already been achieved by conventional pumps.

is to be added, however, that there are recent special nonevaporated getter materials [27] (based on special B

with particularly good sorption performances for N2, which can be used without the necessity of activation, evere exposed to air (for a relatively short time such as minutes) before being used in the vacuum device.

is to be pointed out that some getters which usually need activation can be used without being preliminary acwhen H2 is the main gas to be sorbed and its pressure is relatively high (e.g., in the range of 102 to a few millibeason is related to the mechanism described by van Vucht [28]. H2 can easily physically diffuse through the oayer, particularly if it is not very compact. As a matter of

Fig. 5.6Representation of the activation process for

a nonevaporable getter.





act, there may be enough porosity and/or enough cracks in the oxide layer to allow H2 to flow through it and bbsorbed by the getter metal surface immediately underneath; the local adsorption of H2 expands the lattice of

material, thereby generating sufficient stress on the oxide layer to produce or increase the number of cracks andurther enhancing H2 absorption, and so on. There is therefore a sort of autocatalytic effect and the absorption b

more and more evident after some time (induction time), which may be minutes or hours, depending on hydrogressure and getter temperature. It is finally to be noted that, in principle, the activation of a getter material canerformed either by displacing the atoms of the passivating layer away from the surface into the vacuum side oestroying the compactness of the layer to allow the passage of gas molecules and their contact with the metallurface, rather than promoting the diffusion of the passivating atoms into the bulk. This can be obtained by spuhe surface using ion beams or a gas discharge (e.g., argon discharge) where the ions present are accelerated onetter surface. These activation procedures are generally not very practical and therefore very rarely applied. Tayer can also be destroyed, while new, fresh metallic surfaces are generated, by breaking the getter particles asor example during grinding in vacuum or in an inert atmosphere.

he activation process is repeated whenever the gas sorbed quantity has reduced the speed to unacceptable valuvery time the getter has been exposed to air. If no air exposure occurred, thereactivation of the getter can be made

milder conditions compared to first activation.

After reactivation the initial speed is almost completely restored (depending on the amount of gas sorbed beforhis process). With an increasing number of reactivations the initial speed obtainable decreases to the point thatnacceptable; the getter is therefore considered exhausted. Sometimes it is possible to restore somewhat better ettering performances by using activation conditions that are more drastic than usual.

he typical trend of the sorption curves obtained as a function of the reactivation number is shown in Fig. 5.7.

f the getter is saturated at room temperature (RT), the possible required number of reactivations is high since thurface capacity is generally a small fraction of the total getter capacity. If the getter is operated at high temperhe number of reactivations needed is smaller the higher the temperature of operation; if the operation temperatufficiently high (HT), the total capacity can be reached without need of reactivation. The number of possibleeactivations is limited and depends on the temperatures involved and on the nature and structure of the getter.

Fig. 5.7Typical sorption curves for a nonevaporablegetter after successive reactivations.





After saturation with hydrogen, reactivations (in this case also calledregenerations ), are theoretically unlimited bef the reversible character of the absorption of this gas; in practice, the number of possible regenerations is largmited because of mechanical or embrittlement problems.

.6.4nteraction of Getters with Common Residual Gases

After activation, the getter sorbs the gases which are the residue of the preliminary pumping or which are continenerated in the vacuum system, thus ensuring the required vacuum level. The gases generally responsible of veterioration in usual vacuum applications are: H2, H2O, N2, O2, CO, CO2, hydrocarbons (particularly CH4), ases. The composition of the gas to be removed depends on the gas source (outgassing, leaks, permeation).

ctive Gases . H2, H2O, CO, CO2, O2, and N2 are usually defined asactive gases because they can chemically intwith getter materials.

O, CO2, O2, and N2 are chemisorbed at the surface and fixed in such a way that the adsorption is consideredermanent or irreversible; that is, no re-emission of these gases occurs in usual practical operating conditions. Ietter material is heated, the atom components of these gases diffuse into the bulk and there they sink.

H2 is sorbed forming a solid solution, in a certain range of concentration following Sieverts' law. This is areversibleorption. This gas can actually be sorbed or emitted, depending on the working temperatures and pressures andoncentration of the gas in the getter material.

H2O is dissociated in the two components: hydrogen and oxygen. H2 is then sorbed according to the typical remechanism for this gas, whereas O2 is permanently fixed.

ydrocarbons . These gases are not usually considered active. However, they can be sorbed by surface crackinghe getter material is heated to sufficiently high temperatures. Again, H2 is sorbed in the typical reversible wayarbon is permanently fixed. Heavy hydrocarbons, particularly, can be sorbed at the surface of a getter materialoom temperature mainly by physisorption, with the capacity obviously being limited by the available surface a

oble Gases . Noble gases are not sorbed by a getter material. Their removal has to be achieved by other pumpsbsence of chemical interaction of noble gases with getters can be exploited, for example, in the purification ofases.

.6.5vaporable Getters

vaporable getters used in practice are typically Ba and Ti. Ba getters, particularly, are by far the most commonn a large industrial scale, and their application is well established and dates back several decades; their characave greatly evolved during time, and plenty of studies have been performed on the related applications.





6.5.1a Getters

ure Ba is not used as such, because of its reactivity in air which would not allow its practical handling on a larn the early days of the getter developments, many attempts were made to use Ba in the most convenient formshese was the so-called reactive getter consisting in a mixture of barium strontium carbonate sprayed on a tantaBatalum getter) [29]. Further developments led to the use of various types of Ba containing alloys and, finallyabilization of Ba by alloying with Al. The BaAl phase diagram is shown in Fig. 5.8. Among the different allond Al, BaAl4 has been chosen because of its stability, allowing safe and reliable handling during manufacturin

matter of fact, it is known as Stabil 2 alloy, shortened to St2). Other alkaline-earth metals have been studied [30ossible evaporable gettersparticularly Ca and Sr, which also form alloys with Al and have high vapor pressurehan Ba) as seen in Fig. 5.9. For various reasons, however, Ba turned out to be the best compromise for differenequirements.



Fig. 5.8Constitutional diagram of the BaAl system.





Fig. 5.9Vapor pressures of Ca, Sr, and Ba.

Fig. 5.10Cross sections of a ring-shaped Ba getter:

(a) open center getter and(b) closed center getter.

he BaAl4 alloy can be pulverized and compressed in a metallic container, usually in shape of a ring [31, 32] (open" center or "closed" center) as shown in Fig. 5.10. The container can, however, also be in the shape of a d

wire.



his container can then be heated (e.g., inductively by a radio-frequency coil) to the dissociation temperature olloy so that Ba is rapidly evaporated, thereby forming the active film. The evaporation temperature starts signibove 900°C (the melting point is about 1100°C). The process of rapid evaporation of Ba from a Ba getter is soalled flashing of the getter. This type of getter is calledendothermic [33, 34] since it needs energy for the dissociaf the alloy. It requires high temperatures to start evaporation; and the process is not very well controlled since an also partly evaporate with Ba, thus negatively affecting the gettering





roperties of the Ba film, and partly react with the getter container (generating melted areas, holes, etc.).

o obtain getters having a lower evaporation temperature and more reliable and controllable characteristics, theowder is mixed with Ni powder and then compressed in the container. In this case, during heating, the followieaction takes place between the two components: BaAl4 + 4Ni→ 4AlNi + Ba. Ba evaporates and deposits onto tvailable surfaces while Al is "blocked" by its reaction with Ni. The above reaction starts at approximately 800enerates heat (enthalpy of reaction about 11.2 kcal/mol); the getter is therefore calledexothermic [33, 34].

he time necessary to start the reaction from the beginning of heating is called start time , while the time from theeginning of heating to the end of heating off is calledtotal time of the flashing process. The maximum evaporateuantity, or yield , of the getter is generally a percentage of the total quantity of Ba contained in the getter; howepecial getters it can approach 100% (the getter is said to showtotal yield ).

he flashing process for an exothermic getter is schematized in Fig. 5.11, where the temperature of the getter isersus time. The getter heats up to the point where the above exothermic reaction starts and raises the getter temp to 12001300°C. There is then a decrease corresponding to a slowdown of the reaction. During the process, t

with generation of heat there is obviously also heat dissipation mainly due to radiation losses and vaporization

he quantity of Ba evaporated can range from few milligrams to a few hundred milligrams, depending on the gype and application. A typical "yield" curve for a Ba ring getter (Fig. 5.12) shows the quantity of Ba evaporateunction of start time for a certain total time. If the start time is too short, the getter is excessively heated and caf course, this is not acceptable and has to be avoided.

nteraction of Gases with a Ba Film . The interaction of a Ba film with residual gases in a vacuum device is a veromplex phenomenon as illustrated by Perdijk [35]

Fig. 5.11Typical temperature trend of a Ba getter during the

"flashing" process.





Fig. 5.12Typical "yield curve" of a Ba getter.

Fig. 5.13. The main reactions occurring at the surface of the Ba film with the usual main gases to be sorbed are, howollowing primary reactions:

Ba + O2→ 2BaO (93 mbar·liter g1)

3Ba + 2CO→ 2BaO + BaC2 (107 mbar·liter g1)

5Ba + 2CO2→ 4BaO + BaC2 (67 mbar·liter g1)3Ba + N2→ Ba3N2 (53 mbar·liter g1)

Ba + H2O→ BaO + BaH2 (80 mbar·liter g1)

Ba + H2→ BaH2 (173 mbar·liter g1)

ogether with the reaction type, the stoichiometric capacity of the Ba film for the considered gas is also indicated. Theapacity, however, depends on the film characteristics, as will be seen later.

here could be also secondary reactions, the study of which might lead to a better understanding of the practical behavetters. For example, BaC2 can react with H2, and particularly with H2O, to generate hydrocarbons (especially CH4 a2H2). Also tertiary reactions are possible, whose practical effects are usually negligible. A comprehensive study of tteractions of residual gases with a Ba film has been made by J. Verhoeven and H. van Doveren [36]. During sorption

ollowing sorption of N2, a "displacement" phenomenon has been observed [37]: It consists of emission of previously2 due to its replacement with O2.

orption Characteristics . The sorption properties (speed and practical capacity) of a Ba film depend not only on the typorbed gas and the operation temperature





Fig. 5.13Types of reactions which can take place on or Ba film; besides primary reactions,also secondary and tertiary reactions can take place. The getter film is therefore adynamic means to keep the atmosphere in a vacuum device as low as possible and

in any case in a reducing state (for the benefit, for example, of oxidecathodes present). (From Perdijk [35].)



Fig. 5.14Typical sorption curves (speed

versus sorbed quantity) for variousgases on a Ba film.

(From P. della Porta and L. Michon [38].)





ut also on the physical characteristics of the Ba film itself, which are linked to the flashing conditions (pressuremperature of the substrate, surface characteristics of the substrate, thickness of the film, etc.).

he sorption curves for CO, N2, and H2 are typically represented in Fig. 5.14 [38]. They have been obtained bbout 80 mg of Ba inside a cathode ray tube (CRT) on a surface of a few thousand of square centimeters. CO isor which the initial speed is the highest, and N2 is the gas with the lowest speed. The actual curves per unit arelm, even if they don't substantially change in the relative trend, can be modified in terms of speed and capacitepending on various parameters. The initial speed values can be particularly affected by flashing conditions aorption test conditions, as indicated by the different values shown in Table 5.3 [39,40]. This table shows the strobabilities corresponding to initial speeds measured by different authors for some common gases: N2, CO, H

O2, and H2O.

he kinetics of the sorption process is characterized by surface and bulk diffusion, so that it can be schematicalepresented as in Fig. 5.15. This is particularly

Table 5.3. Summary of Initial Sticking Probability Values for Barium FilmGases Sticking Probabilities

(Initial)

Authors

H21 × 103

Wagener

4.17 × 105della Porta and Origlio

1 × 104Ichimiya, Mizushima, and Oda

N23 × 104

Wagener

5.03 × 105

della Porta

1 Ichimiya, Mizushima, and Oda

4 × 101Wagener

CO1.2 × 102

Bloomer

2.7 × 102Morrison and Zetterstrom

2.8 × 102della Porta and Ricca

0.3 Bloomer and CoxO2 0.4 Verhoeven

0.6 VerhoevenCO2 0.6 Wagener H2O 0.6 VerhoevenReferences



S. Wagener, J. Phys. Chem . 60, 567 (1956).

P. della Porta and S. Origlio,Vacuum 10, 227 (1960).

T. Ichimiya, Y. Mizushima, and Z. Oda, Proc . 1 st Int. Congress on Vacuum Namur ., 1958, Vol.I, p. 641. Pergamon Press, Oxford, 1960.

P. della Porta,Vacuum Symposium, Transactions , p. 317. Pergamon Press, London, 1959.

R. N. Bloomer, Br. J. Appl. Phys . 8, 352 (1957).J. Morrison and R. B. Zetterstrom, J. Appl. Phys . 26, 437 (1955).

P. della Porta and F. Ricca, Le Vide , 85, 1 (1960).

R. N. Bloomer and B. M. Cox, Br. J. Appl. Phys ., 16, 1331 (1965).

J. Verhoeven,Vacuum , 30, 69 (1979).





Fig. 5.15Speed versus time during sorption according to

different mechanisms.

Fig. 5.16Approximate structure of a Ba film.

mphasized by the fact that the actual structure of a Ba film is granular. This structure is depicted in Fig. 5.16, mall circles represent the Ba microparticles forming the film. The particles can be smaller or bigger and the stran be more or less compact, depending on the formation conditions of the film.



he model for the various stages of sorption on a Ba films is schematically shown in Fig. 5.17. At the beginninrocess, mainly the surface adsorption on the ''external" surface takes place since this surface is readily availaborption. Then, surface adsorption occurs at the internal surfaces of the film; bulk diffusion takes place simultanut it is slower and therefore accounts for the part of the sorption curves with lower speed and higher capacity. resence of the diffusion process is evidenced by Fig. 5.18 [39]. This figure shows the amount of CO, N2, and orbed as a function of the square root of time during which the sorption has taken place. As





Fig. 5.17Model showing the different

stages of gas sorption on a Ba film:(a) Surface diffusion, (b) internalsurface diffusion (intergranular

diffusion), and (c) bulk diffusion.



Fig. 5.18Diffusion process for various gases in a Bafilm. The sorbed quantity of a gas at a giventime t , divided by the total sorbed quantityat that time, is plotted as a function of the

square root of time. (From della Porta [39].)

lustrated previously, in a semi-infinite medium the linear dependence of the sorbed quantity versus the squareme is an indication of the presence of a bulk diffusion process. As a matter of fact, the plots in the figure showend, apart from deviations at the beginning and at the end of the curves. The initial deviations from linearity i

he existence of a phenomenon different from bulk diffusion, whose





ate decreases with time less rapidly than in the case of a diffusion process: as mentioned above, in fact, surfacedsorption prevails at the beginning of the sorption process. The deviation from linearity toward the end of the ndicates the influence of the limited film thickness on bulk diffusion (due to deviation from the semi-infinite mssumption).

emperature-Dependence . If sorption occurs at increasing temperatures, also the sorbed quantity increases sinceiffusion is enhanced, as can be seen in Fig. 5.19 with regard to CO [41]. In the case of H2, because of the reveharacter of its adsorption, the increase of temperature can eventually excessively increase the equilibrium preshis gas. The H2 equilibrium pressure in the H2Ba system is shown in Fig. 5.20.

he effect of temperature is found to be different for CO, N2, and H2; this can be seen in Fig. 5.21 [4143], whihe temperature-dependence of nitrogen, hydrogen, and carbon monoxide diffusion in a Ba film (2 mg of Ba onpparent surface of 100 cm2). The figure shows that for CO and N2 there is a critical temperature indicating a che sorption process, from surface diffusion (at lower temperatures) to bulk diffusion (at higher temperatures). Turves allow one to calculate the activation energies for the processes involved, corresponding to the potential

which the diffusing particle must overcome to move from one lattice point to another, when the movement is osurface diffusion) or into the solid (bulk diffusion). On the contrary, H2 does not seem to show a critical tempe

Fig. 5.19Sorption throughput as a function of the sorbed quantity at differenttemperatures. The apparent area of the film were 100 cm2 and the evaporated

quantities were 2 mgexcept at 423 K and 473 K, when this quantity was5 mg and 8.5 mg, respectively. During the tests the conditions ensured that

the same number of molecules were striking the unit area perunit time. (From Ricca and P. della Porta [41].)





Fig. 5.20Equilibrium isotherms for the BaH2 system.

ndicating that diffusion of this gas is already important at lower temperatures and overshadows surface diffusio

hickness-Dependence . The sorption characteristics can change as a function of the film thickness, as can be seeig. 5.22 in the case of N2 sorption [42]. At a very small thickness, all the available Ba reacts with the gas mol

When the thickness increases, eventually the more internal layers of the Ba film are no longer accessible and thuantity of gas sorbed becomes almost independent of the thickness. This trend can be modified by increasing orption temperature thanks to the enhanced diffusion process.



or a compact fully sintered Ba film, it has been found that there is a maximum thickness involved in room temorption which in the case of CO is about





Fig. 5.21Temperature dependence of N2, H2, and COdiffusion in barium films. The weight of the

evaporated Ba is 2 mg, and the apparent surfaceis 100 cm2. (From della Porta and F. Ricca [42].)



Fig. 5.22Total amount of sorbed N2 as a function of

the thickness of the Ba film at 298 K.(From della Porta and F. Ricca [42].)





0 Å [44]. This corresponds to about 0.04 Pa·liter of CO sorbed per square centimeter of a 3.6 µg Ba film as aonsequence of the reaction: 3Ba + 2CO→ BaC2 + 2BaO. When the critical temperature is reached or exceededowever, sorption continues until all the available Ba has reacted.

nfluence of Evaporation Conditions . The physical characteristics of the Ba film strongly depend on the ambientressure during evaporation and on the temperature and characteristics of the surface onto which it is formed [4

matter of fact, depending on these conditions the formed Ba film can be more or less porous, as already mentioructure of a Ba film can change as, for example, depicted in Fig. 5.23 at different substrate temperatures durineposition. The actual surface appearance of a Ba film deposited at room temperature and at 340°C has been stxample, by Perdijk using a scanning electron microscope (SEM) [45].

imilar results are found if Ba is evaporated in the presence of a certain pressure of gases such as noble gases, mr nitrogen. If the film is formed in high-vacuum conditions, it is less porous than a film deposited in low-vacuonditionsas was shown, for example, by Hoshimoto and Kitagawa [46]. The differences in porosity translate i

more or less efficient sorption.

igure 5.24 shows the amount of N2 sorbed at room temperature by a Ba film formed at different condensationemperatures of the film [42]; the higher the temperature the more compact or sintered is the film and thereforeower its capacity.he sorption performances of a Ba film can change by changing roughness and surface porosity of the substrat

which the film is formed [47]. In general, rough



Fig. 5.23Schematic of the structureof a Ba film to show how

porosity of the film dependson the formation conditions.

(a) Highly porous: Glass wall atabout 27°C and pressure (Ar,

CH4, N2) between 5 and 0.1 mbar.(b) Partially sintered with some porosity: Glass wall at about

100°C and some outgassing fromthe getter assembly. (c) Sinteredwith very low porosity: glass wall

at about 350°C and highvacuum (about 105 mbar).

(From Perdijk [35].)





Fig. 5.24Total amount of N2 sorbed by Ba films as a functiontemperature of condensation of the film (Ba weight,2 mg; apparent surface area, 100 cm2; test pressure,5.104 Torr). (From della Porta and F. Ricca [42].)

urfaces tend to produce also higher surface area films with improved sorption characteristics (unless the formeelatively thick).

a Distribution . The distribution of a Ba film is important in determining its sorption characteristics; if the film arge, the total speed will also be large. The same amount of Ba in smaller areas corresponds to a thicker film weduced performances. On the screen of a CRT a high film thickness is to be avoided to prevent an excessive bhe electron beam.

he film distribution is strongly affected by the getter position and by the actual flashing conditions. There are methods developed to determine the Ba distribution [4749], for example, in a CRT. They are used to study the

arameters influencing this distribution and to choose the appropriate getter type and mounting positions.

as-Surface Reactions . As mentioned above, there are various possible surface reactions, among which methanormation deserves more specific attention. In practice, it is found that the considerations made for a Ba film alor a Ti film.

pecific studies have been performed to investigate the possible generation of CH4 on a getter film under sorptases containing carbon and H2 [5052]. For example, results are reported by dosing CO2 and H2 or H2O with equences on Ba and also Ti films [53]. The tests have been performed at relatively high pressures and thereforurface coverages. It is found that the active gases are well sorbed by the films but generate some methane inpproximately the same quantity; this quantity is in the range of 15% of the amount of CO2 admitted. It is alsohat there is some effect of the sequence of dosing; if CO2 is admitted first, more methane is formed.





umping of methane [53] can be obtained with these getter films by cracking this gas with a hot metallic surfaceaction with suitable metal oxides as follows:

MeO x + CH4→ Me/MeO y + H2O + CO2.

he getter films sorb the formed active gases and force the reactions toward the right-hand side of the equationetter Types . Various types of getters have been developed to cope with the evolving requirements of Ba getterpplications (particularly, color television tubes). In addition to the common types, high-performance getters arvailable such as gas-doped getters, total-yield getters, high-yield getters, frittable getters, and low-argon getter

as-doped getters contain, mixed with the BaAl4 and Ni powders, a small amount (usually less than 5% by weiompound which dissociates at the beginning of Ba evaporation generating a pressure peak of N2 (in the range02101 mbar) within the vacuum device to better distribute the Ba and allow the formation of a more porous fihe commonly used compound that generates N2 is iron nitride (Fe4N) [54]. The process is shown in Fig. 5.25 soon reabsorbed by the Ba film. The amount of N2 added is small compared to the capacity of the Ba film, sverall effect is an increase of sorption performances. Figure 5.26 shows the good room temperature sorptionharacteristics of Ba films for CO obtained by evaporating Ba from N2-doped getters as compared to the case woping was present [55]. The curves for N2-doped getters have been obtained at different temperatures of the Culb during flashing to also show the effect of the substrate temperature during film deposition.

ince part of the Ba evaporates when the pressure is already greatly reduced, a second N2 peak, between start total time, can be generated to further improve the gettering performances of the Ba film. The getters exhibitingharacteristics are the so-called delayed N2-doped getters [56].

Fig. 5.25 N2 evolution and barium yield during flashing of

an N2-doped getter.





Fig. 5.26CO sorption curves for doped and nondoped (dashed line)Ba getters at different substrate temperatures during film

deposition (sorption test at room temperature).(From della Porta [55].)

Fig. 5.27Section of a "total yield" getter showing the evaporation paths of Ba.

otal yield getters have been developed to release almost all of the Ba contained in the getter. They need a specrrangement to control evaporation. The structure of the getter (Fig. 5.27) allows evaporation from two surfacencreasing yield [57,58].



igh-yield getters meet the needs for large size CCRTs requiring increased amounts of Ba to cope with the increas load. Closed center getters with special indentations on the evaporating surface have been developed for thurpose [59]. Yields of Ba in the range of 300 mg and more can be obtained.

rittable getters have been developed to withstand the frit cycle in CCRT manufacturing processesthat is, heatinp to 450°C for 1 or 2 h. Under these





onditions, they still show a controlled exothermicity during the getter flashing process [60, 61].

ow-Argon getters reduce the Ar content in a CCRT, which is partially due to a normal getter itself. Ar is nothemically noxious to the CCRT cathodes. However, in some tubes, where impregnated cathodes are used, the artial pressure has to be minimized to avoid damaging the cathodes because of the Ar ion bombardment.

6.5.2itanium Sublimation Getter Pumps

i can be evaporated or sublimed onto a surface to form, as in the case of Ba, a highly active film. In case of Tiublimation is used as a synonym of evaporation (Ti vapor is produced from the solid without passing through thase). Ba has, however, a much higher vapor pressure compared to Ti, so that its evaporation can take place vuickly and therefore fits very well those applications (such as CRTs) where minimization of the process time issential. At 1000°C, for example, the vapor pressure of Ti is about 109 mbar while that of Ba is about 1 mbar.vapor pressure of about 103 mbar, Ti needs to be heated to 1500°C, so a relatively high power is required.

n general, freshly evaporated metals exhibit more or less good chemisorption properties, as can be seen from F62], where the sticking probabilities for O2 are given as a function of the O2 sorbed quantity. Ti is effective anarticularly good, compared to others, at relatively high O2 sorbed quantities. From various sorption studies anractical reasons, Ti turns out to be, in general, the most appropriate metal for use in sublimation pumps. Thesere applied in vacuum systems where the sublimation process can be controlled (using suitable power suppliersdjust the sublimation rates and cycles to the needs of the

Fig. 5.28Reaction probability of oxygen on various metal films as a function

of the gas sorbed quantity.(From Fromm and Uchida [62].)





pplication and where the surfaces available for the metal film formation are generally large.

i sublimation pumps have been extensively studied particularly in UHV systems. A recent comprehensive reveen written by K. Welch [63].

orption Characteristics for Various Gases . For this type of film the sorption characteristics are often expressed erms of sticking probability or coefficient as a function of the surface coverage, expressed for example in molem2 (2.2 × 1019 molecules correspond to about 1 mbar·liter at 20°C). Typical data are shown in Fig. 5.29 [64]een that the sticking probabilities are widely separated for H2 and N2. H2, however, maintains a more constanrobability as a function of the coverage, as expected, because of its relatively high bulk diffusivity combined welatively high solubility. The capacities range from somewhat less than 1 monolayer for N2 to about 10 monol

O2. When about one or a few monolayers, depending on the gas type, are formed, the sorption speed decreasesapidly; the film therefore has to be refreshed by a new evaporation. This continues until the available Ti is usean also be slowly but continuously evaporated to keep a more constant sorption speed.

emperature-Dependence . As in the case of Ba films, Ti films sorption characteristics are influenced by the temf deposition of the film. Figure 5.30a [64] shows the trend of the sticking probability for CO sorption as a functihe surface

Fig. 5.29Room temperature sticking probability for various gases as

a function of the surface coverage of the Ti film.(From Gupta and Leck [64].)





Fig. 5.30Effect of the substrate temperatures and of the sorption

temperatures on the sticking probability (O2 and CO). Foreach curve the numbers indicate first the substrate

temperature during film deposition and second the sorptiontemperature. (From Gupta and Leck [64].)

overage of a Ti film formed at different temperatures. The best results are obtained forming the Ti film at 77 Korbing gases on the film kept at the same temperature. Films formed at lower temperatures are more porous anherefore exhibit higher surface capacities. The effect is less important in the case of O2 (Fig. 5.30b) [64].



Various studies have been carried out concerning the temperature dependence of sticking coefficients [65, 66]. as summarized these data as shown in Table 5.4 [65].

ependence on Thickness . As the Ti film thickness is increased, the sorption capacity does not increase proportiecause the film tends to be more compact





Table 5.4. Summary of Sticking Probability Values and Sorbed Quantities at Saturation at 300 Kand 78 K, for Various Gases with Titanium Film [65]

Initial stickingcoefficient

Quality Sorbed(×1015 molecules/cm2)

300 K 78 K 300 K 78 K H2

0.06 0.4 8230770

D20.1 0.2 611

H2O0.5 30

CO0.7 0.95 523

50160

N20.3 0.7 0.312

360

O20.8 1.0 24

CO20.5 424



Fig. 5.31Dependence of the saturation coverage for N2 onthe film thickness. (From Gupta and Leck [64].)

nd its internal layers become less accessible to the gas [6466]. This can be seen in Fig. 5.31 [64], where the saoverage (corresponding to practically zero sticking probability) for CO is given as a function of increasing thi seen hat if the thickness increases about 20 times, the capacity increases about 6 times. This





means that to better exploit the available Ti one should evaporate less Ti, but more frequently.

isplacement Phenomena and Surface Reactions . When various gases are simultaneously pumped, it is observedome gases can displace others [64, 67]. For example, Gupta and Leck have found that O2 can displace all otheO can displace CH4, N2, and H2; H2 can displace N2 and CH4, and N2 can displace only CH4. This can proccur at relatively high coverage and when no real strong chemical bond has been formed at the surface. As alr

mentioned, there is the possibility of CH4 formation on a Ti film due to the reaction between surface C and theH2O and H2. This effect is reduced if the film is at 77 K. Some authors [64], performing studies in high-vacuumonditions, have also considered methane generation as possibly due also to the displacement of preadsorbed Cydrogen sorption.

eeling . It is observed that when the Ti film has grown to a certain thickness, it starts peeling off. It is reported his effect is observed when the deposition corresponds to about 0.0230.03 g·cm2that is, about 6075 µm (if a deg·cm3 is considered). The film adhesion is poor if the substrate surface is very smooth (it is reported that sand

ubstrate surfaces are less prone to peeling). If peeling occurs, H2 can be released and generate undesirable prencreases. Peeling Ti films are pyrophoric and can ignite when exposed to air. It is therefore necessary to clean oated surface from time to time.

ypes of Sublimators and Pump Structure . The Ti vapor sources can be of different types: filament type (heated byirect passage of current),radiation-heated type andelectron-gun-heated type. Ti is often used in alloy form rathes a pure metal. In the filament type, Ti is commonly used as an alloy with Mo or Ta to have good mechanicalesistance and a convenient electrical resistivity. A typical ''filament" shape [69] is shown in Fig. 5.32. In the raeated type a heater radiantly heats a Ti body of the shape for example shown in Fig. 5.33 [70] (known as the The evaporation rate is finely controlled by regulating the electric current used for heating. These sublimators a

mmersed in a chamber and evaporate Ti onto the inner wall

Fig. 5.32Simple Ti sublimator of the "filament" type.





Fig. 5.33Ti sublimator of the "ball"-type TiBall®.

(From Harra and Snouse [70].)

Fig. 5.34Structure of a Ti sublimation pump, with

LN2-cooled walls.

urfaces. These walls are often arranged to be cooled down to LN2 temperature (Fig. 5.34). The structure of theelatively simple. Of course, in order for these pumps to exhibit high speeds the inner walls should be large. Sohere are baffles to prevent the evaporated Ti from entering the vacuum system; conductance limitation could, hractically prevent full exploitation of the high speeds available.

ractical sorption speeds for various gases are given in Table 5.5 at two condensation temperatures [71]. The tietween regenerative sublimations depends on the pressure of the vacuum system and the gas type to be sorbedublimation can be almost continuous at relatively high gas loads (105 to 106 mbar pressure range) or periodic

ong (1015 h) intervals at low gas loads (in the range of 1011 mbar). Because of the high temperature needed foublimation, the sublimator has to be submitted to careful degassing procedures to reduce particularly H2 genenset and an excessively high steady pressure. H2 turns out not to significantly influence the sorption characterther active gases; on the contrary, H2 sorption is negatively affected by contamination of the Ti film by other 64, 72].





able 5.5. Typical Practical Pumping Speeds per Unit Surface of a Ti Film for the Most Common Gases, at Different Sorptionemperature [71]a

Gas SpeciesTemperature) H2 N2 O2 CO CO2 H2O CH4 Inerts20°C

3 4 9 9 8 3 0 0

96°C 10 10 11 11 9 14 0 0

Temperature is of condensing wall and shows resultant pumping speed of Ti film. Units are liter·s1·cm2.

able 5.6. Some Physical and Electronic Characteristics of Common Base Getter MetalsTi Zr Hf Th

uter electron configuration3d 2 4 s2 4d 2 5 s2 5d 2 6 s2 6d 2 7 s2

(5 f ) 6d 7 s2

tomic radius (6-coord.) (Å)1.49 1.62 1.58 1.82

ifferences in Al atomic radius (%) 4.03 11.66 9.49 21.43

-phase parameters (Å)cpha = 2.9503c = 4.6831

cpha = 3.230c = 5.133

cpha = 3.1883c = 5.0422

bcc5.086

β transition temperature (°C)882 862 1950 1400

Melting point (°C)1670 1860 ~2000 1750

6.6

onevaporable Gettersany different kinds of nonevaporated getter materials have been developed since World War II. Metals of the IVB group and some of tinides and rare earths, as already mentioned, have often been used to make getters. In Table 5.6, the properties of some of these metammarized. Also, in this table the percentage difference of the atomic radius of Al is compared to the other metals. Al is often alloyed e above-mentioned metals to obtain specific gettering characteristics. The use of Al tends to reduce the surface reaction rates with air mperature, but increases the diffusion rates of the adsorbates at higher temperature.

mong the early nonevaporable getters, it is worth mentioning the Th-based getters, calledCeto getters [73] (a similar old type of getter islled Ceralloy 400 [74]). Ceto is a quaternary alloy, made by sintering a mixture of Th powder and powdered alloy called "Ceral" at 90vacuum. Ceral consists of Cermishmetal (80% Ce and 20% La) and Al and has the following chemical composition: (Ce, La) Al2. Th

nal atomic composition of the getter is about 10 Th, 2.5 Ce, 0.5 La, and 6 Al. La can be completely replaced by Ce to obtain a ternaryoy (ThCeAl) having practically the same properties as the quaternary alloy. Also, the Th2Al binary alloy has been studied and used atter, particularly for H2 [75]. The ultimate amount





f H2 in the compound is found to be approximately 16 atoms of H2 per unit cell (Th8Al4). Above this concenhe equilibrium pressure rises rapidly to high values. An extrapolation of the curve for the Th8Al4H4 compounn an equilibrium pressure of approximately 1013 mbar at room temperature [73].

r and Ti are metals now commonly used as getters, particularly in alloy form with one or more additional elemMany alloys have been studied in the last few decades to meet the requirements of gettering all possible gases opecific gases present in various applications. Some of these alloys will be described in the following.

r and Ti can be used as pure elements in powder form to make getters for some applications. Ti is a somewhaetter at room temperature but similar or worse compared to Zr at working temperatures above 400°C [76]. Aomparison is shown in Table 5.7 [76], where the sorption characteristics at 400°C appear to be similar for the

metals for various gases. For comparison, the characteristics for Thorium are also shown. Except for O2, this mxhibits poorer gettering properties than the other two metals. It is also to be pointed out that Ti is more prone tecome sintered than Zr; therefore Zr powders can be more easily activated and work at higher temperatures th

without losing too much surface area. To avoid or reduce sintering, these pure metals when used as getters are umixed with powders of appropriate metals or of other substances.

he equilibrium pressures of H2 with these metals have been studied in detail [77, 78], and the related results a

n Figs. 5.35 and 5.36, where Sieverts' law is found to apply, respectively, in the case ofα -Ti and α -Zr. These curvean be expressed analytically as follows:

where p is in mbar,q is in mbar·liter (of H2) per gram (of getter material), andT is in Kelvin.

he Binary Zr and Ti Alloys . These alloys, particularly those with the addition of Al, have long been investigateery interesting results especially in the case of Zr.

he ZrAl, TiAl, and also the ThAl systems have been studied in a wide range of Al contents [76]. The getteringroperties were measured for various compositions. The results obtained in the case of N2 and at a sorption temf 400°C, after

Table 5.7. Gettering Rates of Ti, Zr, and Th for Various Gases, at 400°C [76]Gettering Rate (cm3·s1·cm2)

Gas Ti Zr ThN2

36 30 5.6

CO 43 44 20CO2

44 38 15

O285 85 122

H2285 222 213







Fig. 5.35Sieverts' plots for H2 inα -Ti.(From Giorgi and Ricca [77].)

ctivation at 900°C, are shown in Fig. 5.37 [76]. It is seen that the behavior of the ZrAl and ThAl systems are romplex, showing maxima and minima in the sorption properties as a function of the Al contents. The TiAl syshe contrary, shows a regular continuous decrement in gettering rates with increasing Al contents and, in any caoorer sorption characteristics compared to the other alloys for compositions above a few percent of Al. The Zhow the best sorption properties compared to the other alloys (and pure metals) in a wider range of Al contentave the highest peak in the gettering rates when Al is about 16% by weight. The Zr(16%) Al alloy has therefoxtensively studied and used in many practical applications [7680]; today it is one of the most common getter mpplied (under the trade name of St101) in vacuum technology.

Among the getter binary alloys, the Zr-based alloys containing V, Ni, Fe, Mn, or Co have also received interestome practical applications.

he ZrAl Getter Alloy . The sorption characteristics for H2 and CO have been studied together with those for N2ifferent compositions of the ZrAl system, still finding a maximum in the sorption properties around 16% Al. Te seen in Fig. 5.38 [80], where, for ease of comparison, the gettering rates are given as the ratio (G/G max) of eachngle sample rate versus a given gas and the rate of the most active sample versus the same gas. The figure als

he phase compositions at various







Fig. 5.36Sieverts' plots for H2 inα -Zr.(From Ricca and Giorgi [78].)

Al contents of the tested ZrAl samples (the ratio of the indicated numbers in the abscissas represents the ratio br and Al atoms). The results refer to getter samples working at 400°C, after activation at 1000°C for 30 s in th

mbar range of pressures. The following main considerations can be made concerning this getter material: (a) Thmaximum activity is in the biphase region containing Zr5Al3 and Zr3Al2 intermetallic compounds. (b) The actncreases rapidly from the eutecticβ-Zr-Zr5Al3 (with 11%Al) to higher Al contents with a maximum around 16%ecreases rapidly with the Al contents greater than 17.5%. (c) The maximum activity is not exactly coincident arious gases. It is maximum for N2, H2, and CO, respectively, at the compositions having the following Al wercentages: 1415.5, 15.5, and 16. The best composition compromise is therefore Zr(15.516%) Al. (d) The relaorption rates found indicate that the getter alloy exhibits a particularly high rate for H2.

he sorption rates of the Zr(16%)Al composition have been investigated for various gases as a function of tempwith the results shown in Fig. 5.39 [76]. It is seen that great increases are observed for all the tested gases abov

and particularly in the case of CO. The diffusion rates are especially high for H2 and their dependence on teman be better seen in Fig. 5.40 [76].

he characteristics of the H2ZrAl alloy system are shown by the isotherms represented in Fig. 5.41 [81, 82]. Thquilibrium pressure of H2 can be very low and







Fig. 5.37Relative gettering speeds of TiAl, ZrAl,

and ThAl alloys, as a function ofcomposition. (From della Porta [76].)



Fig. 5.38Relative gettering speeds for different gases (at 10 min from the

beginning of the sorption test) as a function of the ZrAl alloy compositions.(From Barosi [80].)





Fig. 5.39Gettering speeds for different gases on the Zr(16%)Al getter (activated at 1000°C for 30 s) as a

function of sorption temperature.(From della Porta [76].)



Fig. 5.40Dependence on temperature of the diffusion rates of

various gases in the Zr(16%)Al alloy.(From della Porta [76].)





Fig. 5.41H2 isotherms in the H2-Zr(16%)Al getter system.

(From Ferrario [81].)

ery compatible with operation in ultra- or extra-high vacua. The correlation between H2 concentration, equilibressure, and temperature of the getter can be represented by the Sieverts' equation:

where p is in mbar,q is in mbar·liter·g1, T in Kelvin.

he activation of this binary getter alloy is performed by usually heating up to temperatures in the range of 700he times involved range from a few hours to half a minute. Since, in some practical cases, also partial activatioe acceptable, the various possible activation conditions for this alloy have been investigated and found to be thown in Fig. 5.42 [84, 85]. In this figure the 100% curve corresponds to full activationthat is, the activation coiving the maximum sorption efficiency. This situation can be reached, for example, by heating at 900°C for 30t 750°C for about 30 min. Sixty percent activation can be achieved, for example, by heating the getter at 700°

min or at 650°C for about 90 min. The activation conditions are the results of many sorption curve measuremenowever, the fundamental mechanism accounting for these results has been clarified by specific







Fig. 5.42Activation efficiency for the Zr(16%)Al getter as a

function of temperature and time of activation.

Fig. 5.43Surface composition of the Zr(16%)Al getter

during heating at various temperature.(From Ichimura et al. [86].)



urface analyses based on X-ray photoelectron spectroscopy (XPS). This type of surface analyses has been pern this getter material at different temperatures, and the results are shown in Fig. 5.43 [86, 87]. The surface com dominated by carbon and oxygen until the temperature exceeds about 600°C, when these elements tend to dind the surface finally shows a metallic and therefore reactive character by the dominant presence of Zr and Al





ther Zr- or Ti-Based Binary Alloys . Various other types of binary alloys based on Zr and/or Ti have been studieecent years for specific gettering applications. A few, so far the most common, of these alloys are briefly descrhe following.

rCo alloys have been studied particularly for hydrogen isotopes sorption and storage, especially in experimentuclear fusion machines to replace the efficient, but also unsafe, uranium. The composition having about 61% een thoroughly investigated [88, 89].

rNi alloys have been studied, particularly the intermetallic compound Zr2Ni (75.7% by weight of Zr) [86, 90]etter exhibits good sorption capabilities especially for H2 and H2O.

he presence of Ni in the alloy or simply mixing Ni powder with Zr powder has been shown to speed up and ehe sorption of H2 (when relatively high pressures are involved) even if no previous high-temperature activatioarried out [91]. Ni is believed to act as a dissociation catalyst for H2, thus facilitating H2 sorption according to

mechanism described by van Vucht.

rFe alloys , particularly the Zr2Fe composition (76.5% by weight of Zr), have been developed for some speciapplications. This getter material can be activated at relatively low temperatures but shows higher hydrogen equressures compared to the St101 getter [82, 92, 93]. The gettering capability, very good for other active gases, ound to be very poor for N2 (it improves at temperatures higher than 300°C).

rV alloys have been extensively studied [94] among the materials to be used for H2 storage. The ZrV2 compoppears to exhibit interesting gettering capabilities; however, it is considered to be too pyrophoric for common ractical applications on a large scale. Ternary alloys containing Zr and V have been investigated instead with hat some of the best present getter materials have been produced.

rTi alloys have also been studied as getters showing inferior gettering capabilities compared to the fully activa16%)Al getter alloy; this is illustrated in Fig. 5.44 [95], where Zr is shown for comparison.

6.6.1ernary Alloys

inary and ternary alloys, particularly based on Zr, have been extensively studied as hydride materials. The terlloys have been especially interesting to better modulate the characteristics of interaction between the metal an9699]. Attention was eventually focused on these alloys also from the point of view of gettering.

ebler and Gulbransen [94] have, for example, investigated the formation of hydrides of the Laves-phase binaryompounds ZrM2, where M = V, Cr, Mn, Fe, Co, and Mo. It was found that the absorption capacity (measuredar) decreases significantly with the increase in the 3d orbitals occupation number of the transition element, M, ache 3d series. As an example, the capacity for the ZrV2 compound was found to be 4.8 H2 atoms per formula; w Fe or Co, this capacity is instead 0.2 H2 atoms per formula. Shaltiel et al. [100] have then studied the formatydrides of ternary (pseudobinary) intermetallic compounds of the general formula Zr(A1 x, B x)2, where A designa

V, Mn, or Cr and B designates Fe or Co, with x changing between 0.05 and 0.9. The advantage found versus prev

ydride materials was both economical and related to the fact that these Zr-based compounds did not require hictivation temperature.





Fig. 5.44CO gettering characteristics for different getter

materials, at 400°C. In all cases the material mass inthe same and the test pressure is 3 × 106 Torr.

(From A. Giorgi [95].)

hese types of materials have been studied for storage of H2 isotopes in experimental fusion machines and as gHV and UHV applications.

is useful to point out here that a material having good sorption capabilities for a gas such as hydrogen, at relaigh pressures, does not necessarily imply that it could be a good getter material. The sorption speed may be toeven for hydrogen), or the diffusion characteristics too poor, to allow diffusion of active gases different from h

when low pressures are involved. Therefore specific and sometimes complex studies must be performed to devetter even starting from some known general features.

Among the various ternary alloys studied, the ZrVFe alloy in a certain range of compositions has shown excellettering qualities for all active gases combined with other interesting physicochemical characteristics.

he ZrVFe Alloy . The study of ZrV2 as a getter material showed that good sorption capabilities for H2 could be

chieved. However, this material was found to be pyrophoric to a degree which may be undesirable for industrse. The introduction of Fe and the optimization of the Zr percentage in the alloy allowed the achievement of eettering properties for all active gases, after activation at relatively low temperatures, together with acceptableharacteristics [101]. In particular, the alloys which contain Zr ranging from 45% to 75% by weight, with the olements' percentages also ranging in certain intervals, allow activation temperatures not exceeding about 500°he Zr(70%)V(24.6%)Fe(5.4%) composition (which is also known commercially as St707) is particularly inter

101]. The flammability point of the St707 getter alloy is found to be higher than that of the ZrV2 alloy in simiowder size and with similar getter configuration





haracteristics [101] (the absolute values can change also as a function of particle size, configuration, compressorage conditions, etc.).

n Fig. 5.45 [101] the St707 and St101 sorption characteristics for H2 are compared after activation at 500°C aor 10 min.

f the activation is performed at 900°C, the St101 getter shows a sorption curve similar (or somewhat better at sorbed quantities) to that of the St707 getter, but at 500°C this curve decreases well below the ZrVFe getter cur

which, on the contrary, is not too different compared to the 900°C curve.

oncerning the interaction of the ZrVFe alloy with H2, it is found that Sieverts' law is followed in a relatively wange of H2 concentrations as can be shown by the isotherms of the St707H2 system of Fig. 5.46 [82, 83, 101]quation in the range 108102 mbar is found to be expressed by

where p is in mbar,q in mbar·liter·g1, andT is in Kelvin. The equilibrium pressure of H2 over St707 compared tt101, in the same temperature and concentration conditions, is about two orders of magnitude higher. Howevee expected that with the gas loads usually foreseen in many vacuum applications the H2 equilibrium pressurer also somewhat higher temperatures are quite compatible with the use of this ternary getter alloy in UHV app

As in the case of the ZrAl getter, different activation conditions have been studied for St707, and the resulting df activation are shown in Fig. 5.47. It is seen, as



Fig. 5.45

H2 gettering speed, at room temperature, for the St707and the St101 getters, after activation temperatures of

500°C and 900°C. (From Boffito et al. [101].)





Fig. 5.46H2 equilibrium pressure in the H2-St707 system.

(From Boffito et al. [111].)

lready anticipated, that the activation temperatures with practically reasonable activation times are in the rang50500°C.

ull activation can be obtained, for example, at 500°C in about 10 min or at 400°C in about 100 min. The relatctivation temperatures mean that the bulk diffusion characteristics of this alloy are higher than those of St101.

he XPS surface analyses performed on this getter material have shown that the carbon- and oxygen-rich surfaxhibits a metallic character when the temperature is approximately above 400°C, as can be seen in Fig. 5.48 [his is 200300°C less than in the case of the ZrAl getter; this clearly explains the differences in the activation

emperatures found for the two getter types by performing sorption tests.



he relatively low activation temperature makes this getter very appealing in many practical applications; active performed automatically during the process if temperatures higher than about 350°C are involved during preumping with conventional pumps and does not require a specific step. The activated getter can act





Fig. 5.47Activation efficiency of the St707 getter at different

activation temperatures and time combinations.(From SAES Getters, Catalogue [111].)



Fig. 5.48Surface composition of the St707 getter as a functionof heating temperatures. (From Ichimaru et al. [86].)

s in situ pump and can help speeding up the process besides ensuring pumping during the lifetime of the vacuuevice. Of course this also means that part of the gas load is picked up by the getter during the process, thus coart of the getter capacity.





6.6.2ther Ternary and Multicomponent Alloys

Various ternary alloys with some specific characteristics have been studied and used in certain particular applicAmong them it may be interesting to mention ZrTiNi alloys [103, 104] which have been particularly used in nuuel rods to sorb water vapor with a good retention capability for H2. A Zr(45.4 wt.%)Mn(27.3 wt.%)Fe alloy sgood gettering capability for various gases but relatively high equilibrium pressures for H2 (scarce retention c

or H2) has been recently introduced to pump oxygen from water vapor while essentially releasing H2 (useful, xample, to recover T2 from tritiated water) [105, 106]. Also, various ZrVFe alloys have been developed with ompositions compared to St707 to obtain some specific features such as relatively high H2 equilibrium pressuxploited, for example, in combination with low H2 equilibrium pressure getters in a sort of chemical H2 comp107].

o further modulate the getter characteristics, alloys with four or more elements have been studied [108, 109], aving Zr and/or Ti as the basic components. For example, AB2 intermetallic compounds with the following gormula have been investigated [109, 110]: Ti1aZr aV2cbd FebMncCr d , where 0≤ a ≤ 1, 0 ≤ b ≤ 2, 0 ≤ c ≤ 2, and 0≤2. They are mainly interesting for H2 sorption and storage. The composition variations allow the modulation

lateau pressures, extension of the alpha phase, and modification of the H2 capacity.

7etter Configurations

o practically exploit a getter material, various configurations are developed to fit the requirements and the conf the application. Therefore, the selection of the getter type also depends on the possibility to shape the getter ecessary physical configuration (size, shape, real surface area, total accessible mass available, possibility to be

mounted very close to the gas source, etc.).

Non-evaporable getters can be used just in loose powder or granule form but more commonly are shaped into fuch as pills, rings, strips, and other, more complex structures. It is essential that the getter material be transformowder, whose particle size, in principle, should be as small as possible. The small size is needed to maximize urface area and to have the necessary flexibility to obtain various shapes. It is good practice, however, to reachompromise between the target to maximize the surface area and therefore the surface capacity of the getter anossibility to handle it safely. Particles that are too fine can generate problems related to the possibility of burnandled in air (particularly if used in loose powder getter configuration); moreover, even if they do not burn, thormed on the surface can represent a high percentage of the getter mass, thus making the activation more diffising up a large portion of the getter capacity. The practical sizes of the grains normally used are in the range o

micrometers to a few hundred micrometers.

he most simple and convenient way to use the getter powder is compressing it in pills, in tablets, or in ring-shmetal channels. These configurations are simple and safe to handle and can be easily fitted individually in the apace of a small vacuum device or in a large number if the volume available and the gas load to cope with are lhape and the confined volume occupied by the getter makes it





asier to carry out activation, particularly when it has to be performed by supplying heat externally of the vacuuevice (for example, by a resistance heater or by a high-frequency induction coil). Typical sorption curves of Sompressed pills for various gases are shown in Fig. 5.49 [111]. This figure also shows the effect of increasing peed and capacity by increasing sorption temperatures. For H2 this effect is seen to be less important because elatively high diffusivity of this gas in the getter material already at room temperature.

oose particles and relatively low porosity can be drawbacks of these configurations in certain applications. Tohese problems, porous configurations based on sintered powder have been developed. Depending on the type

material involved, sometimes additives are used either to avoid excessive reduction of porosity or to facilitate tormation of a sintered body in a controlled way [113, 114] and keep a high porosity and surface area. These gee prepared with embedded heaters for activation. Usual shapes available are shown, for example, in Fig. 5.50 16].

he typical porous structure, indicating high accessibility of the gas, can be seen in Fig. 5.51, which is a microgetter portion obtained by an SEM. The getter material used to manufacture these getters can be various and

ypically [113116]: (1) Ti or Zr with the addition of antisintering-nongetter materials to better control sintering.ther getter configurations have been developed to meet various requirements for the increasing number of appsing nonevaporable getters. Getter layers deposited onto various substrates in the shape of strips, foils and cyl

urrently available and widely used in vacuum technology. A typical getter strip structure consisting of a metaloated with a compressed getter

Fig. 5.49Sorption characteristics for various gases by 100 mg St707 pellets with a 50 mm2 surface area at different sorption

temperatures (after activation at 450°C for 10 min).(From SAES Getters, Catalogue [111].)





ayer, usually 50 to 100 micrometers thick, is shown in Fig. 5.52. The most common getter material used are thnd St707 alloys. The getter strip can be used in short or long pieces activated by an external heat source or byeating. St101 getters of this type are used, for example, in the large electron position collider machine at CER

Geneva.

hin, highly porous (over 40%), getter strips and foils (HPTF getters) have been developed recently using speceposition and controlled sintering techniques to cope with the geometrical and physical constraints of certain mall volume

Fig. 5.50Typical shapes of porous sintered getters with embedded heater.



Fig. 5.51SEM micrography of a sintered porous getter.







Fig. 5.53Getter module and dependance of the sorption speedon the ratio of the spacingd and heighth of the getter

walls. Activation at 700°C for 30 minutes and operation at400°C. (B. Ferrario and L. Rosai,7th Int. Vac. Congr ., 1977.)

ecognized specific and sometimes unique features of getters and getter pumps in vacuum technology are: (a) po work with no need of power for operation (at ambient temperature), after activation or evaporation; (b) possi

mounting the getter close to the gas source, thus avoiding the pumping speed limitations due to the connectiononductances; (c) flexibility in structure and size to fit the geometric constraints of the application; (d) possibilis in situ pumps during manufacturing processes; (e) high and practically pressure-independent speed in high anltrahigh vacua, particularly for H2; (f) intrinsic cleanliness (no fluids or lubricants are used); (g) no moving pao magnetic components. On the other hand, getters have a defined capacity and therefore they eventually becoxhausted and, where possible, are to be periodically reactivated and eventually replaced. In sealed-off devicesetermination of the gas load during manufacture and lifetime is important to that the right getter type and sizeelected to ensure operation of the getter during all the foreseen lifetime.

.8.1Nonevaporable Getters Versus Evaporable Getters

n general, evaporable getters are used when large areas or a sufficiently large portion of the total internal area evice is available for the getter film deposition. High speeds and capacities per unit mass are thus usually obtaconomical convenience. There are also possible disadvantages, however. The deposited metallic film may creircuits between electric leads and react with internal components. It is possible that successive evaporations aro cope with the gas load, and film flaking may occur. The necessity to evaporate more getter material also





equires power which may not be available. The local high temperature required for evaporation can be unacce

Nonevaporable getters are used when the above problems arise with evaporable getters and when other featuremportant. Nonevaporable getters do not require large areas, and their speeds can be maximized by suitable geo

Nonevaporable getters can also be made in small size and various shapes, thus better fitting the space constrainan be reactivated or regenerated several times and their structures allow them to work over a wide range ofemperatures.

.8.2tart-up and Working Conditions of Getters

o make a getter work after its introduction into a vacuum system, activation is usually performed. The vacuumwhich activation is performed is usually at least better than 102 mbar, as obtained by a trapped conventional ro

ump, by a dry pump, or by other similar rough pumps. However, most commonly, activation or evaporation iserformed at a preliminary vacuum better than 103104 mbar, as obtained by the conventional high-vacuum pum

n some cases, it is now possible to use very special (nonevaporable) getters which do not require activation ansed at starting pressures even higher than 102 mbar. For example, the Combogetter ™ used in vacuum insulated paor refrigerators. Getters are usually used to maintain or improve the vacuum produced by conventional high vaumps in the pressure range where they loose efficiency (such as UHV) or where their speeds are conductancehey are also used to improve and maintain the required vacuum for the lifetime of isolated vacuum devices suRTs, FEDs, X-ray tubes, metallic dewars, etc. where no other pumping means is really possible or convenient

with outgassing, permeation or microleaks. Also getters are often used to speed up the manufacturing process oevices byin situ pumping. Further getter applications are in removing active gas impurities in devices filled wiases such as fluorescent lamps and PDPs and in purifying gases down to one part per billion or one part per trequired in some semiconductor processes. After start-up getters can work at room or even higher temperaturesepending on the application conditions such as the gas loads involved, required speeds, possible presence ofydrocarbons, etc.





art IIputter-Ion Pumps

Hinrich Henning

putter-ion pumps (SIPs) are devices which use an electric gas discharge to create an absorption of gas. Cathodputtering from ion bombardment distributes getter material to form thin films which act as absorbing surfaces,onized gas particles are trapped by implanting into solid material. This is briefly the principle of the SIP. Thus f high-vacuum pump is a trapping pump which collects the pumped gas within itself, similar to cryopumps.

9as Discharge Vacuum Pumps

he decrease of gas pressure in vacuum devices with an electric discharge has been known for a long time. Plü117] reported in 1858 that "Certain gases react . . . with the platinum cathode and the resulting compounds areeposited on the walls. So we approach . . . the absolute vacuum." He observed that " . . . the metal of the elect

mainly of the cathode, is transmitted to the glass walls of the tube . . . " and in a magnetic field the glowing gasmilar to an electric current and follows " . . . the course of the field lines" [118].

n 1916 Vegard [119] found that absorption is related to the cathode and is not a chemical bonding with the glaupposed by Willows [120] in 1903. Vegard observed a change in absorption when using different materials onathode but not for the anode. The absorption is measured as a pressure difference per electric charge [mbar/Con his discharge tube. In addition, the absorbed amountq depends on the cathode fall. Gas is absorbed only above






minimum voltageU > U ':

~ (U U '), where the offsetU ' is a constant value.

rom his data an internal volume throughput of the discharge may be deduced to a value of about s = 0.001 liter·s1 0.4 mbar. But when the pressure continues to decrease finally the discharge extinguishes because of a low ion

ield. At pressures below 103 mbar the particle density becomes low and the number of collisions between freelectrons and gas particles is too small to produce sufficient ionelectron pairs to compensate for the loss of chararticles:

he conductivity of the plasma becomes too low and finally the discharge extinguishes. To sustain the dischargource for free electrons may be provided. This concept of a discharge device is common in high-vacuum ion gressure measurement, and it was also used for vacuum pumps to generate clean vacuum at low pressure [121]l. [122] and Bills [123] show designs of electrostatic ion pumps where electrons orbit in a radial electric field.erformance of such ion pumps is limited. To enhance the yield, a very intense electron source has to be used.

ettering is only useful when continuous refreshment of the getter layers may be obtained to avoid temporary phanges. Even then the getter is working in a highly selective fashion and shows no pumping action on noble ahemically inactive gas species such as He, Ne, Ar, and methane.

A much better approach to a useable vacuum pump is to utilize the cold-cathode discharge of the Penning type25]. Here the electrode configuration leads to a high-density electron cloud by trapping the free electrons. It ccylindrical anode rather than a ring as in the original Penning discharge tube, but with similar cathode plates

o both ends of the anode tube (Fig. 5.54). This configuration is placed in a homogeneous permanent magnetic oltage of, for example, 5 kV is applied, there is a potential drop between the cathode plates and the center of txis. Free electrons from the discharge cannot move through this potential barrier.

On the other hand, they cannot move freely toward the anode cylinder because of the force from the magnetic f Bn electric chargee moving with speedv:

m·dv/dt = (e/c )·(v·B),

wherem is the electron mass ande is the electron charge. This makes the electrons rotate around a magnetic fieldwith the gyromagnetic radius:

m = (mvc)/(eB).

hus a cloud of free electrons is trapped inside the anode cylinder of a density high enough to give sufficient ioollisions to maintain the electric discharge even at very low pressures where neutral gas particle density becomlectron losses at the anode by collisions with gas particles and the generation of new electrons





Fig. 5.54Penning discharge. Electrode configuration in axial cross section.

ra , anode radius.

ompensate over a wide pressure range to keep the electron cloud density sufficiently constant. Therefore the iurrent is proportional to gas pressure according to Eq. (5.14).

his device serves as a source of energetic ions (the ions are not captured but are accelerated by the cathode falathode because of the inverse electric charge) which are used to sputter the cathode made from getter materialwhich by this build up active getter deposits elsewhere, and penetrate the first atomic layers of the cathode matwhere they are trapped.

he volume throughput of a single discharge cell is low; Haefer [126] gives data which indicate about 0.0015 l03 mbar to 105 mbar. In 1954 Gurewitsch and Westendorp reported [127] an "ionic pump" of the Penning typathodes which had a volume throughputS = 0.03 liter·s1.

hen in 1958, Hall [128] presented an "electronic ultrahigh-vacuum pump" with a multicell anode which has apeed of 10 liter·s1 at 107 mbar. He examined metals such as magnesium, iron, aluminium, molybdenum, and or cathode material, " . . . but titanium is found clearly superior in pumping speed." He varied the upper limit oischarge current and found 140 mA as an optimal value. Lower values (e.g., 50 mA) increased the starting timxcessively, while too high a limit (e.g., 500 mA) again increased the starting time because of thermal effects. Ihoroughly degassed vacuum system after baking the pump itself to 520°C, he obtained an ultimate pressure of

mbar. This pressure was deduced from the discharge current of 3 × 109 µA.

10he Penning Discharge

enning described [124] the basic physical processes of his gas discharge configuration: "The electron . . . is pry the magnetic field from hitting the anode and







Fig. 5.55Sputter ion pump, first design with multicell anode. View

with covering wall and one cathode removed and cross section(partial), showing 36 discharge cells of square-shaped crosssection, the connection tubulation (left), the high-voltage feed-

through (right), and the second flat Ti cathode (below).(From Hall [128].)

moves in helical trajectories towards the plate P2 (cathode), but is reflected because of the retarding electric fiescillates several times between P1 and P2" (Fig. 5.54). Furthermore, "The magnetic field acts as an enhanced ressure making the ignition voltage in the presence of 0.03T and 105 mbar the same as without a magnetic fie

mbar." He recommends that at high pressure a " . . . discharge with high current should be avoided because of tathodic sputtering . . . ". He is concerned with a pressure gauge, not a pump (!), but "One has to take care for that the discharge absorbs gasin air about 1 liter at 0.025 mbar per Coulomb''; the gauge behaves as a pump! Hssumed the discharge may run at " . . . remarkably lower pressures than 105 mbar."

nvestigations of a discharge cell very similar to those used today in vacuum pump design are made by Knauerhe anode cylinder was 16 mm in diameter between cathode plates separated 23 mm. In the early developmentIPs, Jepsen et al. published experimental and theoretical work [130133].

A very detailed investigation, theoretical and experimental, was made by Schuurman [134] in 1966. He includechematic survey of the different discharge modes, which have been observed by others [126, 135], and deduceor their appearance and for transitions from one mode to the other.

n commercial sputterion pumps, only the low magnetic field (LMF) mode, transition mode (TM) and high-preHP) mode occur. Otherwise, magnetic equipment for individual pumps becomes much too expensive and not vffective







Fig. 5.56Modes of a cold-cathode Penning discharge as a

function of gas pressure P and magnetic field B. Modes: N, no discharge; LMF, low magnetic field; HMF, high

magnetic field; TM, transition from low to high pressure; HP, high pressure. Curved lines: . . .extinction limit; ignition limit; Townsend limit

(T very small space charge). The crosshatched field is theoperational region for usual sputter ion pumps, and it

is extended to higher B for "build-in" pumps.(Adapted from Schuurman [134].)

ecause the discharge current will not increase with higher magnetic field. But the high magnetic field (HMF) f interest, for example, for pumps which make use of the high field of bending magnets in particle accelerator

n" pumps) (Fig. 5.56).he following discussion is about the LMF mode.

.10.1ump Sensitivity

he discharge currentia and the sensitivityia/p (A/mbar) are important properties of an SIP. The current at a giveressure will determine the cathodic sputter yield and finally the pumping speed by the getter effect. The termsensitivity" is taken from the Penning vacuum gauge.



or his first sputter ionpump, Hall [128] gave a calibration functionia~ pn with n somewhat bigger than 1. No attemxplain the deviation from linearity was made. From Jepsen [131] a linear characteristicia = f ( p) was measured betw08 mbar and 104 mbar on a multicell SIP with 250 liter·s1 nominal volume throughput. He assumed that this wersist to much lower pressures. Knauer [129] assumed the classical cross-field mobility µr of electrons and a unifo





pace charge

e = (½π) ( E 2/V 0)

n the discharge cell, and deduced an anode current density

wherem is electron mass,e is electron charge, andvc is collision frequency of electron.

he measured anode current in the range of 106 mbar to 104 mbar was in very good agreement,ia = 102 mA to 1.4with good linear dependence with pressure (see Fig. 5.59).

Measurements from Rutherford [136] show dependence ofia/p on magnetic field B and cell diameter D and in mostases also on pressure p. He defined a "cutoff" at low pressure where the sensitivity is 0.5·(ia/p )max. This cutoffressure moves to lower values when B becomes stronger or D larger. A higher anode voltage increases the sensitut does not change the cutoff. The change ofia/p at low pressure is visible in Fig. 5.57 below 108 mbar.

Fig. 5.57Discharge currentia of a SIP as a function of the nitrogen

pressure p. The sensitivityia/p is constant for p > 109 mbar.







ecause the cycloidal movement of the electrons has a cycloid height Jepsen [130] o

whereVa is the anode voltage, L is the cell length,ra is the cell radius,q is the actual electrical charge in the cell,qmhe maximum electrical charge in the cell, andv′ is the minimum electron velocity for ionization, but here the relam is unknown. From numerical evaluation with usual parameter values, he usedq/qm = 0.6 to arrive at an observe= 10 mA/mbar. Schuurman [134] deduced the following equation with the same assumptions as in Knauer [1

epsen [130] for the LMF mode with a secondary electron emission yieldΓ :

which is proportional to pressure by the ionization frequencyvi of the electrons and to the square of magnetic field B

Different from this the measured values showed linear dependence with B which he explained by having not incluxtinction in his theory foria = f ( B). Another estimate ofia/p is given by Jepsen [133], who took the ratio of spacharge q to the product of average timet between collisions of all electrons and the pressure p:

/p = q/(tp).

He stated that this value is too high because only a part of the electrons has the optimum energy to make ioniziollisions.

.10.2on Motion

At a magnetic field of 0.25 T, Knauer [129] observed a sputtering pattern with a diameter D0 between 3 mm and 5 nd a small nearly unsputtered center of diameter Di less than 1 mm. He explained this plateau by assuming that i

motion is predominantly radial: " . . . ions . . . become deflected by the axial magnetic field . . . " and " . . . missischarge axis. . . ."

rom the cyclotron radiusrc he deduced for the pattern dimensions

where ra is the anode radius, M is the ion mass, ande/V is the ion energy.

he Di corresponds to the maximum energy 3000 eV, while D0 is determined by the minimum value 25 eV whereputtering occurs for Ar+ on Mo. Results are in good agreement with measurement by probes behind the cathodrilled holes. Values are given for Ti with N2, Ne, Ar, and Kr at B = 0.25 T and with N2 at B = 0.15 T to 0.3 T.

Although evidence of a radial component of ion motion is concluded, no remark





made that grazing incidence at the cathodes could be important to enhance the sputtering yield.

he average energy of ions striking the cathode was calculated [137] to be at least 460 eV forUa = 2 kV anode voltnd B = 0.2 T (gas not specified). For noble gases withUa = 7 keV an ion energy of 3 keV is measured by Helmeepsen [138].

.10.3lectron Cloud

he cloud of trapped electrons is a very important feature of the Penning discharge. It provides a source for proew ionelectron pairs by collision ionization with gas molecules.

A description of the avalanche process building up the space charge is given by Jepsen [130] for Penning andmagnetron configurations. From Poisson's equation∇ E = ρ/ε0, and for uniform charge distributionρ in the anode ce found the radial electric field strength Er to be

or the space chargeq he obtained

with a maximumqm at V 0 = 0. The potentialV 0 in the center is

A significant depression of the center potential has been verified by experiment from the energy of ions impinghe cathode center [138]. As long as the electron density in the cloud remains constant, the ionization rate is a lunction of gas particle density or pressure.

n the LMF mode the negative space charge fills out the whole cell volume. On transition to the HMF mode it bontract from the cell axis, leaving behind a nearly charge free plasma. On the other hand, when the pressure ishe central voltage dropVa V 0 becomes smaller, the radial field Er decreases toward zero, and finally on transitionhe HP mode the discharge approaches the normal glow discharge. This is discussed in detail by Schuurman [1

he motion of electrons is described [128, 129] as a rotation of the (space charge) lectron cloud with a drift vel

= ωra = c[( E · B)/ B2].

he frequencyω = 70 MHz has been measured as microwave resonance in the anode which was split parallel to tn two parts for this investigation [129]. This rotation represents a current, which was measured as induced voltoil probe when the discharge was switched off and on. The current was found to beie = 0.46 A and clearlyndependent of pressure in the range 106 mbar to 104 mbar. From





Fig. 5.58The radial distribution of the potentialV , electric fieldstrength Er , and electron density Ne in a Penning

discharge cell in hydrogen at a pressurembar in the LMF mode. There is no net space charge

in the center where the densities of ions and ofelectrons are equal.rc is the radius of electron motion("cyclotron radius"). (From Knauer and Lutz [135].)

Knauer [129] the rotational current density is



wherevΘ is the rotational velocity andvr is the radial drift velocity. From this he calculatedie = 1.0 A, which is abwo times bigger than his measurements (Fig. 5.59). In 1980 Swingler repeated these measurements on a more eometry with nearly the same results [139].

Validity of classical mobility for particles in the Penning discharge at pressure of 104 mbar and lower was confKnauer and Lutz [135], who deduced the





Fig. 5.59Anode currentia [mA] and electron ring currentir [A],

measured as a function of pressure p [mbar] by Knauer [129].

lectrical field strength from Stark-effect measurements on the spectral lines Hβ and Hγ in a hydrogen discharge. T

bserved with this method a different behavior at higher pressures, which is the HP mode (see Section 5.10.5 bRedhead [140] gave a review of papers dealing with experimental and theoretical work on cold-cathode dischawhere instability of the electron sheath (e.g., diocotron instability; see Reykrudel and Smirnitskaya [141] and Kl. [142]) is made responsible for lack of linearity [134] between pressure and current at low pressures. Anomalectron motion toward the anode is observed which becomes more significant at lower pressures because it is ndependent.

.10.4econdary Electrons

Knauer made some qualitative measurements [129] to explore the contribution of secondary electrons from iont the cathode to maintain the discharge. This was done with two small hot-cathode probes behind holes in onen the center and near the edge of the cell. From this he assumed that mainly secondary electrons emitted off cehe cathodes are trapped in the anode sheath to participate in ionizing collisions and to compensate for loss by turrent.

rom the equation of the Townsend avalanche for a self-sustaining discharge,



whereα is the number of electronion pairs made by an electron when moving the distancedr , and Γ is the number olectrons captured from the cathode and initiating





n avalanche, Jepsen [130] states that

whered is the typical distance of an electron's travel from leaving the cathode to the recapture on it, andλ is the meee path for collisions with gas particles.

Another source of secondary electrons is the emission by field effect (see, e.g., Good and Müller [143]). The elurrent depends not on pressure but on the electric field as given by the FowlerNordheim equation:

High field strength will occur when sputtered material deposits on the cathode elsewhere and produces needle-whiskers [144]. Theie is usually small at higher pressures but becomes comparable with the discharge currentia if t

ressure decreases and makes the measured effective current constant at low pressures.

.10.5ransition from HMF Mode to HP Mode

or the center space around the cell axis, Knauer [129] assumed a plasma "indicated by a weak glow which is vressures above 105 mbar." Ionization here is from fast radial moving ions, and the number of ionizations per i

n+ ~ (v+/v ±) ( L/2λ i) = 1.2 × 102at 104 mbar,

wherev+ is the radial ion velocity,v± is the thermal velocity, L is the discharge length, andλi is the mean free pathhe ions for ionizing collision.

ecause the density of ions throughout the cell volume is pressure-dependent, he explained that the transition oischarge from the HMF mode to the HP mode occurs at a pressure near 104 mbar, where the ion and electron ecome equal and the space charge is neutralized. Furthermore, at the high-pressure mode, activity ther than clehavior controlled by cross-field mobility of the charged particles is assumed. Schuurman [134] confirmed th

He deduced an expression for the particle densityntr for transition to the HP mode in two ways: First, he took accf (not neglecting it as he did in the low-pressure mode!) the dependence ofni in Poisson's equation E/D = const·ne ·

At ne = ni he obtained

where D is the sheath thickness,mi is the ion mass,vz is the axial ion velocity, andσi is the ionization cross section





Fig. 5.60Potential distribution in the Penning

discharge, plotted in arbitrary units againstdistance on the cell axis from cathode centerK to center C, then radial to anode cylinder

wall A. From left to right there is the cathodefall on the axis, then a plasma region aroundthe cell center with nearly constant potential,

followed by the sheath with linear rise of potential (i.e., the electron cloud). For higher

B the negative charged sheath contracts, andthe cathode fall becomes lower. If the pressureincreases, the electric field in the sheath andthe space charge decrease. The dashed line

is the distribution before ignition.(Adapted from Schuurman [134].)

econd, following Haefer [145], he compared the average transit times of ionst ri and electronst re and again att ri =

where is the mean collision frequency per particle.

omparing Eq. (5.26) with measured values, acceptable agreement is found (see Fig. 5.60). He stated that at thansition point the negative charged sheath first constricts and then vanishes.

.10.6ransition from LMF Mode to HMF Mode



or the transition from the low magnetic field mode (LMF) to high magnetic field mode (HMF), Knauer assumniform space charge to contract from the center region against the anode, forming a ring-shaped sheath. Its thiiminished with increasing B.

or the transition point between the LMF and the HMF, Schuurman gave

which is independent of pressure. This behavior is confirmed by his experiments, but Hartwig and Kouptsidis p

o use in their empirical model [146].





he anode current

as a maximum at Btr. This is linearly dependent on pressure, although confirmation by experiment is less convihe measured relation I max/ p is not constant [134].

.10.7puttering

he refreshment of the getter films is done by sputtering the cathode material. By this the efficiency of pumpineactive gas is related to the sputter yield. Andrew [147] found from observations on a transparent and fluorescoated cathode that the pattern of activity changes from a spot to a bigger ring with increasing pressure from p = 108

mbar to 104 mbar. This is in contradiction to other observations [148] where the area of sputtering will concentlarge to a very small spot at 105 mbar. In flat cathodes a hole is drilled into the sheet by the discharge at highressureabout 2 mm deep after 5000 h at 105 mbar (author's experience). At low pressure, p < 106 mbar, the sputteattern extends to an area similar to the anode cylinder cross section.

At a high magnetic field, B > 0.2 T, the cyclotron radius for ions, is small enough to produce little or no sputterinenter region of the cathode [129, 134] (see Section 5.10.2, "Ion Motion"). With usual values for the magnetic B.1 T to 0.15 T and anode voltageUa = 3.5 kV to 7 kV, this is not observed. But from Knauer's probe measureme129] the radial component of ion velocity is obvious, which gives a striking angle for the impinging ions on thifferent from 90°. Thus a higher sputter yield can be expectedOechsner [149]. For Ar+ ions accelerated to 300i he obtained 76% increase of yield compared to normal incidence. No value for the striking angle is given. G

ncident of ions on the cathode is also obtained by the electrode system design of commercial SIPs. In diode-tyumps, "slotted" cathode plates [132] are used, and in triode pumps the elements of the cathode assembly [150arge areas not normal to the cell axis.

he consumption of the cathode electrode material by sputtering determines the life of an SIP. The limit is giveoss of mechanical rigidity of the electrode elements or decrease of the sputter yield by deformation from the ohape. Usually the life of diode-type SIPs with compact flat cathodes is longer than for triodes, which provide auantity of getter material because of the transparent design of the cathode. In a large SIP it becomes necessaryhange the electrode assembly, which can be easily inserted into the vacuum envelope. Sometimes it is possiblhange the cathode elements. Smaller SIPs usually have a "one-way" design and have to be replaced completel

11IP Characteristics

.11.1Gettering

n the very early stages of working on gas discharges it became clear that gas cleanup is caused by a kind of ch

eaction between solids and gases [118, 119]. This now is called the getter effect and is treated in Part I of this chap





he question here is where in a SIP will the gas be absorbed by gettering. The main area where sputtered matereposits is the inner surface of the anode cylinders. On a virginal anode after a few hours' run a deposit can be s a change in color, which in the midplane is different from that at the ends. After long use the anode surface woated with thick titanium layers. If the pump is sometimes operated at high pressure, a change in temperature

make the deposit flake off. This results in sharp pressure peaks or even short circuits in the SIP. For this reasonnode surface is made rough by sandblasting, etching, or plasma coating (e.g., with Mo) for better adhesion of puttered layers.

Another place for deposits is the surface of the opposite cathode plate. Only in an area where sputtering is low eposited material can build up layers and act as an active getter. If, by design, ion-bombarded areas are restricemaining cathode surface can contribute to active gettering [132, 151, 152]. The use of cathodes made from d

material with different sputter yields have also been used to establish areas where deposition exceeds sputtering53].

Obviously the effective long-term volume throughput is related to the rate of refreshment of the sputter depositnert gas is pumped for some time, the amount of available getter material in the layers is increasing. Then whehanging to a getterable species of gas the volumetric throughput will be clearly enhanced for a transient period

After some time the original level will be reached again, where refreshment by sputtering and consumption by

re in balance. This effect is known asargon treatment or argon shower (see Section 5.11.3, ''Volume Throughput.11.2on Burial

on bombardment of the cathode will not only sputter the cathode material but also capture ions in the upper atayers of the solid.

his ion burial is one of the gas sorption effects known from electric discharges and is supposed to be the mostmportant for pumping of noble gases [128]. Different from gases which are gettered by sputtered Ti layers, theases can be pumped only by mechanically trapping the gas particles. This takes place mainly at the cathode wons are driven in with kinetic energy gained from the accelerating electric field. This effect shows severe saturhe trapping cathode material is sputtered away at the same time. Lafferty and Vanderslice [155] and Andrew e156] showed, by autoradiography after pumping a radioactive tracer, that the surrounding border of the sputter the only place where ions are permanently captured.

Most of the captured gas is remitted, and finally the net volume throughput will be very small. Measured pumpn fact is only 12% of that for air or nitrogen. To a certain degree, argon is also captured at the anode surface [1upposed to come from instabilities of the discharge which energize the ions and allow them to reach the anode

ater Jepsen [133] explained this with the theory of "energetic neutrals": Some of the ions striking the cathode eutralized by picking up an electron and are then reflected without losing all their kinetic energy. They then mf the influence of the electric and magnetic field. The yield of such energetic neutral particles depends on the ncidence of the striking ions and the direction of the reflected particles. Grazing incidence and forward scatteriigher yield.





f the energy of an incident particle is E 0 and that of a scattered particle is E 1, then after elastic collision they are ry

wherem1 is the mass number of the particle andm2 is the mass number of the target. Form2 > m1, any scattering a1 is possible; but whenm2 < m1, only forward scattering withΘ1 < 90 is allowed. Furthermore, the scattered pa

an escape only if 90° <Θ1 < 270° (i.e., back scattering) for normal incidence, but for grazing incidence it can e° < Θ1 < 180° (i.e., forward and back scattering).

Grazing incidence and forward scattering are better realized in triodes than in diodes. So noble gas atoms are cas energetic neutrals on the collector surface where sputtering is prevented by the potential barrier.

his theory is able to explain the much better volume throughput of triode-type SIPs and others of similar desig50] for inert gas compared to diode design here grazing incidence on the cathode surface is limited. The resul

Knauer [129] are not consistent with this because he measured a strong radial component of ion movement relahe cell axis of a diodetype. Perhaps the stronger magnetic field B > 0.2 T in Knauer [129] is responsible for theifference. By calculating the scattered particle energy from Eq. (5.29) Jepsen [133] was also able to explain thrgon volume throughput of the DI-type SIP [153]. From the mass numberm2 = 181 for tantalum the energy E 1 ofrgon is high to provide better sticking probability for the reflected particle.

n the case of hydrogen, Rutherford et al. [157] reported that the majority of the gas following long-term pumpound in the cathode plates by carefully weighing them before and after the experiment. They explained this asbsorption of atoms and molecules at the clean titanium surface together with diffusion into the solid rather thamplantation.

.11.3Volume Throughput

Much effort is made to calculate and measure the volume throughput (VTP)S ("pumping speed") of SIPs because he main property of interest.

ince the theory of the Penning discharge is not yet complete, the existing attempts to evaluate its properties aremiempirical. They all are based on the close relation to the sensitivityia/p (see Sections 5.10.7., 5.11.1.). Malev rachtenberg [158] proposed an algorithm because they had to describe "built-in" pumps for which the parameperation are very different from the usual values. They deduced the volume throughputS for a single cell fromxperimental values of several authors and finally definedS 0 as normalized to a unit of anode cross section:

whereη is a filling factor which is the sum of the effective anode cross sections related to the total area coveredwhole anode cell assembly.





he conductance limitation of an electrode system with distanceδ between anode and cathode and width 2h of thenode assembly is given by

All values are for nitrogen (or air).

aced with the same problem to evaluate distributed SIPs in particle accelerators, Hartwig and Kouptsidis [146egarded the volume throughput relation to sensitivity,S /(ia/p ), as constant. From experimental work they derived

mean value

c = S /(ia / p) = 0.075 torr·liter/(A·s) = 0.1 mbar·liter/(A·s) at p < 107 mbar.

hen they assumed that the observed decrease of this parameter at higher pressures is caused by a gas desorptioon and electron impact on the electrode surface. This effect compensates the VTP. Assuming a gas coverage fohe Langmuir isotherm equation, they corrected thec value to

eff = c · c* with c* = (1 1.5 × 106 p/(1 + 4 × 106 p))

nd

eff = ceff ia/p .

hey followed the theory of Schuurmann [134] but postulated a linear dependence ofS eff on magnetic field B near t

gnition value Bi, as is obvious in their measurements.Now using Schuurman's formalism they obtained the following for nitrogen and a single cell with

in the LMF mode:

nd in the HMF mode:

ecause the discharge extends into the cathodeanode gap for its effective axial length L, they added 25% of this gaoth ends to the length of the anode cylinder! The results show good agreement with experiment in the LMF mhe HMF mode, deviations appear to be mainly related to dependence from cell radius [159, 160]. Therefore fuorrections in Eq. (5.32c) were introduced by Suetsugu and Nakagawa, who made [161] corrections by using aor geometric distribution







f sputtered material on the anode surface:

J = (1 + cos(2Θ))/2with Θ = arctan(ra /( L + δ));

hey also made corrections by using a second, more important factorQn , which represents the dependence of the tlectric charge from the cell geometry. Having calculated severalQn (with FEMsee Fig. 5.61) they offered as annalytical approach the expression

hen Eq. (5.31c) reads

= S (5.32c) · J · Qc .

A very different approach to evaluate the performance of a SIP was given by Suetsugu in 1993 [162]. He used lement method (FEM) to calculate the potential distribution in the cell, with the assumption of a constant elecensityne throughout the volume. The choice of the maximumne value is from the condition that the calculatedotential shall not be negative in volume elements near the cathode. Then for estimatedne the corresponding ion cuto cathode and electron currentie to anode are calculated (see Fig. 5.62).

he trapped electron densityntr = ne is found balancing ion currentii against electron currentie:

= ii,

eglecting secondary electrons from cathodes and ion density in the discharge. Finally fromii and pressure the VTPalculated by introducing a sputter yield for



Fig. 5.61Volume throughput of a commercial SIP with a

nominal pumping speed of 400 liter·s1 for nitrogen.Calculated,• measured, from Hartwig

and Kouptsidis [146].





Fig. 5.62Volume throughput of a distributed "built-in" SIP showing

dependence on magnetic field strength B with anode voltageVa as a parameter. Cell diameter, Da , is 15 mm; cell length, L,

is 26 mm; gap cathodeanode,d , is 5 mm; pressure, p, is 108mbar. Solid line: Suetsugu and Nakagawa [161].

Dotted line: Hartwig and Kouptsidis [146].

oncathode and a sticking coefficient for gasgetter material. The calculations are compared with those from HaKouptsidis [146] and with measurements that Suetsugu and Nakagawa have made on "built-in" SIPs from theRISTAN accumulator ring [163]. Agreement is good with experiment in LMF and HMF modes for dependen

a , and ra but not on pressure p > 107 mbar. Nevertheless, this method, after some improvement in the treatmenarameters, may promise better (perhaps best) approach to the real performance of the SIPs in the future.

or measurement of VTP of SIPs there are some special problems in addition to the common ones because of thmeasurement of very low gas throughput ("flow") and the influence of desorbed gas from the surface of the vacystem. First the emission of sputtered particles in neutral, excited, and ionized state from the electric dischargee encountered. Furthermore, there is also some weak electromagnetic radiation from the discharge. As is com

UHV technology, the design of the pump is open against the pump port to get optimal effectiveness. As a consehese emissions are not screened and prevented from entering the connected vacuum system, because any screeeduce the pumping action of the SIP. These emissions may influence the pressure measurement by BA gaugesperation of other devices.

n a similar manner the stray field from the strong magnets shall be regarded as a source of possible malfunctio

n fact the application of SIPs has given strong impetus to the development of methods for the measurement ofhroughput [164, 165]. This work is described in Chapter 12. Rutherford et al. [157] reported on the pumping sumping mechanism of diode-type pumps for several species of gas: H2, He, N2, O2, Ar, and air.





An important feature of the SIP is the time-dependence of VTP. As in other trapping vacuum pumps or devicesccumulation of gas will influence its performance. Gas release is dependent not only on pressure but also on thf the pumpthat is, the species and amount of gas pumped. With a new or regenerated pump or for a new specihe SIP will show a clear decrease in VTP for some time: minutes or even hours, depending on operational prehis is the time needed to bring all relevant processes to an equilibrium state. After this period, called saturation time

he VTP is generally constant for a much longer timethat is, weeks and months. Hartwig and Kouptsidis [146]alculated the saturated speed by

with S from Eq. (5.32). Finally, behavior of the SIP becomes unsatisfactory at low pressure. The ultimate pressubtained will be high; and at high pressure, strong outgassing occurs when the SIP is warming up by the high-pissipation, so that degassing supersedes pumping and the vacuum pressure will run away [166]. It is assumed athodes partially are heated up to 500°C [148]. For these reasons the SIP now should be degassed by a regeneake-out (see below).

.11.4

umping Mechanismetterable Gases. From the discussion about the properties of the discharge and the SIP, one may easily imaginumping of chemically reactive gases proceeds. Gas molecules are ionized by electron impact; then the ions stathode, they are partially captured in the solid (primary pumping effect), and they partially sputter getter matehe cathode, which is deposited elsewhere in the electrode system, and there the getter material acts as a getter large surface, on which other gas molecules are absorbed and bound as stable chemical compounds (secondarumping effect). The primary effect is time-dependent because continuous sputtering will excavate earlier captarticles, thus reducing the net pumping activity. But after operating for some time, all involved processes willalance and show a stable and constant VTP. Its value depends on the ionization energy of the gas molecules, tngle of incidence of the ions striking the cathode assemble, the sputter yield for the gastarget pair, the surface he getter screen, and the sticking coefficient for the gasgetter material. Further parameters are gas pressure, elend cell design, magnetic field strength, anode voltage (which determines the energy of the impinging ions), thischarge current, and the resulting operational temperature. Most of these values have been taken into considewhen calculating the VTP as described above.

A SIP with an electrode system of about 350-mm × 90-mm cathode dimension and 55-mm distance in a field owith an anode voltage of 5 kV has an effective equilibrium VTP of roughly 80 liter · s1 for nitrogen. In the norange of operation between 105 mbar and 109 mbar · liter, it does not depend much on the type of pump: diode

magnetron, or triode. For other gases the speed relative to N2 is given in Table 5.8 [128, 153, 167].

he described balance between several effects resulting in a net VTP can be observed on an SIP operating at loressure when the anode voltage is cut off. The pressure will suddenly decrease to about 6080% from equilibrind only





Table 5.8. Volume Throughput for Sputter Ion Pumps, Related to the Value for Nitrogen [128,153, 167]Gas Diode TriodeNitrogen

100% 100%Hydrogen

160200% 140180%

Oxygen100% 100%

Carbon monoxide100% 100%

Carbon dioxide110% 100%

Light hydrocarbons

80110% 80100%Air

100% 100%

Helium3% 30%

Argon1% 22%

few seconds hereafter begin to rise. The reason is the immediate stop of resputtering captured gas particles frathode and a residual pumping action from the continuously refreshed getter layers. Their capacity will be con

fter some time, depending on the pressure level. Then the pressure increases. Thus it can be deduced that theefreshment of the getter layers is more effective than consumption of the deposited getter material, giving the pable behavior.

ydrogen. Hydrogen is a reactive getterable gas, but its behavior in a SIP with Ti cathodes is quite different fromthers. Rutherford et al. [157] reported that the majority of the gas following long-term pumping is found in thelates by carefully weighing them before and after the experiment. They explain this as absorption of atoms an

molecules at the clean titanium surface together with diffusion into the solid rather than ion implantation. In a vareful investigation of a single-cell SIP, Singleton [168, 169] showed that when pumping pure hydrogen the o

VTP is comparable with that of other gases, but only after long-term operation. After several hours of pumpingmbar, the H2 speed increases up to three times the initial value. After this procedure the VTP is high even at ve

ressures ( p < 108 mbar). But a small amount of impurities (e.g., N2 from 0.1% to 10%) is ufficient to reduce itemarkably again. If more than 10% N2 is present, the VTP will now increase. The reason is that hydrogen absn the Ti surface is limited by surface layers of other absorbed gas species (N2). Because sputtering by the ligh low, the dominant process of pumping is diffusion of absorbed particles into the bulk of the bombarded cathoong as there are surface barriers from other gases as in a new cathode or from stronger absorbed gaseous impuumping activity for H2 will be poor.

he state of the Ti surface as a limiting factor for the H2 migration between gas phase and solid is reported bychoenfelder and Swisher [170]. Only after sputtering the contaminated layers away, which needs less time at hressure, appreciable amounts of H2 will be absorbed to diffuse into the bulk Ti. With more than 10% of N2 aseavier gas, the sputter yield of Ti is so high as to provide enhanced refreshment of the getter films everywhereigher VTP. This was verified by Singleton [168, 169], who measured the speed after cutoff of the anode volta







bserved pumping action decreases very slowly, indicating some available getter capacity.

oble Gases. For all nonreactive gas species the only effective primary pumping effect is the capture of ions at athode. This was the early experience on SIPs when pumping noble gases: After some time of fairly good pumction the VTP decreases to only a small percentage of the initial value and, finally, to 12% of N2 speed.

Very often, when pumping argon, pumps show severe pressure fluctuations called the Argon instability [132, 171]. In the case of argon, when cathode material already containing pumped gas particles is sputtered, this cauressure rise because no other pumping process is available. Then with the increasing pressure the sputtered arathode surface contracts and reduces the amount of resputtered gas. The pressure now begins to decrease and nters into a new cycle after some time. The pressure fluctuations produce local temperature changes, and thusydrogen sorption and desorption phenomena occur (see Fig. 5.63).

he main advantage of the triode-type SIP is to provide higher VTP for noble gases and stable long-term pumprgon. Its pumping mechanism is well understood by the hypothesis of "energetic neutrals" from Jepsen [133] (ection 5.11.2, "Ion Burial"). Grazing incidence of ions and forward scattering give higher yield of both nergeteutrals and sputtered Ti, which are deposited together on the collector surface.

or helium the behavior of a SIP is governed by the high diffusion coefficient of this light and small atom. Thisumped with a relatively high VTP but is very

Fig. 5.63Argon instability of a SIP. A record of partial pressures for mass number 40 argon and 2

hydrogen in arbitrary units.(From Wutz et al. [172].)







ensitive to changes in temperature. As for all noble gases, the trapped gas is in a "forced" physical solution in i. In fact no spontaneous solubility of noble gas in metal exists. An increase in temperature produced only by a

ncrease of pressure with higher power consumption of the pump causes remarkable desorption of the pumped ccur as the He atoms diffuse quickly through the bulk. Baking an SIP at 300°C will degas it to a large extent fumped He.

he absence of getter action during noble gas pumping is the reason for the enhanced pumping behavior for geases after an Argon Shower. As a heavier gas, pure Ar sputters the Ti abundantly from the cathode, but the deot be consumed by accompanied gettering because no getterable gas is present. When after this a reactive gasdmitted, the unsaturated getter layers will show enhanced getter activity resulting in a transient high VTP.

.11.5akeout

A regenerative bakeout is made to refresh the performance of a SIP by degassing it. Trapping of the light gasesHe is reversible to a high degree, but to some xtent, trapping of Ar is also reversible. The regeneration can be msing external heaters or by operating the SIP at a pressure of about 1 × 105 mbar to 3 × 105 mbar in a heat-inshroud. It is important to bake the whole SIP to avoid gas adsorption at cooler surfaces and to ensure good deg

very part if the pump is to be used later at UHV pressures. Preferably it should be evacuated by an auxiliary puring the bakeout up to the time when the pressure has decreased below 105 mbar. If possible, the power suppIP should be switched on for about at least 10 min before the end of the bakeout to clean most of the electrodey particle bombardment.

.11.6ypes of SIPs

he first SIP design had two electrodes [128] like the Penning gauge. This was called the diode-type pump, anurrently in use (see Fig. 5.64). Its properties as a high-and ultrahigh-vacuum pump are excellent. Sensitivity anolume throughput are high because the discharge cell volume can fill the available magnet gap to a maximummple cathode design avoids sharp edges and burrs, which can be a source of leakage currents by field emissioart a diode pump a starting pressure of p < 103 mbar must be provided.

A restrictive disadvantage is the very low long-term volume throughput for noble gases (mainly for Ar), whicheriodical pressure fluctuations (the Argon instability ; see "Noble Gases" in Section 5.11.4 above). Some attempteen made to optimize the properties of diodes. Tom and James reported on a diode pump which has different or the two cathodes (DI-type pump) [153]. Using cathode plates of Ti and Ta, they measured a volume through027% for argon compared with air and found no argon instability after pumping for 37 weeks at about 2 × 106gainst a constant leak. They guessed that most of the Ar is buried on the cathodes at the border of the sputterend make the higher sputtering rate of the Ta responsible for the better properties. A similar design is used by Bnd Henning [151]. They used different material in small pieces (pills), each for one cell on a stainless steel supheet. Cathodes with Ti, Ta, Mo, W, Ag, and Pb were





Fig. 5.64Diode-type discharge cell (axial section). A is the anodeat positive potential; C is a Ti cathode, grounded; B isthe homogeneous magnetic field. electron, movingon cycloid path and colliding with gas particles;

neutral gas particles, partially gettered on Ti;ionized gas molecules, accelerated toward the cathode by electric field (not shown) and partially captured

in the bulk;• Ti particles sputtered by ionsand deposited as getter layer.



nvestigated. They found an inverse relation between sputtering rate and volume throughput when pumping argxample, best pumping speed and lowest sputtering for cathodes of Ta. The argon instability is observed only fhey argued that the important property is to avoid reemission of earlier trapped gas particles which is foundreferentially on the lower level of the cathode between the pills. In a later commercial SIP, they used pills fromogether with 15% from Ta or stainless steel and obtained 1825% Ar volume throughput compared to N2. Siminvestigations were reported by Vaumoron and De Biasio [166], who found a minimum ratio of 2.5 for the heav

mass number to that of the noble gas necessary for stable pumping. The relative Ar speed of the DI pump as foWutz et al. [172] was confirmed by Komiya and Yagi [173], who measured also a speed of 75% for N2 compar

ump with only Ti cathodes. They found that both properties are significantly higher (40% and 82%) when usiathodes which have a Ti sheet covered by a Ta sheet 1 mm thick with a lot of small punched holes. They assuhe cylindrical borders of the holes provide an area for grazing incident of the strong axial (!) moving ions and equent change on short distance of two different getter materials over the cathode surface is responsible for therformance





ata. Okano et al. [174] have measured the memory effect of some gases when pumping H2, HD, and D2 in a Dwith Al/Zr cathodes. They found better volume throughput at 107 mbar for N2 and Ar but not for H2, which isnly with 84% of the speed of an identical pump with 100% Ti cathodes. For the memory effect see Section 5.

IPs similar to high-vacuum magnetron-type gauges have also been proposed [156]. In the center of the dischatanium rod is placed. Slightly different is another proposal [155] with only short posts which are fixed on the nd protrude only a few millimeters into the discharge cell. Pumps of the magnetron design with a solid cell axom the problem of proper alignment between cathode and anode.

arly in 1958, Brubaker presented the triode-type pump as a new design of SIP with greatly enhanced argon pupeed [150]. It has three types of electrodes and the '' . . . third electrode is of cellular structure . . . ". He called uxiliary cathode. It was energized at 3 kV (anode voltage +3 kV). At 106 mbar argon pressure he observed staumping over > 200 h withS Ar = 0.14 liter·s1 and no instabilities. Today his "auxiliary cathode" is called thecathodnd his "cathode" is namedcollector , which is now at the same potential as the anode for simpler design with noerformance (see Fig. 5.65). The collector is usually identical to the vacuum housing of the SIP. The cathode isegative potential with respect to the two other electrodes.



Fig. 5.65Triode-type discharge cell (axial section). A is theanode, grounded; C is a Ti cathode, grid structuredand at negative potential; D is a collector, grounded

(= vacuum envelope); B is the homogeneous magneticfield. electron, moving on cycloid path and colliding

with gas particles; neutral gas particles, partiallygettered on Ti; ionized gas molecules, accelerated

toward the cathode by electric field (not shown), partially reflected as energetic neutral particles, andcaptured in the bulk of the collector;• Ti particles

sputtered by ions and deposited as getter layer.





Hall [175] described experiments with grid structured cathodes composed of strips of Ti and Zr and measured eVTP for CO2, CO, and Ar. A different design of a triode, which has a grid structure in radial symmetry to eachischarge cell, was presented by Pierini and Dolcino [152].

he starting pressure of a triode pump may be 102 mbar or lower, depending on the volume to be evacuated.

oday, SIPs are usually of the triode type (Fig. 5.66) with radial or stripe structured cathodes or of the diode-tywith flat sheets as cathodes. Typical VTPs are shown in Fig. 5.67. Materials used are mainly titanium, togetherantalum for noble gas pumping. The anode cells are circular tubes. Small SIPs are used as "appendage" pumps

welded connection to devices permanently under high vacuum such as big thermionic transmitter tubes, klystroo on. This was in fact the original application of a SIP after its invention.

n particle accelerators and storage rings where suitable magnetic fields already exist, special SIPs are used as "r "distributed" pumps. Specially designed electrode systems are arranged inside the vacuum chamber, with thedvantage of being very close to the place where the vacuum is needed, and therefore a high VTP is



Fig. 5.66Sputter ion pump (diagram partially in cross

section) with four electrode systems andDN150 connection flange. 1, electrode system(triode type shown); 2, ferrite magnet system;

3, vacuum envelope; 4, high-voltage feed-through.





Fig. 5.67Volume throughput (VTP) of sputter ion pumps for nitrogen as a

function of pressure. IZ270 is a pump with nominal VTP,S = 270 liter·s1,diode and triode; IZ500 is a pump with nominal VTP,

S = 500 liter·s1, diode and triode.

Fig. 5.68"Built-in" SIP for BESSY. Cross section of the double electrode systemin the vacuum envelope. 1, Cathodes (Ti/Ta); 2, anodes (stainless steel

sheets with collinear holes, gaps for better conductance). Cell diameter, Da is 4 mm; cell length, La is 10 mm; anode voltage,Ua is 4.8 kV;magnetic field, B is 0.751.5 T. (From Pingel and Schulz [178].)

esired. The operational parameters of such pumps very often are unusual for SIPs, and the planning phase of tevices is very long. From this, algorithms for the performance of such pumps had to be developed, and in factapers for calculation of the VTP [146, 158, 162] are for this kind of application. There are pumps for extreme

magnetic field with anode cells of 40-mm diameter (only prototype realized [176]) and another with 4-mm diamesigned for B = 0.75 T to 1.5 T [177], built for the Bessy electron storage ring [178], (see Fig. 5.68).

.11.7tarting Properties



he starting pressure of a diode SIP is lower than that of triodes for two reasons:

. To simplify the design the cathodes are grounded and the anodes are at high potential (see Fig. 5.64). At presigher than 103 mbar the glow discharge





will spread into the vacuum housing well outside the Penning configuration; and because of this sputtering of tathodic material is extremely poor and no pumping action will occur. The surface desorbs gas caused by partiombardment, and an auxiliary pump is needed to reduce the pressure again.

. Then if with decreasing pressure the discharge remains in the electrode system, the compact titanium cathodeeated by the local power dissipation and desorb previously pumped and gettered gas, mainly hydrogen. This o

much more than in triodes, where the cathode design is less compact and where gas trapping occurs mostly on lectrode (see Fig. 5.65). Here only the cathodes are at negative potential, and the discharge is forced to develolose surrounding space.

On the other hand, a retarded starting procedure allows the SIP to be heated. The discharge power dissipation idvantage for obtaining low pressures later on. The heating will be in just the place where degassing is desiredthe electrode assemblies. The heat transfer into the vacuum envelope is slow and is negligible into the magnetshe vacuum. The bakeout is effective, and a temperature of 150°C has been observed on the outer surface of thlectrode housing [148]; but consumption of getter material is also high during this procedure, thereby reducinfetime of the cathodes.

.11.8

Memory Effecthe principle of pumping by trapping gas particles implies that the history of operation is documented inside th

Now when the composition of the gas to be pumped is changed, particles of gas species which are not actually n the gas may be desorbed for a certain time. The pump "remembers" the previously pumped gas components.alled memory effect . It will be prevalent for noble gases which are concentrated in the cathodesespecially for he

which diffuses easily through the bulk. This is also valid for hydrogen, but because it is present everywhere in n a vacuum system at low pressure, the effect will not be detected. For the other chemically active gases the mffect is clearly lower because they not only are trapped at the cathodes but are gettered elsewhere.

or the same reason, the memory effect is lower for a triode-type SIP [167, 179] (see Fig. 5.69). The amount oapped in the cathode material is less than that with diodes, even for noble gases. This may be regarded as proumping mechanism discussed for this type of pump.

he memory effect makes it difficult to use an SIP as a pump in He leak testers.

.11.9Ultimate Pressure

At the lowest pressure the VTP of a SIP is in equilibrium with all sources of degassing, such as the walls of theystem and of the gauges, and all vacuum surfaces inside the SIP. The main constituent of the residual gas is hyingleton [168, 169] has demonstrated that well-conditioned cathode surfaces are necessary to have good VTPas in the ultrahigh-vacuum pressure range. A new electrode





Fig. 5.69Memory effect. The residual mass spectra of a SIP (triode)-pumped vacuum system.

1, after pumping of air, p = 9 × 1010 mbar; 2, after pumping of 400 mbar-liter argon, no baking, p = 1 × 109 mbar; 3, same as 2, but after a several hours bake at 300°C, p = 7 × 1010

mbar. The argon partial pressure is not severly increased. (From Henning [179].)

ystem will operate well at low pressure only when the unavoidable contaminating surface layers have been spway. To reduce degassing, the pump itself with the vacuum system should be baked under vacuum at not less . It is preferable to operate the SIP during the whole procedure, but at least for the last 15 min with the magnelace. But pay attention to the high-voltage connector, which is normally the part that is most sensitive to elevaemperatures!

Malev and Trachtenberg [158] obtained an expression for the lowest pressure pmin for existence of the discharge:

whereUa is in V, D is in mm, and B is in T; this pressure is not the cutoff pressure from Rutherford [136]!

At very low pressure the discharge current appears to be independent of pressure but varies strongly with anodehis is from the field emission effect as described in Section 5.10.4. The responsible tips on the cathode may by applying for 1s or 2s a short impulse of high voltage (dangerous!) preferably alternating voltage to avoid ar





.11.10Magnets

he design of the magnet system is an economic problem. Because the SIP is a type of pump for long-time opeower consumption should be minimized. Thus the use of permanent magnets is evident. Care must be taken toood homogeneity of the field inside the electrode systems. Hartwig and Kouptsidis [146] noted the effect of a

misalignment angleφ between cell geometry and magnetic field which consists of a reduction of the effective cef from ra defined by the anode dimension, and they obtained the expression

f = ra cosφ 0.5 La ·sinφ.

his equation shows the disadvantage from which magnetron pumps suffer. The effective cross section is cut twom the outside and from the central rod.



Fig. 5.70Module design of magnet systems. (ac ) With closed

magnetic circuit; (d ) With individual magnets for eachelectrode unit. (From Andrew [147].)





o obtain good performance at low pressures the pump alone or together with the vacuum system has to withstven operate at elevated temperatures of 200°C to 300°C. The magnets should withstand these temperatures wiermanent loss of magnetic energy. Otherwise they have to be demounted before every bakeout; this is not veronvenient with a weight of about 60 kg for a pump having 270 liter·s1 nominal VTP. The weight can be reducubstantially using rare-earth alloy magnets rather than ferrites. But up to now they have been expensive and h

much lower temperature limit (180°C max). Furthermore, the yoke necessary to close the magnetic circuit reduain in weight! That brings us to another point: The field of the magnets may influence other equipment inside utside the vacuum. A design with a closed magnetic circuit and low stray field is preferable; otherwise, shieldie required [147] (Fig. 5.70).

are must be taken when demounting the parts of a magnet system. If it has been magnetizedin situ after assembly,will irreversibly lose some magnetic energy.





art IIIryopumps

ohan E. de Rijke

ryopumping is a means of creating a vacuum through the use of low temperatures. It occurs when gas molecuriking a surface lose enough of their incident kinetic energy to remain absorbed on the surface by so-called diorces or van der Waals forces. Dispersion forces exist between any pair of molecules; and in the case of cryophey are the important forces of attraction that hold a pumped molecule on a surface.

he amount of molecules that can be held on a surface is dependent on a number of physical factors: the tempeoth gas and surface, the chemical nature of gas and surface, the microscopic roughness of the surface, and theux of molecules. Typically, the dispersion forces existing between a surface and a gas molecule are greater thaetween the gas molecules themselves. We speak of cryosorption pumping when these larger forces are needed

molecules on surface to the extent necessary to reach the desired vacuum level. Only several monolayers of gaccrued on the surface before the effect of the surface becomes negligible and the pressure above the surface wncrease. We speak of cryocondensation pumping when the dispersion forces mutually existing between gas more sufficient to keep them on the surface to the degree necessary to maintain the desired pressure levels. In thiypically a very large number of monolayers can be built up. The result is that much more gas can be accumulan the case of cryosorption pumping.

he majority of cryopumps presently in use on vacuum systems for high- or ultrahigh-vacuum applications havumping surfaces cooled by mechanical closed-loop refrigerators utilizing helium as a working fluid. The refriycle generally






sed is the GiffordMcMahon cycle. This cycle employs two stages of refrigeration. The first refrigeration stageormally operates between 50 K and 80 K, whereas the second stage operates between 12 K and 20 K. The temf the second stage is low enough to pump all gases except neon, hydrogen, and helium by cryocondensation. Three gases are pumped by cryosorption on a sorbent attached to this stage.

ryopumping can also be used when clean rough pumping is required. In this case, liquid nitrogen is used to coanister of sorbent material. Gas is pumped by cryosorption, and pressures of 103 Pa can be reached.

At sufficiently low temperatures, almost all gas molecules incident on a surface are captured and the speed of aryopump will approach theoretical limitsthat is, limits imposed by molecular velocities. Therefore, cryopumpsave large pumping speeds as compared to other pumping mechanisms. This is especially the case for water vaecause it is pumped at easily achievable, relatively high temperatures. Also, cryopumping is a clean pumping hat is, no fluids internal to the vacuum envelope are used in cryopumps. Therefore, cryopumps will be found ipplications where clean vacuum production and high water-vapor pumping speed is needed.

ecause cryopumps are capture pumps, regeneration or the periodic removal of accumulated gases is required.rinciple, this is a simple process, consisting of warming all pumping surfaces to room temperature and allowino escape through a valve mounted on the pumpbody. Then the pump is evacuated to sufficiently low pressures

n insulating vacuum between the pumpbody and the pumping surfaces, after which the refrigerator is turned ohe pump to operating temperatures. Correct regeneration is key to maintaining optimum cryopump performanRegeneration is typically performed by automatic controllers; and because the pump cannot be used duringegeneration, considerable effort has been expended in developing efficient and fast regeneration procedures.

12dsorptionDesorption

he operating principle of cryopumps can be best explained by the theory of adsorptiondesorption. This theoryescribes (a) the interactions between gas atoms and/or molecules and a surface and (b) the resulting balance bdsorption and desorption. For the first monolayer building up on a surface, gas molecules striking the surface ound by the dispersion forces existing between gas and surface. These forces are generally larger than the disporces that exist between the gas molecules themselves. This means that as monolayers of gas are built up on thnd the effect of the gassurface interaction diminishes, the equilibrium between adsorption and desorption will he pressure above the adsorbed layer will increase as the magnitude of the dispersion forces decreases. Whenpproximately five monolayers have been built up, the effect of the dispersion forces from the surface will havegligible. Molecules are bound only by the forces mutually interacting between them, and the pressure above ondensate will no longer increase. It will remain constant so long as the temperature of the outermost adsorbedoes not increase. To summarize: As a layer of gas is built up on a surface, the pressure will increase until the ehe surface has become negligible. Then the







Table 5.9. Maximum Theoretical Pumping Speeds for CryosurfacesAtomic Mass

UnitsMaximum Speed (liter·s1·cm2)

with Gas Temperature at:Gas Species 295 K 77 K H2

2 44.2 22.6

He4 31.2 16.0

H2O18 14.7 7.5

N2, CO28 11.8 6.0

O232 11.0 5.6

A 40 9.9 5.1

CO244 9.4 4.8

ausingdN/dt to become zero and then allowing the system to reach the equilibrium pressure:

n Eq. (5.36),σ is the concentration of molecules expressed in molecules per square centimeter. We defineσm as thumber of molecules that form a monolayer, which has an approximate value of 1015 molecules per square cenor adsorbates [180].

f the second term in Eq. (5.36) becomes too large whileσ is less than 5σm, it means that only pumping byryosorption is practical. For cryocondensation pumping,σ can become much larger than 5σm.

rom the above, it can be seen that the general shape of an adsorption isotherm will show increasing pressure aeveral monolayers are built up. Then as the effect of the surface becomes negligible, the pressure will reach a

maximumnamely, the (saturation) vapor pressureand will no longer rise as the amount of gas accumulating incrigure 5.71 [182] shows typical adsorption isotherms showing the transition from less than monolayer adsorpti

hrough multi-monolayer adsorption to cryocondensation.sotherms have been extensively studied, because cryosorption is often required in order to reach the necessaryevels. There are many adsorption isotherm configurations; as many as 13 different types have been categorizednd at resent no unified theoretical model exists which explains the shapes of various isotherms. Langmuir washe first who attempted to model isotherms in terms of gassurface physics. His work dealt with surface coveraghan one monolayer. The equation that he developed for an isotherm takes the form [183]







Fig. 5.71Adsorption isotherms of Xe, Kr, and Ar on a porous silver adsorbent

at a temperature of 77.4 K.

wherek is a constant, p is the pressure,σ s is the number of sites per square centimeter, andm depicts the number ofurface sites which are occupied.

Another important adsorption model was derived by Brunauer, Emmett, and Teller [184]. They expanded on Lheory to include its applicability to gas coverages exceeding one monolayer and derived the following equatio

wherek is a constant,σm is the number of molecules in one monolayer, and pv is the vapor pressure. The above mas proved to be very successful in characterizing certain isotherm configurations and has become an industrialor specifying surface areas of porous materials used in vacuum applications. In recognition of the authors, it iss the BET method for determining the areas of sieve materials.

One case of particular interest is cryosorption of hydrogen by charcoal. Hydrogen commonly occurs in vacuumnd is generated by many vacuum processes. Charcoal is the material most used in the two-stage, high-vacuumooled by a mechanical refrigerator. Figure 5.72 shows the adsorption of hydrogen on charcoal for various tem185].

he pressures represented by the vertical portions of the isotherms shown in Fig. 5.71 represent the (saturation)ressures of the indicated gases at 77.4 K. The vapor pressure is obviously a crucial value, because it representheoretical ultimate pressure that can be achieved by cryocondensation for a given gas at a given temperature. Tressure of a gas is derived from the ClausiusClapeyron equation and is usually presented in the form







Fig. 5.72Adsorption of hydrogen on coconut charcoal at low pressures.

able 5.10. Vapor Pressure of Common Gases as a Function of Temperature in K [187]Vapor Pressure (Pa)

1011 109 107 105 103 101 10 103 105elium

1.0 1.7 4.5

ydrogen2.9 3.0 3.5 4.0 4.8 6.1 8.0 12 21

eon5.5 6.1 6.9 7.9 9.2 11 14 18 28

itrogen18 20 22 25 29 34 42 54 80

rgon20 23 25 29 33 39 48 63 90

arbon monoxide21 23 25 28 33 38 46 58 84

xygen22 24 27 30 34 40 48 63 93

rypton28 31 35 39 46 54 66 86 124

enon39 43 48 54 63 74 92 119 170

arbon dioxide60 65 72 81 92 106 125 154 198

Water

113 124 137 153 173 199 233 284 381

here the value for A is proportional to the sublimation enthalpy (∆H s) and the factor B contains the entropy change associated with the phansition. The values of A, B, and C have been summarized by Haefer [186] for various solid gas condensates. Vapor pressure curves haven developed by Honig et al. [187] in one of the classical vacuum technology papers. Vapor pressures for some common gases are gible 5.10.

3yotrapping

yotrapping is defined as the concurrent or sequential cryopumping of two or more gases for the purpose of trapping a less readily pumthe sorbate of a more







Fig. 5.73Hydrogen speed as a function of hydrogen accumulated on an argon sorbate at 12 K.

(Courtesy of Ebara Technologies, Inc.)

eadily pumped gas [183]. In other words, a gas such as hydrogen can condense on a surface of a sorbate such when hydrogen and argon are simultaneously introduced in a cryopumped system. Or hydrogen can be pumpedeshly condensed argon sorbate. Figure 5.73 shows the normalized pumping speed for hydrogen as a function mount of hydrogen pumped for a pump used in physical vapor deposition applications where the standard secrray using charcoal as a sorbent has been replaced by a similar array without sorbent.

14umping Speed and Ultimate Pressure

n general, when calculations regarding gas flow, conductance, or pumping speed are performed, it is assumed ll components of the vacuum system have the same temperature. This is clearly not the case when using a cryystem. Usually it is not possible to directly observe pumping performance on a cold surface; instead, it has to

erived from measurements of pressure or throughput in a second chamber held at a different temperature. Thewe need to examine the flow of gas between two chambers held at different temperatures (Fig. 5.74). One chameld at a temperatureTw, and the second is held at a much lower temperatureTc . The chambers are connected by aperture with area A. From the Kinetic Molecular Theory, the flow of particles from one chamber to the other cae equated to





Fig. 5.74Thermal transpiration.

Assume first that no pumping is taking place, so there is no net flow of gas from one chamber to the other and ressure in both chambers is constant. Under these conditions,nw (the flow from the warm chamber to the coldhamber) will be equal tonc (the flow from the cold chamber to the warm chamber) and Eq. (5.40) can be reduc

quation (5.42) shows that even if there is no flow of gas between two chambers held at different temperaturesressures in the chambers will not be the same. This effect is calledthermal transpiration (see Section 1.10).

o determine the effective speed at the entrance of the cryopump or, in the above case, the speed at the apertureetween the warm chamber and the cold chamber, assume that there is a net flow of gas from the warm chambold chamber. From Eq. (5.40) the net flow of particles through the aperture,nnet, assuming a sticking coefficient nity, is

quation (5.43) may be simplified by noting that the term preceding the brackets isnw.





he maximum particle flow into the pump occurs when no gas flows back from the pump, ornc = 0. Thennw = nmand Eq. (5.43) can be written as

f we now define (from Eq. (5.42))

hen Eq. (5.44) can be expressed as

where pw(ult) is the pressure at the pump entrance when gas flow is halted. Equation (5.46) related the net flowarticles to the maximum flow of particles; in other words, it relates the net speed to the maximum speed. For aryocondensation pump, pc is the saturated vapor pressure psat. Equation (5.45) shows that pw(ult) will remain cons long as psat does not change and so will the net pumping speed at the pump entrance. For a cryosorption pum pcan be obtained from the corresponding adsorption isotherm. Pressure pc will rise as the surface coverage increasehis means that pw(ult) will also rise. As it approaches the operating pressure pw, the net pumping speed will decrnd become zero when pw(ult) reaches pw. The pump can no longer accumulate gas at that pressure. However, fr5.46) it can be seen that the pump will still retain 90% of its maximum speed if the operating pressure is raisedactor of 10.

o summarize: For a cryocondensation pump, the ultimate pressure will not change as long as the temperature dsorbate does not change. Also, the speed will be near its maximum value as long as psat is much smaller than pw. he case of a cryosorption pump, the ultimate pressure will rise as the equilibrium pressure over the sorbent inc

with the amount of gas adsorbed. From Eq. (5.46) it follows that for cryosorption pumping, speed will decreasehe equilibrium pressure approaches the working pressure pw.

15apacity

ryopumps are capacity pumps, and thus only a finite amount of gas can be stored before the pump has to beegenerated. The need for regeneration is typically determined by the user and will be performed when pumpinerformance for a particular gas has degraded to such a point that it becomes unacceptable in the particular app

he degradation in two pumping characteristics is used to determine when regeneration is required: (a) the decumping speed that occurs as gas accumulates and/or (b) the increase in time needed to reach base pressure.





n other words, capacity is defined as (a) the quantity of gas that can be stored on the arrays at a given pressurehe pump can still maintain a pumping speed igher or equal to a defined percentage (usually 50%) of its initial hat pressure or (b) the quantity of gas that can be stored with the pump maintaining the ability to reach a requiressure in a required time.

here is a third definition of capacity that also has to be consideredthat is, the capacity of the pump when a conas and an adsorbable gas are being pumped simultaneously. The geometry of the pumping surfaces is designemajority of gas molecules will strike the first stage array and/or the outside of the second stage before reachin

orbent. Condensable gases will be removed, and only adsorbable gases will reach the sorbent. In essence, this a compromise between preventing condensable gas from reaching the sorbent (see Fig. 5.75) and maintaininumping speed for adsorbable gas. However, some condensable gas will reach the sorbent and occupy sites on hereby decreasing the ability of the sorbent to accumulate adsorbable gas.

n this case, capacity is defined as the quantity of condensable gas that can be stored at a given pressure whilemaintaining a pumping speed for the adsorbable gas at that pressure that is higher or equal to a defined percentusually 50%) of its initial value after regeneration.

rom the above it is obvious that the operating pressure of the pump is a key factor in determining capacity. Fr

dsorption isotherm and Eq. (5.46) it can be seen that the equilibrium pressure gradually rises as gas is adsorbeurface.

Fig. 5.75Cross section of cryopump used for high-

vacuum applications.






A cryopump can have reached capacity at, for instance, 106 Pa, while still operating efficiently if only a pressua is needed.

16efrigeration Technology

Most modern cryopumps in use today are cooled by a closed-loop mechanical refrigerator using helium as a wouid. The cryopump system consists of a compressor and an expander on which the arrays are mounted. Compnd expander are connected by flexible hoses. The thermodynamic cycle generally used is based on a cycle devy Gifford and McMahon [188] and by Longsworth. This cycle is used because it has proven to be simple and nd has a long service life, and the compressor can be remotely located from the expander and therefore the puchematic of a one-stage GiffordMcMahon (GM) refrigerator is shown in Fig. 5.76. General-purpose highvacuryopumps have two stages of refrigeration in order to achieve temperatures low enough for effective use.

he schematic shows that the GM machine consists of a cylinder, which contains a cylindrical piston called adisplache displacer is connected to a drive mechanism, so it can be moved up and down in the cylinder. There are twolumes, one above and one below the displacer. They are varied from maximum size to zero during the cycle,otal volume remains constant. The two volumes are connected

Fig. 5.76Refrigerator schematic.





hrough a thermal regenerator (inside the displacer) and to the inlet and exhaust valve. These valves are couplerive mechanism so their operation is synchronized to the position of the displacer. At the high-temperature sidisplacer is also equipped with a gas-tight sliding seal to prevent leakage from one side of the cylinder to the oto ensure that helium flows through the regenerator. With two-stage machines the first-stage regenerator consisghtly packed, high heat conductivity metal screens, the second stage regenerator is packed with a lead alloy shssential is that the material of the regenerator has a high heat capacity at cryogenic temperatures. The screenshot also have high surface area to volume ratios.

his construction means that the regenerator can efficiently transfer thermal energy between the screens and thencoming or outgoing helium. Also there will be very little pressure difference between the two volumes, which

minimizes the demand on the seals. Because the pressure is essentially the same in the spaces above and belowisplacer, except for a small drop when helium is flowing through the regenerator, no work is done on the gas aas does no work on the displacer. So, essentially no work is required to move the displacer in the cylinder.

he operation of the refrigerator can best be understood by reviewing a cycle with the expander at operatingemperature (see also Fig. 5.76):

. Pressure Rise . When the displacer is at the top (low temperature) end of the stroke, the exhaust valve is close

he inlet valve is opened. This increases the pressure from the exhaust pressure P 1 to the inlet pressure P 2. Helium wnter the inlet valve and fill the regenerator and the volumeV 1.

. Intake . The inlet valve is kept open while the displacer is moved toward the bottom (high temperature) end oroke. This displaces helium from the volumeV 1 to V 2. The helium is cooled while passing through the regenerahis causes its pressure to decrease, and more helium will enter the system from the compressor.

. Pressure Drop ( Expansion ). When the displacer has reached the bottom end of the stroke, the inlet valve is clond then the exhaust valve opened. The helium will expand and the pressure will drop from P 2 to P 1. This reductioressure causes a reduction in temperature. The decrease in temperature inV 2 is the useful refrigeration of the cycl

. Exhaust . The exhaust valve is kept open while the displacer is moved toward the top (low temperature) end oroke. This displaces helium from the volumeV 2 to V 1. The helium is heated while passing through the regenera

urn, the helium cools the regenerator so as to refrigerate the helium passing through on the next pressure rise aroke.

wo stages are required to achieve low enough temperatures to pump all gases except neon, helium, and hydroryocondensation. The added second stage is essentially providing two engines operating at two temperature lehis multistaging is desirable because it provides a more efficient process in achieving cryogenic temperatures

nstance, multistaging relieves the operating regimen of the regenerators [188].





We define a refrigeration lossQr :

where M is the mass flow of the gas,Cp is the heat capacity of the gas, and∆Tr is the temperature difference betwehe gas entering and leaving the regenerator at the low temperature end.

Assume that the temperature of the gas decreases by∆Te when expanding.∆Te must be greater than∆Tr in order tochieve useful refrigeration.∆Te is proportional to the absolute temperatureT at which the expansion occurs, andypically it is equal to 0.3 T. In a two-stage (GM) machine, temperatures of 10 K can be reached. This means∆Te we 3 K. To achieve useful refrigeration and handle other losses,∆Tr would need to be no greater than 1 K. This isirtually impossible in a single-stage machine operating between 300 K and 10 K because it would require heaxchanger efficiencies that cannot be reached in practice. However, a∆Tr of 1 K can be achieved in a two-stage sy

where the second stage operates between 50 K and 10 K.

he above briefly describes the principles of operation of the mechanical refrigerator used to cool cryopumps tperating temperatures. They are known as closed-loop systems because the helium continually circulates betwompressor and expander. So-called open-loop cryopumps are also used. In these, liquid nitrogen and liquid hesed to cool surfaces to 77 K and 4.2 K, respectively. The geometry of the arrays is similar to those described ahe first stage consists of a bowlshaped structure and a frontal louver, both cooled by liquid nitrogen. The first

orms a radiation shield for the second stage, which is cooled by liquid helium. The cryogens are fed into coolittached to the arrays, and this type of pump is therefore called aboiling pool cryopump . They are calledopen-loopryopumps because the cryogen is allowed to escape into the atmosphere after use. Sometimes gas collection syre used in the case of rare gases in order to recycle them.

17ump Configuration

or mechanically refrigerated cryopumps, array design configurations are, out of necessity, based on the charac

f the refrigerator. Two stages are needed to achieve sufficiently low temperatures to pump all gases except neoydrogen, and helium by cryocondensation. Because these light gases cannot be pumped by cryocondensation,ryosorbing surface of sufficient size for practical pumping performance must be provided on the arrays. The gf the arrays must be designed so that all gases pumped must impinge on a cold surface before reaching the sorhis will remove those gases being pumped by cryocondenstion before they reach the sorbent, whose full pumapacity will be used for removing neon, hydrogen, and helium.

he efficiency of the refrigeration cycle decreases rapidly as temperatures approach absolute zero. Therefore, important that the available refrigeration power for the older second stage array be used for condensing gas andissipated through parasitic loads. A key design feature for the first-stage array, which operates at a much higheemperature and which has much more refrigeration power available, is that its geometry is such that it shields econd stage from radiation heat loads.





he above considerations lead to an array design as shown schematically in Fig. 5.76. The first-stage array hasowl-shaped configuration. Attached to the can is the frontal array which for pumps used in high vacuum applionsists of a louver. The design has to be a compromise of providing efficient radiation shielding for the second

while providing as high a conductance as possible for gases that will be pumped on that stage. The second-stagonsists of a set of cones as shown in Fig. 5.76. A sorbent, usually charcoal, is attached to the underside of the he second-stage design is also a compromise between ensuring efficient shielding for the sorbent and still proigh conductance for neon, hydrogen, and helium, along with high pumping speeds.

ndium gaskets are used in connections between the frontal array and the first-stage can, as well as in connectioetween the arrays and the refrigerator, so that high thermal conductance is provided over the joints. Charcoal

most commonly used sorbent because water vapor can be removed from it at room temperature. It has a greaterhan man-made molecular sieve material and is less affected by impurities. Molecular sieve has to be heated to rder to remove water vapor. This temperature would melt the indium gaskets and would damage internal refriomponents, such as the seals on the displacer.

he temperature of the arrays is determined by the total heat load imposed on the pumping surfaces. The loads re from radiation, convection, and condensation. As discussed below, loads from convection and condensationgnored when the pump is operating at a pressure below 101 Pa. The main load under these conditions are radia

om the pumpbody and from the vacuum chamber. Additional radiation loads can be imposed by sources insidacuum chamber, such as bake-out heaters, plasmas, and so on.

An estimate of the radiant heat flow on to the arrays can be derived from calculating the heat flow (Q) between twooncentric cylinders at different temperatures [189]:

where the subscriptsc and w refer to the inner, colder cylinder and the outer, warmer cylinder, respectively, and

σ = StefanBoltzmann constant,e = coefficients of emissivity,

A = surface areas,T = temperatures in Kelvin.

f both emissivity coefficientsew and ec are equal to their maximum value 1, this reduces to





or a cryopump with an inlet diameter of 200 mm, the area of the first stage is approximately 0.130.15 m2. If thumpbody and vacuum chamber are at 295 K and the average first-stage temperature is 60 K, this means that t

maximum heat load the first-stage would have to absorb would be approximately 60 W. This heat load is usualarger than the first-stage refrigeration power of this size pump. It is clear that the radiant heat load must be redhis is done by reducing the emissivity of the internal pumpbody surface and the outside of the first stage can telow 0.1 through electropolishing or nickel-plating. This treatment will reduce the heat load to a value of 12 W

Many gases, specifically water vapor, will have a high emissivity (0.80.9) when condensed. This means that thmissivity of the first stage will rapidly increase in applications where water vapor is present, which means mopplications! In order to minimize this effect, the diameter of the first stage is designed to be only slightly mallhat of the pumpbody, so that only a minimal amount of water vapor will condense on the outside of the first-stnd its emissivity will not be affected significantly while pumping for long periods.

Radiation from the first-stage to the second-stage does not play a significant role. For a 200-mm-diameter pumurface area of the second stage is approximately 0.07 m2. Assuming an average first-stage temperature of 60 Kecond-stage temperature of 12 K, from Eq. (5.53) it can be calculated that the maximum heat load imposed is lW. In many cryopumps the inside of the first stage is purposely made to have high emissivity. This will adsor

adiation entering through the frontal array, minimizing the heat load on the second stage.

As mentioned above, convection heat loads can be ignored when the pump is operating at a pressure below 101ump then will be operating in the molecular flow regime, and the mean free path of the molecules will be signreater than the distance between the second stage array and the pump body. A high degree of insulation betweumpbody and the arrays is provided under these conditions. Convection loads become significant at pressures01 Pa, certainly if a major constituent of the gas pumped is hydrogen.

Also, the heat load imposed by condensation is negligible at high-vacuum operation. For instance, the enthalpyitrogen is 15,580 J/g·mol at room temperature and 134 J/g·mol at 20 K. A total amount of 15,446 J must be rey the refrigerator when condensing 1 mol of nitrogen. Some of this heat will be removed when the nitrogen strst stage. Ignoring this effect and assuming a worst case where all heat is removed by the second stage, calculhow that a second stage in a pump operating at 104 Pa with a nitrogen speed of 1500 liter·s1 will adsorb a heapproximately 1 mW. The obverse is that the heat of condensation becomes significant when the pump operateressures above 101 Pa (for example, when it is used in physical vapor deposition applications).umps used in physical vapor deposition applications have a different first-stage can and frontal array design thsed in high-vacuum applications (see Fig. 5.77). In the first place, the pumpbody and first-stage can are longerhose of a high-vacuum pump, increasing the distance between first and second stage. This allows more gas, tyrgon, to be accumulated before capacity is reached. In the second place, a barrier made of an insulating materilaced between the pumpbody and first-stage can at the pump entrance. This minimizes the amount of gas entepace between the first stage and the pumpbody. In addition,





Fig. 5.77Schematic of cryopump used in physical vapor deposition.

penings are made in the can in the area where it attaches to the refrigerator, so that any gas entering the space

umped away. This geometry results in a pressure differential over the barrier. This differential is such that wheressure above the pump is on the order of 1 Pa, the pressure between body and can below the barrier averagesressure below 101 Pa, effectively removing the convection heat load.

inally, the conductance to the second stage is deliberately reduced by changing the geometry of the frontal arrypically, the frontal array consists of a disk. The disk has a series of openings, sized so that the total conducta

he second stage is on the order of several hundred liters per second. The conductance is calculated to result in roper process gas flow at the required operating pressure. The reduction in gas flow through the use of a smalonductance results in a smaller heat load imposed on the second stage and in longer times to reach capacity. Fapor pumping speed is maintained as the frontal array operates at temperatures below 100 K. So pumping peruring pumpdown is not significantly affected.

One of the key parameters for a cryopump is the heat load that the pump can adsorb at the moment when the vaolating the pump from the chamber is opened during pumpdown. The load imposed is called theimpulsive heatload

he amount of gas impinging on the pump is too large, the arrays will warm up to the point where previouslyccumulated gas will evolve from the arrays to the extent that a runaway condition occurs. The pressure will beigh that the resulting convection load will overwhelm the refrigerator. Hydrogen is the most critical gas in thisn that it evolves at lower temperatures than other gases and causes a higher convection load at a given pressurecommended that the impulsive load imposed on the pump be limited to the amount that will allow the secondemain at or below





0 K. At this temperature the hydrogen capacity is approximately 50% of the capacity existing when the sorbenK, and the amount of hydrogen desorbing will be limited. If no hydrogen has been accumulated, the pump willecover when the second-stage array temperature is raised to approximately 30 K.

18egeneration

ryopump operation entails regenerating the pump periodically. Proper regeneration is key to optimum performhe pump. If not done correctly, pump performance can be significantly degraded.

When the pump is operated at high vacuum, hydrogen usually will be the first gas for which capacity is reachehis happens, pumpdown times will become longer and the ultimate pressure will become higher. When the pumsed in sputtering applications, argon capacity will be reached first. The pump will apparently behave normallyrgon is flowing; but when argon flow is halted, large pressure bursts will be seen during pumpdown. This is duact that the amount of argon accumulated on the second stage has become so large that the sorbate surface is ndequately shielded from radiation by the first stage. Argon will sublimate irratically as it is exposed to roomemperature radiation.

he need for regeneration is best determined experimentally. First, measure the time that the pump can operateiven application before behavior as described above appears. Regeneration should then be performed at appro0% of this time limit to ensure optimum performance.

ssentially, regeneration is a simple process. The pump is warmed to room temperature. During warm-up, gas wscape through the safety pressure relief valve attached to the pumpbody. The pump is then roughed to a pressuetween 5 and 10 Pa in order to establish an insulating vacuum inside the pump. Then the refrigerator is turnedhe pump cooled to operating temperature.

here are several important considerations to be observed. Large amounts of sorbate might be accumulated on econd stage when regeneration is started. The second stage is shielded from convection and radiation loads. Iteveral hours before it warms up to a temperature at which significant amounts of gas evolve and the insulating broken. Therefore, one of the first steps usually taken when regenerating the pump is to raise the internal pretmospheric by purging it with a dry inert gas, typically nitrogen. The purge gas is usually heated to shorten theeeded for the arrays to reach room temperature.

he second, most important consideration is to ensure that accumulated water vapor will be adequately removeegeneration. Purging with dry nitrogen during pump warm-up will assist in sublimating water vapor from the fage. Once a temperature of 273 K has been reached, the residual water vapor will liquefy. This means it can bansferred to the second-stage sorbent. The capacity of the sorbent for pumping hydrogen will be decreased if apor is not removed before subsequent pump chilldown. It is therefore necessary to determine that this residuaapor has been removed before operating the pump. This is done empirically by purging the pump for an exten

with dry gas and then performing a test to determine the amount of water evolving from the sorbent by measurincrease in pressure with time at the end of roughing. Because it is





ncertain how much water has been accumulated since the previous regeneration, this method can lead to errormore accurate method is to attach a hygrometer to the pressure relief valve and measure the dewpoint of the esas during the purge. Dewpoint levels that do not affect hydrogen pumping at subsequent operation can be meauring each regeneration, and more repeatable performance can be attained.

19artial Regeneration

Regenerating the pump to remove all gas as outlined above is called full regeneration . The pump has to be warmedoom temperature, roughed, and chilled to operating temperatures. Another regeneration method, called partialgeneration , has been developed. In this process the arrays are only warmed to temperatures between 120 K an

K, so that only gases accumulated in the second stage are removed. This process can be used in applications whither hydrogen or argon capacity will be reached long before enough water vapor has accumulated to affecterformance. The process can be accomplished in approximately 45 min, instead of several hours as with fullegeneration (see Fig. 5.78).

here are potential difficulties with partial regeneration. To complete the process in 4560 min, the accumulatedo be removed in less than 15 min. In many applications, especially physical vapor deposition, large amounts o

asily be accumulated in the second stage. The rate of gas removal needs to be high in order to remove it rapidmeans that the pressure in the pump will be high, essentially atmospheric pressure or higher. Conditions of viscwill exist for several minutes. Large amounts of condensable gas (argon, nitrogen, oxygen, etc.) will be able to orbent and will be partially condensed and/or sorbed. The amount of gas accumulating on the sorbent will dephe type of gas, its pressure, and the temperature of the sorbent.

or optimum results, after array warm-up and gas removal at atmospheric pressures through a one-way valve, teeds to be roughed to a low pressure while the sorbent is at a relatively high temperature (> 120 K). This will ny amount of condensable gas (nitrogen, argon) remaining on the sorbent before the array is subsequently cooown. Also, first- and/or second-stage array temperature should not exceed 180 K during the evaporation and rrocess. This will exclude the possibility of water vapor sublimating off the first stage and reaching the sorbent

he efficacy of partial regeneration on a pump can be checked by measuring the hydrogen pumping speed as af the amount of hydrogen accumulated after a partial regeneration has been performed. That data can then be o hydrogen pumping performance after a full regeneration, because full regeneration is the standard method byryopumps are restored to their original performance.

20orption Roughing Pumps

orption roughing pumps or sorption pumps are used for pumping systems from atmospheric pressure to a prespproximately 101 Pa. They rely on the





Fig. 5.78(a) Full-regeneration timetemperature cycle (200 mm diameter pump).

(Courtesy of Ebara Technologies, Inc.) (b) Partial-regeneration timetemperature cycle(200 mm diameter pump). (Courtesy of Ebara Technologies, Inc.)

ispersion forces existing between a gas and a surface to bind gas molecules on chilled surfaces inside the pumther words, they pump by cryosorption.

orption pumps typically consist of a cylindrical canister that is filled with an absorbent (see Fig. 5.79). The ad usually molecular sieve material, or zeolite, which consists of pellets made of a calcium or a sodium aluminorystalline matrix [183]. The canister is placed in a dewar cooled by liquid nitrogen. Zeolite is a poor heat condn array of aluminum fins inside the pump is used to improve thermal contact with the sieve material.



orption pumps need liquid nitrogen to operate; and, as with any capture pump, they have to be periodicallyegenerated. Therefore in present-day high-throughput applications, they have been replaced by dry mechanicaoughing pumps. However,





Fig. 5.79Cross section of sorption roughing pump(Courtesy of Varian Vacuum Products).

orption pumps are very clean noncontaminating roughing pumps and are mostly used in low-throughput appliwhere this feature is of prime concern. They are used in conjunction with getter pumps, ion pumps, or mechaniryopumps.

n a sorption pump, molecules are held on the adsorbent surface by physisorption. The number of molecules theld on an adsorbent is dependent on the temperature of both gas and surface, the chemical nature of gas and suhe microscopic roughness of the surface, and the incident flux of molecules. There is a constant interchange b

molecules residing on the surface and molecules arriving from the gas phase. The key is to have equilibrium couch that practical amounts of gas can be captured at the desired pressures.

or nitrogen, the major gas load when air is pumped, the dwell timeτ of a molecule on a surface at room temperatpproximately 5 × 1011 s [183]. At a pressure of 102 Pa, about 2 × 106 molecules per square centimeter can bedsorbed. Considering that a monolayer of gas on a surface consists of 10141015 molecules per square centimeollows that a negligible amount of nitrogen will be pumped.

At liquid nitrogen temperatures, the dwell time will have increased to 8 × 103 s and the amount of nitrogen reshe surface at a pressure of 102 Pa is approximately 3 × 1014 molecules per square centimeter or half a monolaroviding large surface areas, practical amounts of nitrogen can be pumped (see Fig. 5.80).

As coverage increases to above half a monolayer, the effect of the surface is rapidly lost and the equilibrium prwill quickly rise to the saturation vapor pressure, which for nitrogen by definition is atmospheric pressure.

A cross section of a sorption pump is shown in Fig. 5.79. Key elements of the pump are the aluminum body, thns removing heat from the zeolite, and the pressure relief valve. The adsorbent used is usually Linde 5A moleeve. This material, with an internal pore diameter of 11 nm [189], has a high affinity for nitrogen and oxygen

eolite also has a very high affinity for water vapor. Water vapor accumulated when repeatedly pumping downhamber filled with ambient air will eventually





Fig. 5.80Adsorption isotherms for nitrogen, hydrogen, neon, andhelium for a liquid-nitrogen-cooled sorption roughing

pump with a 1.35-kg zeolite charge.

aturate the sieve material, eliminating its capacity for adsorbing nitrogen and oxygen. The pump must then beut to 250°C or higher to remove the water. The sorption pump therefore usually comes equipped with a bake-eater. Normally, during operation of the pump, the heater is also immersed in liquid nitrogen.

igure 5.80 shows the adsorption isotherms for nitrogen, hydrogen, neon, and helium for a pump as shown in Fhis pump has a charge of 1.35 kg of molecular sieve, which can pump approximately 107 Pa·liters of nitrogenressure of 101 Pa. Figure 5.80 shows that noble gases such as neon and helium are pumped poorly. If, for insteon is pumped together with air, its capacity will be less than that shown in Fig. 5.80 because the neon will bey the active air gases, starting at pressures below 103 Pa. For this reason, sorption pumps are quite often stage

wo pumps are staged, one pump is used to achieve a pressure of 103 Pa and is then valved off. The second pumhen valved in and the pressure is further reduced. By this method, 99% of the air is removed by the first pumpoble gases are also swept into this pump. They cannot backstream into the system when pressure is further redigure 5.81 shows a pumpdown curve for a 200-liter chamber being pumped by three-staged sorption pumps.

is not useful to characterize sorption pumps by their pumping speed due to their batch nature [190]. Howevere shown (Fig. 5.81) that by using recommended sequencing and sizing, speeds approaching 300 liters per mine obtained.





Fig. 5.81Pumpdown for staged sorption pumps.

A key safety element of the sorption pump is the pressure relief valve. When the pump is saturated with air ando warm up to room temperature, very high pressures can be built up. The operation of this valve should never bstructed.



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7. T. A. Giorgi and F. Ricca, Nuovo Cimento, Suppl . 1(5), 472 (1967).

8. F. Ricca and T. A. Giorgi, J. Phys. Chem . 71, 3627 (1967).

9. B. Kindl, Nuovo Cimento, Suppl . 1(2), 646 (1963).





0. A. Barosi, in Residual Gases in Electron Tubes (T. A. Giorgi and P. della Porta, eds.), p. 221. Academic Pressondon, 1972.

1. B. Ferrario et al., Proc. Symp. Fus. Technol., 13th , Vol. 1, p. 395 (1984).

2. C. Boffito, F. Doni, and L. Rosai, J. Less-Common Met . 104, 149 (1984).

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5. P. della Porta, Gettering, an integral part of vacuum technology, Natl. Symp., 39th (1992).

6. K. Ichimura et al., J. Vac. Sci. Technol. A 5(2), 220 (1987).

7. G. Sancrotti, G. Trezzi, and P. Manini, J. Vac. Sci. Technol. A 9(2), 187 (1991).

8. R. D. Penzhorn, M. Delvillers, and M. Sirch, J. Nucl. Mater . 179181, 863 (1991).

9. T. Nagasaki et al., Fusion Technol . 9, 506 (1986).

0. K. Ichimura et al., J. Vac. Sci. Technol. A 6(4), 2541 (1988).

1. G. Kuus and W. Martens, J. Less-Common Met . 111 (1980).

2. M. Succi and P. Manini, Proc. Semicon/East 189, 62 (1989).

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4. A. Pebler and E. A. Gulbransen, Electrochem. Technol . 4(56), 211 (1967).

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00. D. Shaltiel, I. Jacob, and D. Davidov, J. Less-Common Met . 53, 117 (1977).

01. C. Boffito et al., Proc. Natl. Vac. Symp., 27th , Detroit; J. Vac. Sci. Technol . 18(3), 1117 (1981).

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04. U.S. Pat. 4,126,449 (1978).

05. U.S. Pat. 5,180,568 (1993).

06. J. D. Baker et al., J. Vac. Sci. Technol. A 12(2), 548 (1994).



07. F. Doni, C. Boffito, and B. Ferrario, J. Vac. Sci. Technol. A 4, 2447 (1986).

08. J. M. Park and J. Y. Lee, J. Alloys Compd . 182, 43 (1992).

09. O. Bernauer and C. Halene, J. Less-Common Met . 131, 213 (1987).

10. O. Bernauer and K. Ziegler, Ger. Pat., DE 3151712C1 (1981).

11. SAES Getters, 707 Non Evaporable Getter Activatable at Low Temperature (Catalogue).

13. A. Barosi and I. A. Giorgi,Vacuum 23(1), 15 (1972).

14. B. Ferrario, F. Figini, and M. Borghi,Vacuum 35(1), 13 (1984).

15. E. Giorgi, C. Boffito, and M. Bolognesi,Vacuum 41(79), 1935 (1990).

16. U.S. Pat. 4,428,850 (1984).

17. Plücker, Poggendorf's Ann . 105, 84 (1858).

18. Plücker, Poggendorf's Ann . 103, 88 (1858).

19. L. Vegard, Ann. Phys . ( Leipzig ) 4, 769 (1916).





20. Willows, Philos. Magn . 6, p. 502 (1902).

21. A. Klopfer and W. Ermrich,5th Natl. Vac. Symp ., 297 (1958).

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31. R. L. Jepsen, Le Vide 80, 80 (1959).

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35. W. Knauer and M. A. Lutz, Appl. Phys. Lett . 2, 109 (1963).36. S. L. Rutherford,10th Natl. Vac. Symp ., 185 (1963).

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59. R. J. Reid and B. A. Trickett, Proc. Int. Vac. Congr., 7th , Vienna,1977 , Vol. I, p. 89 (1977).

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70. C. W. Schoenfelder and J. H. Swisher, J. Vac. Sci. Technol . 5, 862 (1973).

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73. S. Komiya and N. Yagi, J. Vac. Sci. Technol . 6, 54 (1969).

74. T. Okano et al., J. Vac. Sci. Technol. A 2, 191 (1984).75. L. D. Hall, J. Vac. Sci. Technol . 6, 44 (1969).

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79. H. Henning, Z. Vakuum Technik . 24, 37 (1975).

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82. J. P. Hobson, J. Phys. Chem . 73(8), 2720 (1969).

83. K. M. Welch,Capture Pumping Technology . Pergamon, New York, 1991.

84. S. Brunauer, Emmett, and Teller, J. Am. Chem. Soc . 60(1), 309 (1938).

85. S. A. Stern, J. T. Mullhaupt, R. A. Hemstreet and F. S. Di Paulo, J. Vac. Sci. Technol . 2, 165 (1965).



86. R. A. Haefer,Cryopumping, Theory and Practice . Oxford University Press (Clarendon), Oxford, 1989.

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90. F. Turner,Varian Rep . VR-76 (1973).

General References

H. DeBoer,The Dynamical Character of Adsorption , Oxford University Press (Clarendon), London, 1953.

. Dushman and J. M. Lafferty,Scientific Foundations of Vacuum Technique . Wiley, New York, 1962.

D. Fast, Interactions of Metals and Gases , Vols. 1 and 2. Macmillan, London, 1971.





. J. Gregg,The Surface Chemistry of Solids . Chapman & Hall, London, 1965.

R. I. Masel, Principles of Adsorption and Reactions on Solid Surfaces . Wiley, New York, 1996.

V. Ponec, Z. Knor and S. Cerny, Adsorption on Solids . Butterworth, London, 1974.

G. L. Saksagansky,Getter and Getter-Ion Vacuum Pumps . Harwood Academic Press, London, 1994.

. M. Trapnell,Chemisorption . Butterworth, London, 1955.

K. Welch,Capture Pumping Technology . Pergamon, Oxford, 1991.





Vacuum Gauges

R. Norman Peacock

n Chapter 1 the pressure of a gas was defined as the force per unit area exerted by the gas on its confining walhown that this pressure is the result of molecular motion and is given by

wheren is the number of molecules per unit volume,m their mass, and their mean square velocity. Since

for particles with a Maxwellian velocity distribution, wherek is the Boltzmann constant andT the

bsolute temperature, Eq. (6.1) may be written

his equation is fundamental to vacuum measurement, since it provides a relationship between pressure and moensity. Some gauges such as liquid manometers and capacitance diaphragm gauges actually sense force per unnd thus measure the pressure ''directly." These are often called "direct gauges". Others, including ionization gaiscosity gauges and thermal conductivity gauges are sensitive to the molecular density, n. These are said to beauges" since gas density must be converted to pressure by Eq. (6.2). It is customary to report all vacuum measn pressure units even though the instrument may sense density. Direct gauges

Foundations of Vacuum Science and Technology , Edited by James M. Lafferty.

ISBN 0-471-17593-5© 1998John Wiley & Sons, Inc.





rovide pressure information independent of the gas. The sensing methods of thermal conductivity, viscous draonization are indirect and gas-dependent.

Only a limited number of pressure- or density-sensitive effects are available for use in vacuum measurements.ommonly used transducers are based upon:

. displacement of a liquid column, diaphragm, or other deformable element by force due to a pressure differen

. viscous drag acting upon a moving element;

. thermal conductivity;

. ionization by electrons, nuclear radiation, or laser photons, and sensing either ion current or emitted light.

eldom used techniques or those of historical importance include:

. transmission of sound;

. scattering of neutral atoms from a molecular beam;

. flash filament, adsorption/desorption method;

. Brownian motion.

Vacuum measurements today cover approximately 17 decades below atmospheric pressure. No one type of gaurinciple is useful over this range. For most applications, two or more sensors must be used from atmospheric t

working pressure. Figure 6.1 shows the working ranges of several commonly used vacuum gauges.



Fig. 6.1Ranges of commonly used vacuum gauging instruments. Solid lines represent the typicalrange, while dashed lines are extensions applying only to certain examples or to regions

where, although the gauge is sometimes used, the accuracy is poor.





1essure Units Used in Vacuum Measurements

ercury manometers have been used since the earliest days of vacuum technology. It is not surprising that the mmHg, or Torr (1 Torr), is a commonly used pressure unit. However, the Torr or mmHg is not allowed under the Système International (SI), wherent system, permits only those units which are derived from the fundamental quantities of mass (kilogram), length (meter)econd) by simple multiplication, without the use of numerical factors such as the density of mercury.

essure is force per unit area. The SI unit of force is the Newton (symbol N), which has the dimensions kg·m·s2. Thus the dimessure must be

) = (kg·m·s2/m2).

he N/m2 is named the pascal, abbreviated as Pa. It is easy to find the conversion factor from Torr to Pa. Looking ahead in this q. (6.3), the pressure due to a mercury column of heighth is P = hρ g , whereρ is the density of mercury (1.3595 × 104 kg·m3 at 0nd g is the acceleration due to gravity (9.806 m·s2). Then forh = 1 mm

P (1 Torr) = 103 m·1.3595 × 104 kg·m2 × 9.806 m·s2= 1.333 × 102 Pa.

he bar is a pressure unit defined as 105 Pa. It is approximately equivalent to a standard atmosphere pressure (760 Torr):

1 std. atm = 760 Torr = 760 Torr × 1.333 × 102 Pa/Torr = 1.013 × 105 Pa.

he bar and millibar (mbar) are temporarily allowed by the ISO, although they do not differ from the Pa by a factor of 103n as is usuquired. The mbar has the advantage of having the same magnitude as the Torr (1 mbar = 0.750 Torr), and it is commonly usedurope. Other pressure units are encountered occasionally. Table 6.1 has conversion factors for some common pressure units.

able 6.1. Conversion Factors for Some Common Pressure Unitsa

Pa mbar Torr in. Hg atm.a

1 1.00 × 102 1.33 × 102 3.39 × 103 1.01 × 105

mbar 1.00 × 102 1 1.33 3.39 × 101 1.01 × 103

orr 7.50 × 103 7.50 × 101 1 2.54 × 101 7.60 × 102

n. Hg2.95 × 104 2.95 × 102 3.94 × 102 1 2.99 × 101

tm.9.87 × 106 9.87 × 104 1.32 × 103 3.34 × 102 1

Multiply quantities given in the units shown along the top row by the factor in the table to obtain the units desired from theertical column on the left.





2iquid Manometers

igure 6.2 illustrates a simple manometer consisting of a glass U-tube filled with a liquid of densityρ. The pressure n the left arm is balanced by the pressure P 2 in the right ( P 1 > P 2) plus the pressure due to the difference height,h,

he mercury columns in the two arms, or P 1 = P 2 + hρ g , whereρ is the density of the liquid and g is the localcceleration due to gravity. This equation may be written in terms of the pressure difference

Mercury and diffusion pump oils are the liquids commonly used in manometers. Because the density of oil is mdecade less than mercury,h for a given pressure differential will be correspondingly larger. Traps are usually n

when using mercury since the vapor pressure of mercury is 0.16 Pa at 20°C, while that of modern diffusion pum less than 106 Pa.

he accuracy attainable with a manometer is highly dependent upon the uncertainty in measuringh. With a ruled scehind the arms of the "U" tube,h may be estimated to perhaps ± 0.1 mm with the naked eye. This could be imp

y a factor of 10 using a cathetometer. An electrical contact with micrometer adjustment can determine the posmercury surface to ± 102 mm. Interferometric methods as used today are accurate to about ± 1 × 105 mm.

Highly developed liquid manometers are the primary pressure standards for many countries. Heydemann, TilfoHyland [1] of the (then) U.S. National Bureau of Standards reported a precision mercury manometer utilizing unterferometry to determine the heights of the mercury columns. The resolution of this instrument was 1.4 mPa

Ueki, and Kaneda [2] of the National Research Laboratory of Japan in Tsukuba described a mercury manometewhite light Michelson interferometer. This instrument, which is the primary pressure standard of Japan, has anncertainty at 100 kPa of about 0.4 Pa.

Fig. 6.2The U-tube manometer. Thegas pressure in the left arm is

P 1 and is greater than the pressure in right arm, P 2. The

difference in height of theliquid in the two arms ish.







Ueki and Ooiwa [3] also made an oil manometer with a laser heterodyne interferometer for use at lower pressuncertainty of readings from 1 Pa to 1 kPa was reported to be 0.01%, or 2 mPa.

egras and Le Breton [4] of the Laboratoire National D'Essais in Paris reported a manometer using liquid galliquid position was sensed with a capacitance transducer. The advantage of operation with gallium is the extremapor pressure of the liquid. The resolution was said to be about 103 Pa, with a repeatability of 0.01 Pa for presess than 4 Pa.

onsiderable care is needed in using liquid manometers. A mistake can cause the liquid to be violently ejectedystem. Because the vapor pressure of mercury is about 0.16 Pa at 20°C, it is necessary to use a cold trap betwe

mercury manometer and system to prevent mercury vapor from entering. Contamination of the laboratory maymercury is spilled. If mercury vapor were present in the air at equilibrium concentration at room temperature, i

e a serious health hazard [5].

Many precautions and corrections are needed if accurate results are to be obtained with liquid manometers. Thef the liquid must be known at the operating temperature. With mercury, surface tension effects depress the liquurface, and with oil they elevate it. Surface effects depend upon purity of the liquid. At low pressures, special uch as ultrasonic or optical interferometry are needed to determine column height.

n spite of the simplicity of the manometer concept, liquid manometers are probably best used in standards labowhere proper care can be taken in their use and their importance as primary standards justifies the effort. Note a

quid manometers are not suitable for following rapidly changing pressure. For general use there are alternate without the disadvantages of liquid manometers.

3McLeod Gauge

he McLeod gauge [6] makes use of Boyle's law to extend the range of the manometer to lower pressures. Figulustrates a simple form of the instrument. The capillary tubes (1) and (2) must have exactly the same bore diam

hat capillary depression will be identical. The volume of the bulb plus capillary (1) and the tubing above the che open tube at the top of the gauge is connected to the pressure to be measured. A liquid nitrogen trap is requrevent mercury vapor contamination.

n one mode of operation the reservoir is slowly raised, and the mercury reaches the cutoff point. At this time thressure in the bulb is taken to be identical to that at the inlet to the system. As the reservoir is raised further, thhe bulb and capillary (1) is compressed. The mercury level in capillary (2) is brought to the same height as theapillary (1). If the pressure in the bulb was greater than zero at the time of cutoff, the height of the mercury in 1) will be lower than in (2) by an amounth. The pressure in the small volume at the top of capillary (1) is greateρ g . By Boyle's law, where P and V are the values at cutoff, Pf and Vf are as above, and A is the cross-sectional arehe capillary (1),





Fig. 6.3Simple form of McLeod gauge. (a) Overall view.(b) Detailed view defining the symbols used. The

figure is drawn for operation in the quadratic mode,whereh is the height difference between the mercury

columns when the level in capillary 2 is broughtto the level of the top of capillary 1.

olving this equation for P gives

ypically the volume Ah is negligible compared toV , thereby giving as a good approximation

A McLeod operated according to the assumptions above is said to be used in the "quadratic mode" because P isroportional toh2. In this mode it can cover about four decades.



f the mercury is always raised to a fixed position in capillary (1), leaving a fixed distance,d , between the mercuryurface in capillary (1) and the closed end of the capillary, while the height of the mercury in capillary (2) is allary, and ifh is the height difference between the levels in the two capillaries, then by Boyle's law,





Again making the assumption that Ah V , the approximate result is

his is known as the linear mode of operation of a McLeod, and it is useful over a range of about two decades.

here are many sources of error when using a McLeod gauge. For a more detailed discussion see Bermann [7]ther manometers, measurement ofh is critical. The density of mercury, the local acceleration due to gravity, andore of the capillary must be known. Use of a McLeod assumes that the gases to be measured obey Boyle's Lawondensible gases and vapors do not. It is assumed that the temperature of the gas in the cutoff volume is ident

hat in the system. Unless the mercury is absolutely clean, it tends to stick, especially in small capillaries.

treaming of mercury vapor from the inlet to the cold trap produces an error due to the pumping action of thisnidirectional vapor flow. This error can be as large as 20% for a mercury temperature of 25°C when using conubing of 20-mm bore. This effect was first noted by Ishi and Nakayama [8] while studying the long-term stabiauge constants for a group of ionization gauges. They observed that the gauge constants seemed to vary seasohe temperature of their laboratory at the old Electrotechnical Institute in Tokyo varied from 10°C in January t

n August, causing a periodic error in the pressure as measured by a McLeod. Gaede [9], in his original paper oiffusion pump, published the complete theory of this effect in 1915. His apparatus for verifying the pumping oreaming mercury vapor consisted of a McLeod with an additional mercury reservoir whose temperature couldontrolled. But it is not clear that Gaede was aware of the error caused by vapor streaming in normal operation

McLeod.

Operation of the McLeod is very slow, and it cannot follow changing pressure.

he cold trap can become a hazard when a calibration system is used with a condensible gas. Peacock [5] descccident where argon condensed in the trap. The gauge and trap were isolated from the system by a closed valvhe Dewar of liquid nitrogen was removed from the trap, thereby permitting the trap to become warm. The isoland Mcleod exploded, thereby peppering the operator with flying glass and distributing many kilograms of merver the laboratory.

4iston Pressure Balance Gauge

A simple form of the piston pressure balance gauge is illustrated in Fig. 6.4. This instrument is used for creatinressure differentials to calibrate other gauges. A small amount of leakage past the piston is of no consequenceiston, of massm and area A, is a very close fit in the cylinder. This gauge is similar to the liquid manometer, sinperation the piston is supported by the pressure differential





Fig. 6.4Cross section of an idealized

piston pressure balance gauge.The piston of massm and cross-

sectional area A is a close butfriction free fit in the cylinder.

1 > P 2. Setting the sum of the forces acting on the piston equal to zero for equilibrium,

Although useful for measuring large pressure differences, this form of the piston gauge is of little use for smallifferences because of the piston mass,m.

Ooiwa [10, 11] described a variation of the piston gauge as shown in Fig. 6.5. The piston is counterbalanced byummy piston on the other arm of the balance beam, and the force due to the pressure differential is sensed by lectronic balance attached to the piston. Ooiwa was able to measure pressures in the range of 1 Pa to 10 kPa wensitivity of about 5 mPa. This is adequate to permit direct calibration of some higher-range diaphragm gauge

he piston gauge as a basic standard. With a calibration system of the expansion type, measurements can be extower pressures.

Ooiwa [10] and Solis [12] discussed sources of uncertainties in the use of the piston gauge. These include: the mrea, and buoyancy of the piston; vertical adjustment of the cylinder; magnetic fields; local gravity; and temperffects. More detail on the piston pressure balance gauge is given in Chapter 12.

5ourdon Gauge



Gauges using the deflection of an aneroid cell, Bourdon tube, or a tensioned membrane also measure true pressndependent of the gas. The deflection of a sensing element may be measured in many ways. Mechanical couplell to an





Fig. 6.5Piston pressure balance gauge by Ooiwa. With the mass of the piston counterbalanced, the range of the piston gauge can be

extended down to 1 Pa with a sensitivity of 5 mPa. Reprinted with permission from A. Ooiwa, Metrologia 30, 607 (1993/1994) [Ref. 10].

Copyright 1993 Springer-Verlag.

ndicating needle is one means. For example, Wallace and Tiernan [13] manufacture a dial-type gauge measuritmosphere with 100-Pa resolution. Simple, inexpensive Bourdon gauges are sometimes used on vacuum cham

monitor the progress of roughing. Bourdon gauges use a flattened tube of elastic material formed into a circulas shown in Fig. 6.6a. The Bourdon tube tends to straighten as the internal pressure increases. In Fig. 6.6a the mommunicated to a needle for direct reading. Greater sensitivity can be obtained with a multiturn helical Bourdhe theory of the Bourdon tube is given by Lorenz [14]. Several related gauges were discussed by Dushman [1

he most sophisticated instrument of this type is the quartz helix Bourdon gauge (QBG). An example is thatmanufactured by Ruska Instruments Corporation [16] and is shown in Fig. 6.6b. It operates on the force balanc

rinciple with magnetic nulling. The null position is sensed optically via a mirror on the free end of the helix. Sates that the rotation is primarily a function of the pressure differential, the cross-sectional area and geometry

ube, the diameter of the helix, and the number of turns. For the Ruska instruments with full-scale (FS) pressurhan 500 psi (3 × 106 Pa), the repeatability is ±0.002% FS. The resolution is ±0.001% FS, the linearity is ±0.00nd the hysteresis is < 0.001% FS.







Fig. 6.6Bourdon gauges: (a) Inexpensive Bourdon gauge;

(b) quartz Bourdon gauge used for precision differentialmeasurements. Partb reprinted with permission from

K. Solis, "The Fused Silica Helix Bourdon Tube: Its Placein Measurement and Control." Ruska Instrument Corp.,

Houston, TX 77063 (no date) [Ref. 17].

ince the settling time is about 90 s, the QBG is best suited for a standards laboratory or similar facility.



6apacitance Diaphragm Gauges

ommercial capacitance diaphragm gauges (CDGs) appeared around 1960. They have been improved to the exhey can replace liquid manometers in most applications other than as primary standards. Their use avoids mesazardous





quids along with the possibility of contaminating the system or laboratory. Only inert materials at or near ambemperature are exposed to the gas. Accurate measurements over four decades using a single head are possible

here are other diaphragm gauges since other techniques may be used for observing the deflection of a diaphranductive transducer methods were examined early in the history of diaphragm gauges [18]. Various sensing msed by the manufacturers of industrial diaphragm gauges for the pressure region above 1 Pa, including strain giezoresistive films, and inductive. However, these products are seldom seen in vacuum applications relevant took.

apacitance sensing is a simple and precise technique for observing the diaphragm position. As early as 1936, 19] described a functional single-sided CDG. Others who published descriptions of CDGs before commercialnstruments were available include Lilly, Legallais, and Cherry [20], Alpert, Matland, and McCoubrey [21], Dr22], Hecht [23], and Macdonald and King [24].

DGs may have a sense electrode on one side of the diaphragm only, or on both. Both sides may have ports sonstrument can be used for differential pressure measurements, or one side may be evacuated and sealed so thatauge is for absolute pressure sensing. See Fig. 6.7.

.6.1ensitivity of the Capacitance Method

A simple numerical example will illustrate the value of the capacitance method for sensing diaphragm deflectiohe same time it will make evident those characteristics of the CDG helpful in understanding its characteristics.

igure 6.8 shows the diaphragm and sense electrode of a simple CDG sensor. Let the diameter of the diaphragmmm, and let area of the capacitance sensing electrode be 1 × 104 m2, spaced 0.1 mm from the diaphragm. Theapacitance may be estimated using the parallel plate formula

whereC is the capacitance in farads (F),ε0 is a constant 8.85 × 1012 F/m, K is the dielectric constant, A is the area ohe electrode, and s is the separation.

or the numbers of this example the sense electrode to diaphragm capacitance is 8.9 × 1012 F. Allowing for soapacitance, a total of 15 pF is reasonable.

Fig. 6.7Capacitance diaphragm gauges: (a) Two-port CDG for differential pressure

measurements; (b) single-port CDG with sealed and gettered vacuumreference for absolute pressure measurements.







Fig. 6.8

The diaphragm and capacitance sensing electrodeof a simple CDG sensor. The area of thecapacitance probe is A, and the separation

from the diaphragm is s. The thin membraneis deflected a distanceY by the pressure P .

Assume that a capacitance change of 3 × 1017 F is a practical limit of resolution for an inexpensive instrumenthat if 15-pF capacitance were used in an LC circuit resonant at 10 MHz, an incremental change of 3 × 1017 F hange the resonant frequency by 10 Hz. Solving Eq. (6.12) for s and taking the derivative, the change in spacing ncremental change of capacitance is

or δC = 3 × 1017 F and the numbers of the present example, a resolvable deflection is 3 × 1010 m, or about thn atom.

.6.2Deflection of a Thin Tensioned Membrane

Referring to Fig. 6.8, the center deflection,Y , of a circular thin flexible diaphragm of radiusa tensioned at the edgeadial tension,T , per unit length of the circumference is, for small deflections, given by Rocard [25] as

where P is a uniformly distributed pressure. For aδY just resolvable by a capacitance measurement, the resolvablδ y Eq. (6.14) is 2.2 × 103 Pa. This example is similar to a 100-Pa full-scale sensor. That is, forδ p = 100 Pa theeflection would be about 2 × 102 mm. This is one-fifth of the 0.01-mm diaphragm to sense electrode separatio

was assumed for zero pressure differential.



he capacitance method senses not only movement of the diaphragm caused by pressure change, but also dimehanges due to temperature effects, gravity, and vibration. Hysteresis, or return to zero after deflection, must alonsidered. All of these problems can cause shift of the zero pressure setting. Zero stability is often a problem wDGs in the lowest decade of their range.





Fig. 6.9Schematic of a valve arrangement for verifying the zero on

(a) a differential CDG and (b) an absolute CDG.

n designing a sensor, attention must be given to choice of materials to avoid differential motion and zero shift y temperature effects. When using a CDG, it is imperative that means be provided for verifying the zero. For ort differential CDG, this may simply necessitate valving means to make possible equalizing the pressure at thorts. For a single-port, sealed reference CDG, verifying the zero requires a pumping system capable of reduciressure to about 1% of the lowest resolvable pressure. Valving arrangements for the two-port and single-port gre shown schematically in Fig. 6.9.

Residual temperature effects are dealt with in two ways: A temperature sensing element may be used in a circuiompensate for temperature variations, and/or the sensor may be placed in a constant temperature enclosure maomewhat above the highest expected ambient. This temperature is usually between 45°C and 50°C.

.6.3Accuracy of Commercial Gauges

resent commercial instruments cover a wide range, are convenient to use, and are remarkably stable and accuircuits attached to the pressure sensing cell process the capacitance information and give analog or digital out

nexpensive single-port heads with sealed vacuum reference are available with full-scale ranges from 133 Pa (1.3 × 106 Pa (25,000 Torr). Claimed accuracy after subtracting zero drift is ± 0.5% of reading, and optional ± 0ccuracy is available. These uncertainties are due to causes such as non linearity and hysteresis. These sensor heed only be supplied with + 15/0/ 15 V dc, and the output is 0 to 10 V dc [26].

or critical laboratory use, precision temperature-controlled sensor heads with sealed reference are available incale ranges from 13.3 Pa (0.1 Torr) to 3.3 × 106 Pa (25,000 Torr). For heads 133 Pa to 105 Pa full scale, accur.05% of reading is available [27].

ullivan [28] and Sullivan and Uttaro [29] discussed the various sources of uncertainty in the CDG. They assumnstrument with stated uncertainty of 0.08% of reading due to nonlinearity and hysteresis, resolution of 0.0001%ero drift coefficient of 0.0004% of FS per °C, and span temperature coefficient of 0.002% of reading. The relamportance of these errors is apparent if they are applied to





he example of a 1-Torr (133-Pa) head used at 1 × 104 Torr (1.33 × 102 Pa). Then the uncertainty due to nonlinnd hysteresis is 8 × 108 Torr; due to resolution, 1 × 106 Torr; due to zero temperature drift, 4 × 106 per °C; anpan temperature coefficient, 2 × 109 per °C. The total uncertainty is 5.08 × 106 per °C; and at this pressure, 1 .08% of reading per °C. The significance of temperature zero drift is clear.

everal international standards laboratories have studied the long-term stability of CDGs for use as transfer staHyland and Tilford [30] examined 14 different temperature controlled gauges at the US National Bureau of Staver long times of up to four years. Percentage shift at midrange pressure for the various CDGs varied from 0.0.02%, with most shifts well under 1%. Grosse and Messer [31] of the Physikalisch-Technische Bundesanstalt alibrated two CDGs in many gases several times between 1980 and 1985. The deviation of the pressure indicahe calibration pressure never exceeded 1%. M. Bergoglio and A. Calcatelli of the Istituto Metrologia G. Colonorino, found similar stabilities [32].

he result of these studies has been the acceptance of CDGs as secondary or transfer standards within their preange. It should be noted that the CDG has improved in stability, the variety of products available, and convenise, since the instruments were purchased for the tests described above.

.6.4

hermal TranspirationWhen temperature-controlled sensor heads are used, the temperature of the sensor usually is greater than that ohamber whose pressure is to be measured. The gauge reading will be a few percent high under some conditionrror becomes significant when the pressure is lower than that where the mean free path of the gas is similar to iameter of the tubing connecting chamber and sensor (see Section 1.10).

A plot of an experimental transpiration error measurement by Jitschin and Röhl [33] is reproduced as Fig. 6.10emperature of the chamber was about 26.5°C, and the sensor was 40.5°C. The diameter of the tubing where themperature change occurred was about 4.6 mm. The curves show the error to be negligible above 100 Pa. It ino about 2% at 102 Pa. In the low-pressure limit the ratio of the gauge to chamber pressure should approach

where p2 is the pressure in the heated gauge at temperatureT 2, and p1 is the chamber pressure at ambient tempera1. Similar results were found by Poulter et al. [34].

.6.5onclusions

Measurements made with a CDG are independent of the gas except for the small transpiration correction. Withded gauges, only noncorrosive metals such as stainless steel or Inconel are exposed to the vacuum, making th

nert for most gases, not decomposing or otherwise altering the gas. Its volume is small, and its response is fastong-term accuracy, when used properly, can exceed 1%, justifying its use as a secondary standard or transfer g

may be purchased with





Fig. 6.10Plot of the thermal transpiration error for two sets of experimentaldata (triangles and inverted triangles). Reprinted with permission

from W. Jitschin and P. Röhl, J. Vac. Sci. Technol . A5, 372 (1987)[Ref. 33]. Copyright 1987 American Vacuum Society.

wo ports for differential measurements, or with an evacuated reference for absolute pressure measurements. Therious disadvantage of the CDG is the lack of an absolute zero. It is usually necessary to provide a pumping orystem to check the zero.

he American Vacuum Society ''Recommended Practices for the Calibration and Use of Capacitance DiaphragGauges as Transfer Standards" [35] is a valuable source of information.

ome Suggestions to Help Obtain Good Results with CDGs

. Avoid over pressurizing the gauge. If the chamber is frequently vented to the atmosphere, an isolation valve DG inlet will prolong life.

. For units with heated heads allow a warm-up time of several hours.

. Maintain a stable ambient temperature.

. Prevent mechanical stress on the sensor cell by proper installation, using a bellows when necessary.

. Avoid vibration.

. Avoid particulate contamination that could inhibit diaphragm motion.

. Recalibrate frequently.



7iscosity Gauges

Viscosity gauges utilize the drag effect observed when gas molecules act upon a moving object or surface. Gasmolecules leaving a surface moving with a velocity





arallel to the surface plane gain momentum in the tangential direction, while that of the moving body is decreigure 6.11 illustrates several types of viscosity gauges: (a) those based upon observing the decrement of an oscilane; (b) those of an scillating disc in torsion; (c) those of an oscillating fiber; (d ) those based upon the coupling ofotating disc to a stationary disc; (e) those using the pressure dependence of the impedance of an oscillating objes a quartz crystal tuning fork; and ( f ) those measuring the decrease of the angular velocity of a freely suspendedpinning sphere.

Dushman [36] covered the early history and application of the first two of these varieties of viscosity gauges. Inteckelmacher [37] reviewed the theory of viscous drag for planes and cylinders moving in a gas, just before thpinning rotor gauge (SRG) of Fig. 6.11 f became important.

Although investigators from Edwards High Vacuum International and the University of York have revived the cisc viscosity gauge of Fig. 6.11d in recent publications [38, 39], the viscosity gauges of Fig. 6.11ad are mostly oistorical importance.

wo gauges of Fig. 6.11 are worth detailed consideration. Since 1984 the vacuum group of the Electrotechnicaaboratory in Japan has published a series of papers concerning the quartz oscillator gauge. It may have some

mportance in the future and is discussed later in this section. The spinning rotor gauge is one of the newest ins

or vacuum measurement. Although mentioned briefly in the 1962 edition of this book, it was not practical at thAdvances in digital electronics now make accurate timing of rotational speed possible, and the SRG has becommportant as a secondary, or transfer, standard.

Fig. 6.11Viscosity gauges: (a) Oscillating vane;

(b) oscillating disc in torsion; (c) oscillatingfiber; (d ) gas coupling of a rotating disc to a

torsion disc; (e) oscillating quartz crystal, here inthe shape of a tuning fork; ( f ) spinning rotor gauge.





.7.1pinning Rotor Gauge

he SRG determines pressure from the decrement of the angular velocity of a small spherical rotor suspended iacuum. The frictional loss due to gas at a pressure of 104 Pa is small. At this pressure, a steel ball 4.5 mm in dpinning at 410 rps would require about 18 h for a decrease of 1 rps. A nearly frictionless support is necessary iecrement in rotational speed of a small sphere is to be used as a measure of high vacuum. Beams and associat

University of Virginia were the first to apply a magnetic "bearing" to an SRG [40]. They compared it to an ioniauge over the range 1.3 × 102 to 6.5 × 106 Pa and found good agreement. However, they stated that their SRGery sensitive to shock.

lectrostatic suspension can provide an even lower loss bearing for a rotating sphere. An electrostatically suspeacuum gyroscope suggested by Nordsieck [41] was developed during the 1950s at the University of Illinois. Vrag due to gas was observed to pressures as low as 107 Pa. The feasibility of using electrostatic suspension foacuum gauge was discussed by Nuttall and Witt [42]. They concluded that it might be possible to build such anabling measurements at pressures lower than existing instruments with magnetic levitation.

However, electrostatic levitation of a massive rotor is possible only at low pressures because the high electric fi

equired for suspension would cause a gas discharge. This probably makes a wide-range electrostatically suspeRG impossible. Today, the only commercially available SRG uses magnetic suspension.

7.1.1heory

A spherical rotor freely spinning in a gas at low pressure is slowed by interaction with the gas. An equation foreceleration may be derived if three reasonable assumptions are made about the gassurface interaction:

. The mean free path for the gas must be greater than rotor-to-wall separation . This ensures that gas arriving at thotor has a proper Maxwellian velocity distribution and does not come from a gas cloud spinning with the rotortuation at higher pressures is more complicated and not covered here.

. Most of the gas molecules arriving at a surface dwell there briefly, and they leave with a symmetrical cosine spatialstribution and with a velocity distribution corresponding to the temperature of the surface . The alternate is specul

eflection, where the molecule "remembers" the tangential component of its momentum. These cases are illustrig. 6.12. The effective accommodation coefficient,σ, is defined as the



Fig. 6.12Molecules departing fixed (a) and

moving (b) surfaces. The moleculestransfer momentum from the moving

surface since, as seen in the rest frame,the velocities of the departing molecules

are the vector sum of the usualcosine velocity distribution and the

velocity of the moving surface. Partbshows the resultant velocity for

one molecule.





Fig. 6.13Coordinates and element of area for integrating

the loss of tangential angular momentumover the surface of a spherical rotor.

action of the molecules that are scattered diffusely. Typically,σ is near unity. It may exceed unity for rough surf

. Angular momentum is conserved in the gas/rotor system . To make use of the conservation of angular momentumxpressions must be found for the angular momentum of the rotating sphere and for the component of the momansverse to the spherical surface lost by the gas. Figure 6.13 shows the first quadrant surface of a spherical ro

adiusa spinning with angular velocityω. An element of area at azimuthal angleφ is

he surface elementdA, having radiusr , has a tangential velocityvT (dA):

A molecule of massm striking the surface elementdA and accommodating will depart with increased angular

momentummvTr , while the angular momentum of a specularly scattered molecule will not change. The incremhange of tangential angular momentum,δ LT , of a gas molecule strikingdA is

rom Chapter 1, the number of molecules, ν, arriving at a surface per unit time and area is







wheren is the number of molecules per unit volume, and is the mean molecular velocity, .ssuming perfect accommodation, the time rate of change of LT for all gas molecules colliding with the surface el

A per second Substituting fordA from Eq. (6.16) gives

his may be integrated over the surface of the sphere to give the total rate of change of transverse momentum,dT/dt he colliding gas

he angular momentum of the sphere is Ls = I ω. If Ls changes because of change of I caused either by thermalxpansion or by change ofω, then the rate of change of angular momentum for the spherical rotor may be writte

he moment of inertia, I , of a solid sphere of radiusa made of a material of densityρ is

aking the derivative of Eq. (6.23) with respect toa , wherea may change because the temperature is time-dependnd noting that the mass of the sphere is constant whileρ and a vary givesdI/dt = I ·2αdT/dt . Substituting in Eq. (6.nd simplifying yields

y conservation of angular momentum, we obtain

ubstituting Eqs. (6.21) and (6.24) into Eq. (6.25), introducing the accommodation coefficient,σ , to permit less-thaerfect accommodation, and using Eq. (6.23) for I gives





rom Chapter 1,n = P/kT , where P is the gas pressure in Pa, andk is the Boltzmann constant 1.38 × 1023 J/K.ubstituting forn and solving for P , Eq. (6.26) may be written in terms ofv as

r, substituting forv,

he negative signs of the terms in the parentheses are proper sinced ω /dt due to viscous drag will be negative, andositivedT/dt will cause a negatived ω /dt at P = 0. If the residual drag (RD) is defined as the relative decelerationero pressure, it may be included in a term with the pressure-dependent deceleration for the spinning rotor:

is clear from Eq. (6.29) that since the molecular weight, and possiblyσ, depend upon the gas, then measurementmade with a SRG are gas-dependent.

remerey [43] suggested extending the range of the SRG from the limit of about 104 Pa assumed in deriving Eo higher pressures approaching an atmosphere. This requires that the viscosity of the particular gas be includedressure calculation made by the SRG controller.

7.1.2ommercial Gauges

he present commercial magnetically levitated SRG is largely the result of the work of Fremerey and colleaguehe University of Bonn and then later at the KFA, Jülich. In 1971, Fremerey [44] described an early SRG utilizlectronic damping in the suspension and optical sensing of rotational speed. He examined the decay ratio (d ω /dt )/ωeveral spheres of differing diameter for rotational frequencies from 2 × 104 to 1 × 105 Hz. The residual drag aressure, mostly due to eddy currents, corresponded to a few times 104 Pa nitrogen equivalent. In 1972 he intronductive sensing of rotation [45].

igure 6.14 shows the construction of an SRG head. A thimble (T) attached to the vacuum chamber contains a pherical rotor (R) of ferromagnetic material such as SAE 52100 carbon steel or 440C stainless steel. The outsiiameter of the thimble is approximately 8.5 mm, and that of the ball is 4.5 mm. Two permanent magnets (M), ositioning coils (A) and lateral damping coils (L), are used with associated circuits to suspend the ball. Rotatioall is sensed inductively by two pickup coils (P). There are four drive coils (D) to drive the ball up to speednductively. Figure 6.15 illustrates how the rotation of the ball is sensed. To induce a signal in the pickup





Fig. 6.14View of the internal structure of a spinning

rotor gauge head. The components areexplained in the text.

Fig. 6.15Inductive sensing of the rotation of amagnetized spherical rotor in an early

SRG head with two pickup coils.



oils the rotor must be slightly magnetized, and the magnetic moment must not coincide with the spin axis.

When turned on, the controller quickly brings the rotor up to about 410 rps. The ball is allowed to coast, and thecrement of the angular velocity is measured by a digital timer system in the controller. When it slows to aboups, the drive





ctuates briefly to bring it back to 410 rps. A good discussion of the operation of the SRG is given by Fremereylong with consideration of an algorithm used to obtain the average decay rate.

he commercial SRG controllers provide statistical information on the measurements. A pressure determinatioonsist of 1 to 99 independent measurements, each between 0.5 and 30 s long [46]. The controller averages thendividual results and prints the average pressure, the signal scatter, and the standard deviation of the measuremcatter of values is caused by timing errors, pressure drift during the measurement period, and vibration.

he fluctuations due to timing errors are unavoidable. Figure 6.16 from Redgrave and Downes [47] is a plot ofandard deviation versus the sampling interval for a second-generation controller. Note that the random noise iquivalent to a pressure of 104 Pa for a sampling interval of 10 s.

ooney et al. [48] placed all of the control electronics for an SRG on an accessory plug-in board for a personalomputer (PC). The PC then performs all of the functions of the present controllers, including levitation, spinniming, and the statistical calculations with the pressure data. Greater control of some parameters such as the



Fig. 6.16Standard deviation of SRG measurements versus

the duration of the sampling interval in seconds. Datawere obtained using a SRG-2. Reprinted from

F. J. Redgrave and S. P. Downes, "Some Commentson the Stability of Spinning Rotor Gauges,"Vacuum ,

Vol. 38, 839842 [Ref. 47]. Crown Copyright 1988, withkind permission from Elsevier Science Ltd., The

Boulevard, Langford Lane, Kidlington OX5 1GB.





measurement time and rotor frequency is permitted. By using long measurement times the useful range can be elow 105 Pa. These authors also derived an algorithm for measuring the deceleration rate. Another advantagelug-in board is that one board will operate up to four gauge heads.

7.1.3tability

he accommodation coefficient,σ, of a rotor must be constant if the SRG is to be used as a secondary standard.Numerous papers have examined the value ofσ and its stability over periods as long as several years [47, 4952].

he range of values ofσ found with uncalibrated balls is quite limited. Dittmann, Lindenau, and Tilford [52] mefor 68 smooth balls. The results are shown in Fig. 6.17. For this group we have 0.96 <σ < 1.06. From references appears that 0.95 <σ < 1.05 for new ball bearings. For Grade 5 bearings the surface roughness is about 0.8 µim), and the departure from sphericity is 5 µin. (0.13 µm).

Redgrave and Downes [47] of the National Physical Laboratory (NPL), Teddington, calibrated one rotor severaver a two-year period with an SRG-2. Table 6.2 shows thatσ can be very stable under laboratory conditions. Theccommodation coefficient does not change unless the surface of the ball is damaged. Significant changes inσ resul

when the ball suspension fails while it is rotating ("crashing"), or when a head is shipped with the ball free in thhimble [31, 52].

igure 6.18 reproduces a plot from Messer et al. [53] showing repeated determinations ofσ for four balls during9811986. The sudden changes were presumably caused by damage to the ball surfaces. The value ofσ may be as hs 1.2 for intentionally or accidentally roughened balls [50]. Surface contamination, or damage by chemical etc

will changeσ also. Subject to the possible ± 5% error resulting when a rotor is not calibrated, the SRG may be un absolute gauge as proposed by Fremerey [43].



Fig. 6.17Histogram showing the distribution of effective accommodation

coefficients for 68 smooth steel bearing balls used as rotors. Note that the accommodation coefficients of all fall in the

interval 0.961.06. Reprinted with permission from S. Dittmann,B. E. Lindenau, and C. R. Tilford, J. Vac. Sci. Technol., A 7,

3356 (1989) [Ref. 52]. Copyright 1989 American Vacuum Society.





able 6.2. Repeated Calibrations Over a Two-Year Period of the Accommodation Coefficient,σ, for One Spherical Rotor a

Pressure (Pa)Date 3 × 104 3 × 103 2 × 102 3 × 101 3 × 100Nov. 1987 1.041 1.035 1.035 1.030 0.973

uly 1987 1.029 1.030 1.035 1.032 0.974an. 1987 1.034 1.034 1.034 1.030 0.972ept. 1986 1.037 1.028 1.030 1.030 0.974an. 1986 1.042 1.038 1.035 1.029 0.973From Redgrave and Downes [47].

ccording to Eq. (6.16), the temperature dependence in pressure determination by SRG enters in two ways: (1) through and mperature of the gas and (2) through thermal change of the moment of inertia of the rotor. The equilibrium temperature of theessure is the same as the thimble. Transient inductive heating of the ball occurs during "spinning up," causing a temperature rveral degrees. In the thermally isolated rotor, it requires many hours to reach thermal equilibrium [5458].

gure 6.19 is a curve by McCulloh, Wood, and Tilford [58] showing that the measured residual drag changes for five hours afteo avoid this problem it is advisable to suspend and spin-up the ball the day before an SRG is to be used as a reference gauge.

lthough the frictional loss resulting from the use of a magnetic bearing is small, it is not zero. It results primarily from eddy cue ball, as well as from those induced in the thimble by the magnetic field of the ball [5961]. It can be dependent upon the ball 2]. Normally, the residual drag at high vacuum corresponds to a nitrogen pressure of 104 to 103 Pa.

his residual drag should be measured every time the ball is spun-up, and occasionally during a long sequence of measurementimble must be evacuated to a pressure negligible compared to the residual drag. The indicated " pressure" at P = 0 is the residual dhe residual drag is then entered into the controller, where it is automatically subtracted from each pressure measurement.

he effect of vibration on SRG measurements has also been studied [54]. The suspended ball tends to remain fixed in space whbration causes the head with its pickup coils to move. The result is a timing error of the induced signal in the pickup coils.

ecent heads use four coils for rotation sensing as sketched in Fig. 6.20. They are not sensitive to vibration as the older head illg. 6.14. However, it is beneficial to minimize vibration due to causes such as mechanical pumps, air conditioning, and walkinfect of vibration is to cause an apparent increase in the residual drag. But the contribution due to vibration may not be stable. Tesence of periodic vibration may be seen with an oscilloscope used to view the induced signal output.





Fig. 6.18Repeated argon calibrations of four rotor balls at the PTB (Berlin) over

a period of several years. The SRG thimbles were transported to theinternational laboratories shown on the top line with the balls free to move

in their thimbles. Reprinted with permission from G. Messer, P. Röhl,G. Grosse, and W. Jitschin, J. Vac. Sci. Technol. A 5, 2440 (1987) [Ref. 53].

Copyright 1987 American Vacuum Society.



7.1.4econdary or Transfer Standard

he reproducibility of measurements made with an SRG can be within 1%. Factors influencing long-term stabieen discussed above. Tests of SRGs as transfer standards in international comparisons have verified their longability over periods of several years (see Section 12.3.2). The long times and shipping hazards make internati

ntercomparisons demanding tests.





Fig. 6.19Change in residual drag due to cooling of ball after spin-up. The

curve shows that about five hours is required for the residual drift toapproach a stability of 1 × 106 Pa nitrogen equivalent. Reprinted with

permission from K. E. McCulloh, S. D. Wood, and C. R. Tilford, J. Vac.Sci. Technol. A 3, 1738 (1985) [Ref. 58]. Copyright 1985American Vacuum Society.



Fig. 6.20Four rotation sensing coils used in

improved SRG head provide reducedsensitivity to vibration. If the ball

changes position with respect to thehead because of vibration, the outputsignal of the four phased coils tends

to remain constant.

Messer et al. [53] of the Physikalisch-Technische Bundesanstalt (PTB) in Berlin reported an intercomparison waboratories of eight countries. They found thatσ changed during shipping if balls were free to move about in thehimbles. Even so, they concluded that calibration data for most of the participating labs were within





1%. The following year, using a spring-loaded device to prevent motion during transport, another intercompawas made between the PTB and NIST without change of the rotor calibrations [63]. The authors suggested thatntercomparisons might be possible to an accuracy of ± 0.2%. Sharma and Mohan [64, 65] of the National Phyaboratory (India) also participated in these intercomparisons.

7.1.5se Precautions

Most of the precautions recommended when using an SRG are evident from the above discussion. They are coelow:

. To prevent changes of the accommodation coefficient of calibrated balls, the rotor surface must not be damaandling, either out of the thimble or during transport while free to move within the thimble. It is especially imhat the rotor suspension not be interrupted while the ball is spinning. Damage could result from power interruphe storage battery within the controller is not maintained. An uninterruptable supply is desirable

. Install the SRG head using a level to ensure that its axis is vertical. This helps to minimize the residual drag.

. Verify the ability to suspend the ball immediately after pump down. Some balls will not suspend and spin uproperly. It is disappointing to learn this after processing the system and it is time to make a measurement.

. Avoid magnetic fields from external sources.

. A stable ambient temperature is desirable. Avoid locating where sunlight can strike the head or near air-condents.

. Allow at least several hours for temperature equilibrium after spin-up.

. Use only in clean systems which will not contaminate or damage the rotor surface.

. Know the gas in the system. SRG measurements are dependent upon the gas.

. Verify that the parameters entered into the controller are correct for the gas, rotor, and current temperature.

0. Check the residual drag frequently while the SRG is pumped to a pressure not higher than 1% of the lowesto be measured.

1. Avoid locations with significant vibration. Look for effects of vibration as evidenced by an unstable residuar as vibration frequencies superimposed on the induced signal output.

2. Experiment with rotor magnetization. It may be changed by bringing a small permanent magnet near the thwith the head assembly removed. An excessive magnetic moment of the ball increases the residual drag. Too li

weak induced signal that does not permit accurate timing. Viewing the signal with an oscilloscope is necessarerify the induced signal voltage.

3. Verify occasionally that the accommodation coefficient,σ, of the rotor is nchanged. Comparison to a capacitaiaphragm gauge at about 102 Pa may be adequate. If two SRG systems are available, they should be comparene another.

7.1.6dvantages and Disadvantages

A careful worker can make gauge comparisons with an accuracy of about 2% over the range 104 to 103 Pa. Th







verlaps with that of the ionization gauge, so that the calibration factor for ionization gauges may be found. Thecessary investment, although significant, is not unreasonable. The SRG is inert; it does not alter or contaminas to be measured.

roper use of the SRG requires a suitable system, an expensive instrument, and trained personnel. The system mapable of pressures low enough to determine the residual drag. Determining a single pressure may require sev

minutes, during which the pressure must be stable. The SRG is unsuited for following changing pressures.

n situ comparison must be carefully evaluated in each case. Process systems would often contaminate or damaotor surface. The SRG is best suited for use in separate calibration systems.

.7.2Oscillating Quartz Crystal Viscosity Gauge

n 1959, Pacey [66] was the first to report vacuum measurements with an oscillating quartz crystal viscosity gased as the sensor a 200-KHz DT cut crystal operating in a face shear mode. It was driven by a triode circuit. Phowed calibrations for the gases argon, hydrogen, and air over the range 10 to 105 Pa. The pressure corresponiven output current differed by about a factor of 100 for the gases argon and hydrogen.

he oscillating quartz crystal gauge was revived about 1985 by the vacuum group at the Electrotechnical Labosukuba, Japan, and has been the subject of a number of papers. In one of their early papers, Ono, Hirata, Koku

Murakami of the Electrotechnical Laboratory, with Tamura, Hojo, Kawashima, and Kyogoku of Seiko Instrumublished results for an instrument based upon a miniature quartz crystal tuning fork as used in wristwatches [6esonant frequency was 32,768 Hz. The circuit drove the resonator at a constant ac voltage, and it measured thempedance of the crystal fork as a function of pressure. Calibration data extended from 7 × 101 to 1 × 106 Pa. Meading as a function of pressure was linear over this interval.

igure 6.21 reproduces a set of curves showing the output meter reading as a function of pressure for several gawhen the controller was direct reading for nitrogen. One of the disadvantages of the quartz oscillator gauge is tpproximately two-decade uncertainty in pressure when the gas is not known.

n another paper, Hirata et al. [68] explored quartz oscillators of differing sizes and operating modes and propostring of beads" model to analyze the results. Low-frequency tuning forks were best, and some showed pressuresponse from 102 to 105 Pa.

emperature sensitivity of the crystal oscillator was found to limit the lowest useful pressure for a practical gaua. The shift of resonant frequency of the quartz oscillator with temperature was then used to make a self-compensor useful to 0.01 Pa [69]. In a 1995 paper given at the Thirteenth International Vacuum Congress in Yokoh

Kobayashi et al. [70] proposed using the differing sensitivity of the oscillator gauge for different gases as a meanalysis. A quartz oscillator gauge based upon this research at the Electrotechnical Laboratory is manufactured

Vacuum Products Corp [71].

7.2.1

dvantages and Disadvantages

he sensor is very small, and it is inert. The effective measuring range is 101 to 105 Pa. The differing calibratioarious





Fig. 6.21Calibration of the quartz oscillator gauge in H2, He, N2, Ar, and Kr. The

plot shows indicated pressures when the instrument is calibrated for nitrogen.Reprinted with permission from M. Ono, M. Hirata, K. Kokubun, H. Murakami,F. Tamura, H. Hojo, H. Kawashima, and H. Kyogoku, J. Vac. Sci. Technol. A 3,

1746 (1985) [Ref. 67]. Copyright 1985 American Vacuum Society.

ases is a problem. Referring to Fig. 6.21, assume a gauge calibrated for nitrogen, but unknown to the operatorystem gas is hydrogen. At an indicated pressure 3 × 103 Pa, the actual pressure would be 105 Pa (one atmosphAttempting to back fill to an indicated pressure greater than 3 × 103 Pa would cause an overpressure condition

8hermal Conductivity Gauges

A hot wire in a gaseous environment loses heat (thermal energy) in three ways: (1) radiation, (2) conduction tond (3) transfer by the gas. Let the rates of energy loss beWR, WC , and WG, respectively. These energy transfer

mechanisms are illustrated in Fig. 6.22. LetWT be the sum of the rates of energy loss by these means, or

nergy transfer by the gas is pressure-dependent. It is this effect that is used to make a thermal-conductivity-baressure sensor. Ignoring the change ofWR and WC with pressure caused by the pressure dependence of theemperature distribution along the length of the wire,WR + WC , establishes a constant background loss. The magnnd stability of this background determine the lowest useful pressure of the gauge.

wo types of thermal conductivity gauge are in general use. In the Pirani gauge the temperature of the hot wireom its resistance. In the thermocouple gauge,





Fig. 6.22Energy loss mechanisms for a heated

wire in a gas at reduced pressure.

thermo-junction of dissimilar metals provides a temperature-dependent output voltage. Descriptions of both gwere first published in 1906. Manfred von Pirani was the first to describe the gauge based on wire resistance [7was followed in a few months by Voege's paper on the thermocouple gauge [73].

n the introduction to his paper, von Pirani explains why he undertook the development of a new gauge. It is wepeating, since his reasons are as valid today as in 1906. He was employed in the incandescent lamp factory o

nd Halske. He writes [74]: "I was assigned the task of developing a simple, inexpensive, vacuum measuring inwhich could replace the McLeod gauge. The project had not only the technical goal of making possible rapidecognition of small pressure changes at high vacuum, but it also had significant importance from the health sta

As is well known, there is an increasing effort to remove harmful mercury from the workplace."

Voege [73] was constructing thermocouple based ac measuring instruments when he noticed that the output vounction at a constant ac input was pressure dependent. Both the Pirani and thermocouple gauges are in widesperhaps there are more of them than any other vacuum gauge. Figure 6.23 illustrates a simple form of each of tauges.

.8.1heory

rom a fundamental standpoint, Pirani and thermocouple gauges differ only in the means of observing the wireemperature. The discussion of the three modes of energy transfer given below applies equally to both. Althougensor based upon a hot wire is assumed, it is clear that the reasoning could be extended to other geometries whensor element was in the form of a disc or a spherical bead. For simplicity, the equations are written for an ele

wire of lengthdl at positionl with temperatureTl . This makes it possible to examine the functional dependences eglecting the actual temperature distribution.





Fig. 6.23Construction of a Pirani gauge

(a) and thermocouple gauges (b).

o examine the loss by radiation, consider an incremental lengthdl of a long wire of diameterr 1, emissivityε1, andemperatureT 1 centrally located in a long cylinder of radiusr 2, emissivityε2, and temperatureT 2. AssumingT 1 > The rate of energy transfer by radiation,WR, is [75]

whereσ is the StefanBoltzmann constant 5.673 × 108 W·m2·K4. In the limiting case where Eq. (6.31ecomes

he emissivity of a clean bright metal surface such as platinum is about 0.05, while for a surface coated with sopproach unity. In designing a gauge it is desirable to choose a sensor wire with a low and stable emissivity. Lohermal conductivity and a large temperature coefficient of resistance are also important. Commonly used matenclude platinum, nickel, and tungsten.

Heat transfer by conduction from the wire to the cooler support is also shown in Fig. 6.22. Assuming the same t each end, the local rate of energy transfer by conduction along the wire, ½Wc(l ), for an elementdl at positionl is



whereG is the thermal conductivity of the material of the wire, anddTl/dl is the temperature gradient. Roberts [76erived an equation for the temperature distribution along an electrically heated wire in vacuum. The temperatuistribution





hanges somewhat with pressure as heat transfer by the gas becomes the dominant loss mechanisms. For manyn adequate model is a temperature distribution constant over the central region, with a linear decrease at the enaction of the heat loss due to conduction can be reduced by using a long wire of small diameter.

Heat transfer by gas molecules is simple to analyze for the case when the mean free path is greater thanr 2 r 1. Gasmolecules arriving at the hot wire will have a Maxwellian energy distribution corresponding toT 2. These moleculesually dwell on the surface for a short time and depart with an energy distribution corresponding toT 1. Anccommodation coefficient,α , is defined as the probability of this process.

Kennard's text [77] on the kinetic theory of gases has an equation for the heat transfer between coaxial cylinderase where the molecular mean free path is long. Specializing to the present case where his result be

n this equation,γ is the ratio of specific heats of the gas,Cp/Cv, m is the mass of a gas molecule in kilograms, andkhe Boltzmann constant, 1.38 × 1023 W·s·K1. The numerical value ofγ is dependent upon the number of degrees eedom of the molecule. The classical value ofγ for a point mass is 5/3, for a rigid dumbbell 7/5, and for a diatom

molecule with vibration 9/7. Values ofγ according to both classical theory and experiment are tabulated in Kenn78]. Substituting numerical values for the constants and letting M be the molecular weight gives the result

he region of linear behavior ofWG with P extends to about 10 Pa for nitrogen. At higher pressures, energeticmolecules departing from the wire collide with others before getting far from the wire, and they deposit their enorm a sheath of hot gas near the wire. This prevents further effective heat transfer until the onset of convection

.8.2alibration

igure 6.24 is a plot of data from the calibration of a constant temperature Pirani gauge with the gases He, N2, he plot extends to atmospheric pressure for the two heavier gases. The sensor wire was 150 mm of 0.0254-mmiameter platinum wire. A control circuit similar to that used in taking the data is shown in Fig. 6.25. The bridgoltage,V br, used as the pressure-dependent output signal plotted on the ordinate in Fig. 6.24. If R1 = R2 in the bridircuit of Fig. 6.25, the sensor resistance, Rs, is equal to Rc when the bridge is balanced. Rc is chosen to provide theesired operating temperature of the sensor wire using known temperature versus resistance data. One-half ofV br is

pplied to the sensor when R1 = R2. The total power supplied to the sensor wire is then This must equW

f Eq. (6.30).





Fig. 6.24Experimental calibration curves in helium, nitrogen, and argon for a

constant-temperature Pirani gauge.

Fig. 6.25Bridge amplifier for constant

temperature operation of a Pirani gauge.

As an example, the experimental sum ofWR and WC may be found for the data of Fig. 6.24. The bridge voltage i.3907 V as the pressure approaches zero. The value of Rc (and therefore Rs) was 43.61Ω. Then



he experimental values for the rate of energy transfer by the gas may be found by subtracting this backgroundower supplied to the sensor for each data point. The resulting values ofWG are plotted against pressure in Fig. 6.he plot is





Fig. 6.26Energy transported by the gas in a Pirani gauge. A plot ofWG versus

pressure for the nitrogen data of Fig. 6.24.

straight line until the long mean free path assumption fails above 10 Pa. The value ofWR + WC from Eq. (5.36) islotted on Fig. 6.26.

is interesting to calculate a point according to Eq. (6.35) and compare it to the experimental curve forWG plotted ig. 6.26. Assume the same gauge parameters, molecular weight of 28 for nitrogen, a wire temperature of 400 nvelope temperature of 300 K. Letα and ¼[(γ + 1)/(γ 1)] both be unity. Then, for P = 0.13 Pa the result isWG = 1.04 W, in good agreement with the experimental value of 1.3 × 104 W from Fig. 6.26. The fact that the backgrWC is almost an order of magnitude greater thanWG at this pressure will be used below in discussing the low

ressure limit.

.8.3

owest Useful Pressurehe radiation component of the background, given by Eq. (6.31), may not be stable. The emissivity may vary f

or a clean wire to unity when contaminated. Choice of wire material and temperature is important for stabilitymissivity. The stability of the background in actual use, and therefore the lower useful pressure limit, is largely

matter of experience. It is reasonable to use a lower pressure limit for the thermal conductivity gauge determineondition



or the gauge used in Fig. 6.26, which was optimized for low-pressure performance, it as found above that thisbout 0.1 Pa. The fact that the gas term can be





Table 6.3. Comparison of Accommodation Coefficients as Measured by Dickins [80] and byThomas and Olmer [81]Gas Dickens Thomas and Olmer H2 0.35 0.22He 0.51 0.24CO 0.91 0.75O2 0.90 0.74N2 0.90A 0.88 0.89CO2 0.92 0.76

ollowed below 103 Pa in the laboratory under ideal short-term conditions is of little practical value. Ellett and 79] decreased the importance of radiation in a Pirani by cooling the envelope to 90 K and using a moderate seemperature. Measurements to 105 Pa were possible. However, there is no inexpensive and energy efficient waresent time to cool a gauge for continuous operation.

he accommodation coefficient,α , in Eq. (6.35), is a function of the gas, the metal surface, contamination, and temperature. Table 6.3 compares experimental values ofα by Dickins [80] and Thomas and Olmer [81] for severaases on platinum at about 20°C.

.8.4onstant Temperature Pirani

he benefit of operating the sensor wire at constant temperature is an extended high pressure range. If, in makialibration similar to that of Fig. 6.24, the bridge voltage had been fixed at 0.3907 V, and the bridge-out-of balaoltage used as the signal, the resulting nitrogen curve would have negligible slope above 100 Pa. With constan possible to choose a wire temperature to optimize performance for a limited pressure range. Leck [82] invest

his for a Pirani, while Teledyne-Brown Hastings Engineering [83] offers a number of thermocouple gauge senach optimized for a different pressure range. With this approach the total useful range of each is between one ressure decades less than for a thermal conductivity gauge operated at a constant temperature.

efore electronic feedback control circuits became feasible, operating a Pirani sensor wire at constant temperatequired manual adjustment at each pressure. Von Ubisch [84] published the first feedback circuit for constantemperature operation in 1948. Today most commercial Pirani control circuits hold the wire at constant temperalthough many low-cost thermocouple gauge controllers continue to have constant voltage circuits. The constaemperature mode is possible with a thermocouple gauge, although it has been used less. Zettler and Sud [85] d

control circuit for a thermocuple gauge which programmed the junction temperature for better results in eachegion.

Another advantage of the constant temperature mode is the faster response to pressure transients. Since the wiremperature is constant within the error of the





eedback circuit, the response time is largely a function of the amplifier gain and any limitations on high-frequeesponse of the circuit that may be needed for high-frequency stability.

.8.5alibration Dependence Upon the Gas

quation (6.35) forW G has explicit M 1/2 dependence upon the molecular weight, andγ is also a function of themolecule. Thus the calibration of a thermal conductivity gauge is dependent upon the gas. The curves in Fig. 6ypical examples. The departure of the curves from one another is particularly serious at the higher pressures. Witrogen the output is insensitive to pressure change above 104 Pa. With argon, it would never reach an indicattmosphere, even with a large overpressure. With helium, the gauge would indicate a pressure greater than atmor any pressure above 300 Pa.

he differing sensitivity of the thermal conductivity gauge to various gases can be used to make a simple leak dlears and Leck [86] analyzed the Pirani leak detector in terms of the minimum detectable pressure change.teckelmacher and Tinsley [87] reported the construction of a "sniffer" Pirani leak detector which gave one-tenfull-scale deflection) on the most sensitive range with hydrogen search gas and a leak rate of 5 × 104 std cm3/harma and Gupta [88], Minter [89], and Aleksandrovich, Sokovishin, and Sazanov [90] also published variati

he Pirani leak detector.oday, commercial Pirani controllers often incorporate leak detector circuits that provide a large leak signal whressure change is too small to see. Depending upon the pumping system, leaks as small as 106 std cm3/s may etectable.

.8.6Upper Pressure Limit

At higher pressures where the mean free path becomes comparable to the diameter of the hot wire, molecules dom the wire lose their thermal energy within a few wire diameters. This forms a hot sheath of gas that inhibitseat transport. There are at least two means of increasing high pressure gas heat transfer described in the literat

move the wire or (2) allow convection to move the gas. The moving wire technique was described by Birshert xperimental curve shows good sensitivity extending to one atmosphere without the inflection near 104 Pa comonvection gauges.

he inside diameter of the envelope of the Pirani sensor used in recording the data plotted in Fig. 6.24 was intemall (9.7 mm) to inhibit convection. When convection is encouraged by making the tube diameter larger and mhorizontally, a calibration as in Fig. 6.27 results. With nitrogen, convection starts near a pressure of 5 × 104 P

ohnson [92] was the first to use convection to extend the range of an experimental thermocouple gauge. The lhange of output with position caused him to suggest possible application of the gauge as an inclinometer. McMnd Buch [93] described a convection-enhanced Pirani gauge the following year. These papers were ignored foears before commercial convection enhanced Piranis appeared.

ust as with a normal Pirani, the calibrations of a convection enhanced Pirani for gases of differing molecular w

iffer widely at higher pressures. It is important





Fig. 6.27Calibration of a convection enhanced Pirani gauge with nitrogen.

hat the gas be known if a convection gauge is to be used at higher pressures. This is discussed in Section 6.8.1he reader interested in the theory of heat transfer by convection is referred to texts on heat transfer, such as th

Kreith [94] or Eckert [95].

.8.7Ambient Temperature Compensation

quation (6.35) forWG contains explicit dependence upon the envelope temperature,T 2, of the form

. The accommodation coefficient and the ratio of specific heats are also temperature-dependhus stable operation of a thermal conductivity gauge requires either temperature control or temperature comp

wo types of temperature compensation are used for Pirani gauges. An early method, found in Pirani's original72], uses an identical sealed-off gauge, or temperature-sensitive coil of wire, as Rc. The intent is to keep the differemperature (T 1 T 2) constant. In 1952, von Dardel [96] published a complete circuit for a controller using aompensating coil wound on the outside of the sensor tube. With proper choice of compensating coil wire and ood compensation is possible over the normal ambient range.

n the other approach [97], all component values within the bridge remain fixed. A network of resistors containhermistor in contact with the gauge envelope is used as a variable gain voltage divider operating on the bridgeoltage. The design of the network requires temperature behavior data for the gauge and the thermistor. The resompensation is effective for the ambient temperature range of 1050°C.







.8.8omparison of Pirani and Thermocouple Gauges

More depends upon whether a particular gauge operates in the constant temperature or constant input mode thahe way the wire temperature is measured. However, one fundamental difference is the sensor output signal levutput of a thermocouple gauge is a few millivolts, while the bridge voltage output signal of a Pirani with feedbeveral volts. Noise immunity near sources of electrical noise, as well as compatibility with long leads, may difecause of this. The bridge can be located in the head assembly of a Pirani; and by using potential leads, the voeaching the controller can be made independent of cable length. Pirani gauges have operated well with 150-mhe Pirani systems are usually more expensive, better corrected for ambient temperature, and more accurate th

hermocouple based systems.

eak detector capability is a feature included in some Pirani controllers.

.8.9tability

Only limited information exists in the literature about the accuracy or repeatability of measurements made withonductivity gauges. This may be because the usual applications in monitoring fore and roughing pressures do equire high accuracy. Poulter, Rodgers, and Ashcroft [98] undertook a six month's evaluation of several gaugeom one manufacturer. The maximum change in the mean nitrogen calibrations did not exceed 1.6% for any ghey concluded that pressure measurements made with thermal conductivity gauges should have a total uncertxceeding ± 4.4%. Jitschin and Ruschitzka [99] found accuracy to be a function of the pressure, and they attrib

much of the drift at low pressure to change of emissivity. The power loss at zero pressure drifted several percenew months.

.8.10hermistor Pirani Gauges and Integrated Transducers

he preceding discussion has assumed sensors using metallic wires. The large temperature coefficient of thermmade with semiconducting materials suggests their use in place of wire. Becker, Green, and Pearson [100] wero build and test a gauge using a thermistor. Used in a bridge, with the out of balance voltage as the output, theyhe output to be a nearly linear function of pressure from 102 to 100 Pa. Varicak * and Saftic* [101] mountedhermistors on discs of tin foil 30 mm in diameter by 0.01 mm thick to obtain a large surface with low emissivihey supported the discs on 0.05-mm manganin wire. Their circuit covered 104 to 100 Pa in three ranges.

hioyama et al. [102] made a Pirani using semiconducting thin films of TaN. They were able to calibrate their om 102 Pa to atmosphere.

hese papers using high-temperature-coefficient sensors appear to describe gauges with improved low pressureapability as compared to those using metallic wires. However, gauges using thermistors are seldom found inommercial instruments designed since 1975.

ntegrated silicon microtransducers are available and will increasingly compete with the hot wire types in the fusashi [103] of Tohoku University wrote a review paper describing silicon micromachining of integrated pressuansducers.





eledyne-Brown Hastings Engineering [104] manufactures an instrument using a microelectronic sensor. The sange is 103 to 105 Pa. Van Herwaarden and Sarro [105] reported a silicon integrated thermal sensor 6 × 6 mmood sensitivity from 0.1 to 100 Pa. Weng and Shie [106] using a transducer with a largest dimension of only am were able to measure from 102 to 8 × 102 Pa in the constant temperature mode.

.8.11ommercial Gauges and Applications

he above discussion covers most of the properties of these gauges that determine whether an application is apHowever, there is another important characteristic of the thermal conductivity gauge. Their output is a single-vaunction of pressure over the range from high vacuum to atmosphere. This fact, combined with a response time

milliseconds, makes them ideally suited for protective functions, as in determining when hot-cathode ionizationhould be activated. Their range makes them the usual choice for measuring backing and roughing pressures. Bheir calibration is highly gas-dependent, they are not well suited for most backfilling applications. They are noecommended for use in contaminating environments because of their sensitivity to surface conditions.

ontroller/gauge systems are available from numerous manufacturers. Figure 6.28 illustrates a controller with ro 104 Pa, leak detector capability, LCD display, and RS232 digital output option [97]. ''Transducer" units com

ensor and a simple controller as part of the head are popular. The user need only supply them with low-voltagbtain a logarithmic dc output signal.

A hazard can arise when using a thermal conductivity gauge because of the multidecade difference in calibratioifferent gases at higher pressures. Consider

Fig. 6.28Photograph of HPS Series 315 Pirani gauge controller

and gauge head. Photograph courtesy of MKSInstruments, Inc. HPS Division, 5330 Sterling

Drive, Boulder, Colorado, 80301.







gauge calibrated for nitrogen. Then, according to Fig. 6.24, the gauge would indicate an atmosphere at an actressure of 300 Pa when used in helium or other light gas. With a heavy gas such as argon, the gauge will not iressure greater than a few hundred pascals, even for several atmospheres overpressure. The first situation can mplosion, whereas the second one can lead to explosion. Peacock [5] discusses an accident of each type. To avccidents, the following precautions are recommended:

. Include an inexpensive gauge that is not gas-dependent, such as a Bourdon gauge, in applications where a lameasurement error would be hazardous.

. Provide overpressure protection by a relief valve or burst disc on any system connected to a source of pressu

. If the principal use of a gauge is to be at pressures greater than 100 Pa, it is advisable to use a gauge whose ognal is not gas-dependent.

hermal conductivity gauges using platinum or platinum alloy wires should not be used with gases capable of fxplosive mixtures with air. Fine wires of these metals heat autocatalytically in explosive gas mixtures and mayhem. It is not necessary that the gauge be turned on. Any gauge made with any wire could initiate an explosionircuit failed and overheated the sensor wire.

9onization Gauges

Virtually every high-vacuum system uses some form of ionization gauge for pressure measurement below 102 a. Below 104 Pa there are no realistic alternates. Ionization gauges are used to the lowest attainable pressures 012 Pa.

Although Buckley [107] has long been credited with the invention of the hot cathode ionization gauge (HCG), 108] has pointed out the prior work of von Baeyer [109]. Until 1950, HCGs were of normal triode design. Ma

were simply standard triode vacuum tubes with a tubulation. A major improvement took place in 1950 when BAlpert [110] revealed a new electrode configuration allowing pressures measurements two to three decades lowwere possible with the old standard triode geometry.

Another frequently encountered ionization gauge is the crossed field magnetic discharge gauge, which was invenning [111]. It is often called the coldcathode gauge (CCG). The electron trapping was improved by Beck anrisbane [112] using a central wire anode, a concentric cylindrical cathode, and an axial magnetic field. This isn "inverted magnetron" arrangement. Hobson and Redhead [113] developed it into a practical gauge usable fro 1010 Pa. It has come to occupy an important position among ionization gauges because of its relative freedoutgassing, its ruggedness, and wide range. Cold cathode ion gauges are discussed in Section 6.9.9.

.9.1Hot-Cathode Gauge Equation

igure 6.29 represents a generalized ionization gauge. Ionizing particles (arrows) arrive from the left. They arelectrons from a thermionic source with an





Fig. 6.29Generalized ionization gauge.

nergy of 100180 eV. However,α or β particles from nuclear decay have been used, and laser excitation is a suburrent research. The electrons enter the ionizing space containing gas molecules (circles) at reduced pressure. ollisions of the electrons with gas molecules produce ion/electron pairs (shown as circles with + or ). Ions are y the suitably biased lower electrode. The electrometer in the external circuit measures the ion current as an in

measure of gas pressure. Figure 7.2, page 450, is a plot of ionization probability versus electron energy for seve

he number of ions formed, and therefore the current in the circuit, is a function of the number of gas moleculenit volume, the ionization cross section energy, arrival rate, and path length of the electrons.

he ionization gauge equation provides the relationship of these quantities to one another. To derive it, letσi be theotal ionization cross section for a gas molecule, L the length of the ionizing space, and A the cross-sectional area olectron beam. The number of molecules in this volume isnLA, where the number density,n, is related to the gasressure byn = P/kT . The projected area, Aσ , of the gas molecules within this volume isnLAσ i = σ iLAP/kT . Theaction of the incoming electrons which participate in ionizing collisions will be Aσ /A. Let N be the number oflectrons arriving per unit time, each of chargeq. The number of ionizing collisions per unit time isσiLP/kTN . Or,onverting to current, the ion current,i+, is

he incident electron current is Nq = i, and σiL/kT can be defined as the gauge constant, K . Then Eq. (6.38) becomesual ionization gauge equation





is preferable to use the term "gauge constant" or "gauge coefficient" for K . Then "sensitivity" (symbolized byS ) cae reserved for the product K ·i, which is also an important parameter of an ionization gauge.

is known from experiments that the collector current,ic, as measured by the electrometer is the sum ofi+ from Eq6.38) and a residual current,ir , which may have contributions from different sources. A more general gauge equhen

he gauge constant, K , as defined above, is a function of the gas, the geometry of the gauge, the electron energyhe absolute temperature of the gas. These dependencies are inherent in ionization gauge measurements.

Until 1950 the ionization gauge was similar to the triode vacuum tube with its thermionic electron source, fine urrounding the cathode, and outside that an electrode of sheet metal (anode or plate in vacuum tube terminoloood description of a 1930 triode gauge was given by Jaycox and Weinhart [114]. Examination of their data suhat they reached pressures at least a decade lower than their triode gauge could measure, or about 107 Pa.

A schematic circuit for use with a HCG is illustrated in Fig. 6.30. It is drawn with a triode gauge. A grid voltagV, and cathode bias of 30 V are typical. The effective energy of electrons in the ionization space will range betwero and 150 V. The electrons have enough energy for ionization over a portion of their path in the space betwend ion collector.

n the late 1930s it was general knowledge that the triode gauge never indicated a pressure lower than about 10his was hard to understand since vacuum techniques had improved a great deal, and surface contamination timxtended to hours or even days. Anderson [115], in his studies of contact potentials, had good evidence that theressures were much lower. Apparently the collector current consisted of a pressure-dependent ion current andesidual current as anticipated in Eq. (6.40). In 1938, Bell, Davies, and Gossling [116] correctly recognized tha

Fig. 6.30Basic circuit for operating a hot-cathode

ionization gauge.





urrent in vacuum tubes was caused by soft x-rays. Perhaps because of World War II, their paper went unnoticeeventh Physical Electronics Conference at the Massachusetts Institute of Technology in 1947, Nottingham [11uggested independently that the residual current is the result of a two-step process: (1) Electrons striking the groduce soft x-rays, and (2) these x-ray photons then cause the emission of photoelectrons from the surroundinollector. To the electrometer this current is indistinguishable from an ion current. This was discussed again at t

meeting. In the summer of 1948, D. Alpert of Westinghouse Research Laboratories, who had attended theseonferences, asked Robert Bayard to investigate the validity of the x-ray hypothesis [118]. The immediate resunvention of the BayardAlpert gauge (BAG), illustrated in Fig. 6.31, an ingeniously simple solution to the prob

Whereas in the triode gauge the ion collector was a metal cylinder surrounding the grid and cathode, in the BArid was cylindrical, the cathode was external to the grid, and the ion collector was a fine wire centered in the g

Operating voltages were similar to those of the triode gauge. The cross section for interception of the x-rays waeduced 1001000 times. The x-ray limit (the pressure where the x-ray current equals the ion current) decreased× 109 Pa. Bayard and Alpert [110] compared the x-ray limits of the new gauge and the old



Fig. 6.31BayardAlpert ionization

gauge. The figure shows agauge as made at the

Westinghouse ResearchLaboratories in the early

1950s. The grid ismolybdenum and is intended

for electron bombardmentdegassing. Reprinted with

permission from D. Alpert, in Handbuch der Physik(S. Flügge, ed.), Vol. 12, p. 609.Springer-Verlag, Berlin, 1957

[Ref. 125]. Copyright1957 Springer-Verlag.





iode using plots of collector current versus grid voltage made at pressures as low as the 109 Pa decade.

A production BAG was sold by Westinghouse as the WL 5966. It had a Nonex glass envelope, and a molybdenntended for electron bombardment degassing. The grid was 19 mm in diameter by 38 mm long. There were twungsten filaments. The ion collector was made of 0.13-mm tungsten wire. The gauge constant of the Alpert BAbout 0.09/Pa for nitrogen, and the x-ray limit was about 6 × 109 Pa. Its simplicity made it easy to degas andnexpensive to manufacture. Figure 6.32 shows a nude BAG for use in metal systems.

A period of rapid exploration of variations of the BAG followed, although it was difficult to improve upon the However, it will be helpful to discuss two additional contributions to the residual current before beginning the

AG modifications and other new gauges. BAG users noted that the residual current changed with the presencebsorbed active gases on the grid. It was the custom in Alpert's laboratory in the mid-1950s to operate BAGs atmission current to keep the grid clean. When the grid current of a gauge operating at a pressure below 1010 wwitched from 10 to 1 mA the initial pressure reading was the same, but

Fig. 6.32 Nude BayardAlpert gauge, for use in metal systems.







Fig. 6.33Section through a BayardAlpert gauge illustrating the origin of the

"normal" and the "reverse" x-ray effects. Reprinted with permission fromW. H. Hayward, R. L. Jepsen, and P. A. Redhead, in10th Natl. Vac.

Symp. 228 (1963) [Ref. 123]. Copyright 1963 American Vacuum Society.

slow upward drift started, eventually stopping at a new value. Moore [119] investigated the ion emission fromurfaces of Mo and W covered with adsorbed CO and bombarded by electrons. The ion yield from the surface 0100 times that from the volume. This surface ionization process is often calledelectron-stimulated desorption (ES

Ackley, Lathrop, and Wheeler [120], examining the effects of different grid currents on the collector current, prhat an ESD ion current as found by Moore was one possible explanation of their results. Redhead [121], using

modulated BAG, then showed that ESD ions can make a large contribution to the residual current. With a cleanesidual current was 6 × 1012 A. However, adsorption of a monolayer of oxygen caused the residual current toy 400 times. He also noted that the modulated BAG measured true pressure in the presence of absorbed layers

Huber and Rettinghaus [122] analyzed ESD ions using a quadrupole analyzer, and they gave ion yields for sevdsorbed gases from Pt, PtIr, and Mo surfaces. It was proposed that Pt was a desirable construction material foronization gauges.

Another component of the residual current was explained by Hayward, Jepsen, and Redhead [123]. It is called verse x-ray effect . Both the normal and reverse x-ray effects are shown in Fig. 6.33. X-ray photons striking th

wall of the gauge can free electrons. Since both wall and collector may be at ground potential, some of these m

he collector, causing a current of sign opposite to the normal x-ray current. Thus the name reverse x-ray effect..9.2

Geometric Variations in the BayardAlpert Gauge

n conceiving new gauges intended to function at lower pressures, it is necessary to improve the ratio ofi+ to ir . Eithncreasing the gauge constant K or decreasingir is





elpful. The original Westinghouse BAG had a grid in the form of an open cylinder. Electrons orbiting the collaving an axial velocity component could escape through the open ends. Nottingham [124] found that the gaugonstant could be increased by about a factor of two by adding grid structures to close the ends of the grid. He shield grid enclosing the other electrodes to prevent charges on the glass walls from influencing the electronajectories.

Alpert had tried earlier to reduce the x-ray current with smaller ion collectors made by electrochemically etchinollector wires to a taper [125]. However, the grid ends were open in his experimental gauges. The smaller collombined with the open grid decreased the probability of ion capture. The x-ray current and the ion current botecreased, so there was little improvement in the x-ray limit.

At Philips Laboratories, van Oostrom [126] made BAGs with closed grid ends and collectors as small as 4 µm.auge constant with the 4-µm collector, although reduced, was 0.03/Pa for nitrogen, and the x-ray limit was este 2.1 × 109 Pa. However, with this small collector the grid and collector biases had to be considerably higher sual.

A longer ionizing path length and larger K would be expected with increased grid diameter. It is less evident that lament to grid separation is very important in determining the gauge constant. Redhead [127] and Pittaway [1

xamined electron path length within the grid as a function of launch angle. Near-diametric entry gives deeperenetration and longer paths. The divergence of entering electrons can be decreased with greater filament to grpacing. However, the separation cannot be greater than a few millimeters because the cathode must be emissiomited with moderate cathode-to-grid potential differences. Redhead found that an auxiliary electrode behind tathode served the same purpose and increased the gauge constant. One interesting item in Pittaway's paper is halculation of the number of passes of an electron through the grid as a function of grid transparency. For 90%ansparency, an electron will average four passes.

Ohsako [129] also designed a BAG using an auxiliary electrode behind the cathode at ground potential. His puo extend the linear range to higher pressures. With a small grid of 12-mm diameter, an emission current of 1 ×ave good linearity to 27 Pa for nitrogen or argon, while retaining a sensitivity of 0.03/Pa.

omsa [130, 131], through the calculations and experiments in these and other papers, contributed to a betternderstanding of the factors influencing ion collection efficiency in the BAG. In the 1972 paper he calculated tollection efficiency as a function of collector diameter. The fall-off is extremely rapid as the collector diameteecreases to 0.1 mm.

A large body of literature exists on BAGs with collector wires just entering, or perhaps not quite entering, the ghese are often called "buried collector" gauges. The intent is to reduce the cross section of the collector to x-r

while maintaining ion collection efficiency. The success in achieving these aims varies. Groszkowski's 1966 pa132] is one of many that he published on this subject. He was able to maintain K = 0.15/Pa for nitrogen with the "xmit an order of magnitude lower than for a BAG". Melfi [133] describes similar results, and Beitel and Gosseescribe somewhat better results. Fletcher [135] found a lower-gauge constant of 0.075/Pa for argon with a resiurrent of 2 × 1012 A. Watanabe [136] described a "point collector gauge" shown in Fig. 6.34 that belongs in ty its design. It used a spherical grid 26 mm in diameter, and the collector was 0.03 mm in diameter by





Fig. 6.34Watanabe point collector gauge. The operating potentials are: filament, +200 V; grid, +310 V;

shield, +200 V; modulator, +310 V, 0 V. Reprintedwith permission from F. Watanabe, J. Vac.Sci. Technol. A 5, 242 (1987) [Ref. 136].


nly 0.05 mm long. The gauge constant was 0.4/Pa, and the calculated x-ray limit was 2 × 1012 Pa. This gaugeifficult to fabricate because of the precision required.

.9.3Modulated BayardAlpert Gauge

Redhead [137] was the first to use modulation to overcome the residual current problem. It can be used with mHCGs, but it is especially associated with the BAG. It requires only a very simple modification of a BAG: the if a wire probe, similar to the collector, within the grid space. The use of modulation to determine the residual nd true ion current is explained in Section 11.7. When using a modulated BAG, the ion current is not masked urrent. In this paper, Redhead describes switching the potential of the modulator electrode between grid and g

otentials. This is known as Mode 1 modulation. Lange and Singleton [138] describe problems encountered wi, including modulation ofir . An assumption of the modulation method is that the x-ray photocurrent is not chanltering the modulator potential. The authors reported better results switching the modulator potential from gridalue corresponding to maximum ion current collection, or about 20 V below grid potential (Mode 2). Lange aingleton state that Mode 2 operation was possible only with open grid ends. Redhead [139] defines five mode

modulation.

erhaps the highest development of the modulated BAG is that of Benvenuti and Hauer [140]. Several hundredauges were installed at CERN, Geneva to monitor XHV pressures in the ISR (intersecting storage rings). This

manufactured by Thompson/CSF, had a grid volume that was larger than usual: 35 mm diameter × 40 mm long0-µm collector,ir was 4 × 1013 A, the gauge







onstant was 0.32/Pa, and x-ray limit was 1.3 × 1010 Pa. This paper also reports measurement of the backgrouvaporation of the tungsten filament, as well as selection of operating parameters.

.9.4xtractor Gauge

he extractor gauge by Redhead [141] is shown in Fig. 6.35. It is probably the most widely used XHV gauge. Ionstruction is relatively simple, which facilitates degassing. The extractor gauge discriminates against ESD ioons leave the grid with about 6 eV energy, while gas phase ions originate within the grid in a region here the p depressed by the electron space charge. ESD ions are unlikely to reach the ion collector. Because of the locat

he ion collector the x-ray effect is inherently small, but the extractor gauge can also be modulated. Redhead reauge constant of 0.1/Pa for nitrogen, with the gauge useful to 7 × 1011 Pa. The commercial extractor gauge T11 from Leybold Inficon, Inc. [142] has a gauge constant [143] of 0.067/Pa for nitrogen and an x-ray limit bela equivalent. There are many papers concerning variations of the extractor gauge. One interesting one is that noue, and Kanematsu [144].



Fig. 6.35Extractor gauge. The operating potentials are:

filament, +200 V; grid, +305 V; ion collector, 0 V;modulator, +305 V, 0 V. Reprinted with permission

from P. A. Redhead, J. Vac. Sci. Technol . 3, 173(1966) [Ref. 141]. Copyright 1966 American

Vacuum Society.





.9.5Helmer Gauge

he gauge described by Helmer and Hayward [145] and illustrated in Fig. 6.36 was manufactured by Varian, aery few were made. It is important both because of its use as an XHV reference gauge and because it has beenasis of other XHV gauges with good characteristics. There is the possibility that an energy analyzer gauge macommonly used UHV/XHV reference gauge in the future.

n the Helmer gauge the ions are extracted from the end of a cylindrical grid and introduced into a 90° electrosnergy analyzer. Since, as stated above, the energy of ESD ions differs from that of gas phase ions, the analyzerovides a means of distinguishing them. The energy resolution of the original Helmer gauge is limited, and fueparation of gas phase and ESD ions is not possible. Helmer and Hayward gave the gauge constant as 0.13/Pamission 6 mA, and the residual current 1.5 × 1014 A without suppressor and 1.5 × 1015 A with it. This corresn x-ray limit of 2 × 1011 Pa.

Han et al. [146] also studied the performance of the standard Varian Helmer gauge. They found a smaller gaugonstant of 0.067/Pa for argon and found an x-ray limit of 2 ± 2 × 1011 Pa nitrogen equivalent. This is reasonagreement since the gauge constant of a Helmer gauge will depend upon the entrance and exit apertures of the

nalyzer.envenuti and Hauer [147] made some modifications to a Varian Helmer gauge and were able to reduceir to 1012 Pquivalent. They found it a valuable reference gauge in the XHV region.

Watanabe [148] has published results for an improved ion energy analyzer gauge. Using a spherical grid andemispherical energy analyzer, he obtained good separation of gas phase and ESD ions. The sensitivity with

molybdenum grid was

Fig. 6.36Helmer ion energy analyzing gauge. The operating potentials areshown in the figure. Reprinted with permission from J. C. Helmerand W. D. Hayward, Rev. Sci. Instrum . 37, 1652 (1966) [Ref. 145].

Copyright 1966 American Institute of Physics.







Fig. 6.37Ion spectrum made with the Otuka and Oshima ion

energy analyzing gauge. The gas phase and ESDion peaks are resolved. Reprinted with permissionfrom C. Oshima and A. Otuka, J. Vac. Sci. Technol.

A 12, 3233 (1994) [Ref. 150]. Copyright 1994American Vacuum Society.

.5 × 104 A/Pa for nitrogen at 5 mA emission, giving a gauge constant of 0.09/Pa. The lowest useful pressure ws 1010 Pa.

Otuka and Oshima [149] investigated a variation of the ion energy analyzer gauge, also with good results. OshiOtuka [150] gave the limit of their gauge as 4 × 1013 Pa and reported the gauge constant 0.018/Pa for hydroge.37 illustrates its energy resolution.

.9.6ong Electron Path Length Gauges

ncreasing the ionizing electron path length at a given emission current has the effect of improving the ratioic/ir . Wihe magnetron geometry shown in Fig. 6.38 Lafferty [151, 152] was able to measure pressures to 1011 Pa. To pnstabilities and space charge effects it was necessary to use small emission currents in the range 109 to 106 A.nformation from Fig. 7 of Lafferty [152], for 107 A emission in a field of 0.025 T, the sensitivity was 5.3 × 10nd the gauge constant was 5.3 × 103/Pa. The test gas was air [153]. An example of a recent related gauge is thmission magnetron suppressor gauge of Chen, Suen, and Kuo [154]. With an emission current of 1 × 106 A, a.03 T, and pressure of 1.3 × 106 Pa they obtained a sensitivity of 6.75 × 104 A/Pa, and a gauge constant of 6.7a. The x-ray limit was estimated to be 6 × 1013 Pa, although the gauge was not tested below 1010 Pa.







Fig. 6.38Lafferty magnetron gauge. The operating

potentials are: filament, 0 V; ion collector,45 V; shield, 10 V; anode, +300 V,magnetic field, 0.025 T. Reprinted

with permission from J. M. Lafferty, J. Appl. Phys . 32, 424 (1961) [Ref. 151]. Copyright

1961 American Institute of Physics.

he Orbitron gauge of Mourad, Pauly, and Herb [155, 156] uses the electrostatic field created by a wire anode xis of a cylindrical cathode to trap electrons, giving very long electron path lengths. At a pressure of 1 × 107 Pitrogen, a sensitivity of 5.3 × 105 A/Pa was found, giving a gauge constant of 5.3 × 102/Pa. This is a rather lo

ensitivity: The sensitivity of a typical BAG is 1 × 104 A/Pa. The stability of the Orbitron is poor. Slight changlectron injection conditions, caused, for example, by warping of the filament, cause large changes in sensitivit

.9.7econdary Standard Hot-Cathode Gauges

Although the stability of the BAG (discussed later in this chapter) is good, special gauges with precise geometrwell-defined electron paths can be better (see Section 12.3.3). The need for a transfer standard ionization gaugeecreased as spinning rotor gauges have come into general use. Hirata et al. [157] of the Electrotechnical Laboapan described a normal triode gauge, Type VS-1, used as a standard. The standard deviation of the gauge con58 VS-1 gauges was ± 6.5%



Gentsch, Tewes, and Messer [158], in association with the Physikalisch-Technische Bundesanstalt in Berlin (PTuilt and tested a gauge for use as a standard.





Many features were incorporated for stability: well-defined electron paths; gold coatings for constant surface pnd a shielded ionizing volume. The x-ray limit was 2 × 107 Pa hydrogen equivalent.

.9.8High-Pressure Ionization Gauges

he high-pressure limit of BAGs is often thought to be 102 Pa. In fact, for tungsten cathodes in active gases, 10xcessive. But B-A gauges with suitable cathodes can be used to 1 Pa. Special high-pressure gauges can be use

more than 100 Pa. Although there are other gauges better suited for accurate work at high pressures, sometimesonization gauge is convenient. There is a paper by Wang [159] on the theory of the high-pressure ionization ga

chulz [160] tested the performance of standard WL 5966 BAGs from 103 to 101 Pa in argon, helium, neon, hitrogen, and SF6. He found that linearity extended to 5 × 101 Pa with electron emission currents of 104 A or lsing argon gas. The high-pressure linearity of wide-range gauges was the concern of Ohsako [129], who foun

was improved by an electrode behind the cathode. Peacock and Peacock [161] were interested in the overlap ofanges of the SRG and typical BAGs. Operation above 103 Pa required reduced emission current. Peacock andlso found the high-pressure linearity to be poorer when grid end closures were used.

Another approach to high-pressure operation of a standard BAG is given in a patent by Paitich and Briglia [162atent describes a method of measuring up to 100 Pa with a BAG by modulating the grid voltage. Controllers bpon this concept are manufactured by Terranova Scientific, Inc. [163]. Gauges with very small electrode struc

would be preferable for use at pressures above 0.1 Pa. In a later paper, Schulz and Phelps [164] described two sigh-pressure ionization gauges with small dimensions. The one that was more linear at high pressure was the pype, shown in Fig. 6.39. The electron and ion collector were parallel plates 12.8 × 9.5 mm spaced 3.2 mm, andlament was 0.13-mm-diameter wire × 12.8 mm long spaced midway between the plates. The linearity extendeetween 13 and 130 Pa depending upon the gas. This gauge was manufactured for many years as the WL 7903

igure 6.40 illustrates the JHP (jauge haut pression), or Choumoff gauge, which was intended primarily as a hiressure secondary or transfer standard. Electrons pass through a box containing two ion collector rings. The lehe box was about 6 mm. Poulter et al. [165] gave the results from the circulation of several of these gauges amhree European national standards laboratories. The stability found during these comparisons was good. The gaonstants found for gauge No. 20 by the three laboratories were 0.0212/Pa, 0.01987/Pa, and 0.0202/Pa. In 1989eacock [166] compared gauge No. 20 to a spinning rotor gauge. The gauge constant after 10 years in storage wound to be 0.019/Pa. The JHP appears to be one of the more successful high-pressure ionization gauges, but itvailable commercially.

here are many more high-pressure ionization gauge papers in the literature. Kudzia and Stôwko [167] used a mall, spherical, ionization volume. This gauge was linear to 103 Pa. Edelmann [168] investigated a SchulzPheauge. Y. H. Kuo [169] described a high-pressure ionization gauge of simple construction. The linearity





Fig. 6.39SchulzPhelps gauge type WL 7903.

The operating potentials are: filament, +60 V;anode, +120 V; ion collector, 0 V. Reprintedwith permission from G. J. Schulz and A. V.Phelps, Rev. Sci. Instrum . 28, 1051 (1957)

[Ref. 164]. Copyright 1957 AmericanInstitute of Physics.

was excellent up to 133 Pa. Depending upon the mode of operation, the gauge constant ranged from 1.1 × 103 03.

.9.9old-Cathode Gauges

n the HCG the ionizing electrons are supplied by a thermionic cathode. In the CCG they are part of a self-sustas discharge. Several differences result. The emission current in the HCG can be adjusted by control of the caemperature. It is not changeable in a CCG. Since the emission current is held fixed in the HCG, the x-ray curreonstant, determining the lowest measurable pressure. Although there is always a dense space charge in the CCnode current, and therefore x-ray production, decreases with pressure. There is no background current to maskurrent. The total power into filament and grid of a HCG may exceed 30 W, independent of pressure, and the reeat is a cause of outgassing within the gauge. The power into a CCG is only about 0.1 W at high pressure andecreases with pressure.



he CCG was invented by Penning [111]. Figure 6.41 illustrates the electrode and magnetic field arrangement auge of Penning type. From 1937 until about 1960, gauges like this were the only CCGs available. They wererimarily in





Fig. 6.40Choumoff gauge. The operating

potentials are: filament reflector, 0 V;filament, +50 V; anode box, +150 V;

electron collector, +350 V; ion collector,0 V. Reprinted with permission from

K. F. Poulter, A. Calcatelli, P. S.Choumoff, B. Iapteff, G. Messer, and

G. Grosse, J. Vac. Sci. Technol .17, 679 (1980) [Ref. 165].

pplications where the pressure was not below 104 Pa and where cost was more important than accuracy. Thesrovided only crude pressure measurement.

he curves given by Conn and Daglish [170] are an excellent illustration of the discontinuities which can occuressure versus current curve of a Penning gauge. These authors found sudden shifts between 101 and 102 Pa a0% of reading. The other problem with commercial gauges of original Penning design was that the discharge xtinguished at pressures below 103 or 104 Pa, and the gauge then gave no reading. The triggered discharge ga

Young and Hession [171] shown in Fig. 6.42 was of Penning design. It contained a filament used momentarily rovide initial electrons to start the discharge. Lange, Singleton, and Eriksen [172] calibrated a gauge of the typescribed by Young and Hession. To examine the detailed structure of the pressure versus current curve, they ualving system providing a linear rate of pressure rise combined with a strip chart recorder for current. Their reeproduced as Fig. 6.43, consisted of a series of line segments separated by abrupt changes. The average slope itrogen was 1.19.



eck and Brisbane [112] published one of the early papers describing a CCG with cylindrical geometry. Their ad an axial wire surrounded by a coaxial cylinder, along with a magnetic field in the axial direction. After tryi

wire as the negative electrode, they ''soon found experimentally that the current was much increased when





Fig. 6.41Electrode arrangement, fields, and trajectories

in the Penning gauge.



Fig. 6.42The Young and Hession triggered

discharge gauge. Reprintedwith permission from J. R. Youngand F. P. Hession, inTrans. Nat.Vac. Symp . 10, 234 (1963) [Ref.171]. Copyright 1963 American

Vacuum Society.

he wire was made the anode." This arrangement, commonly known as theinverted magnetron , has been the key tobtaining good results with the CCG gauge. Their plots of gauge current versus pressure follow a straight line fo 106 Pa. The acceptance of the inverted magnetron owes a great deal to P. A. Redhead and colleagues at the N

Research Council of Canada in Ottawa. In 1958, Hobson and Redhead [113] described an inverted magnetron ketched in Fig. 6.44,





Fig. 6.43Calibration of a Young and Hession triggered dischargegauge by Lange, Singleton, and Eriksen showing breaksin the gauge current versus pressure curve. Reprintedwith permission from W. J. Lange, J. H. Singleton, and

D. P. Eriksen, J. Vac. Sci. Technol . 3, 338 (1966) [Ref. 172].Copyright 1966 American Vacuum Society.

esigned for UHV with features such as guard rings to prevent measurement of field emission currents. They vwell-behaved operation of the gauge from 101 to 1010 Pa. The slope of their current versus pressure plot was 1

eacock and Peacock [173] studied the inverted magnetron shown in Fig. 6.45. The gauge had feedthroughs fonode and cathode, making the circuit of Fig. 6.46 convenient. The electrometer and high-voltage supply are beferenced to ground; and should there be leakage currents in the anode cable or feedthrough, the leakage curreot measured by the electrometer. Figure 6.47 is a plot of current versus pressure data obtained with this gauge

magnetic field of 0.12 T [173]. The slope of the linear portion is 1.09. Another typical feature evident in CCGalibrations is the increased slope below about 107 Pa.

he plot of Fig. 6.47 is typical for a CCG. The straight-line portion of a CCG characteristic may be fitted to a pquation

where ig is the gauge current, andn and K are constants. The departure from linearity is not great; values ofn foundhe literature usually fall between 1.05 and 1.2. Peacock and Peacock [174], investigating the nonlinearity, founn tfunction of the magnetic field. It decreased to 1.02 at 0.22 T for pressures in the straight-line portion above 10







Fig. 6.44UHV inverted magnetron gauge. Reprinted with

permission from J. P. Hobson and P. A. Redhead,Can. J. Phys . 36, 271 (1958) [Ref. 113].Copyright 1958 NRC Research Press.

he magnetron gauge [175] is similar to the inverted-magnetron gauge but has the positions of the anode and cnterchanged; a schematic diagram of the original gauge design is shown in Fig. 6.48. The magnetron gauge haperated in the pressure range 105 to 1011 Pa; above about 108 Pa the currentpressure characteristic is linear [n = 1 q. (6.41)], and below that pressure the value ofn increases. The magnetron gauge sensitivity (A/Torr) is generaligher than that of the inverted-magnetron gauge by a factor of about 10 at pressures above 108 Torr.

here is a large body of literature on the theory of the crossed field discharge. Redhead [176] briefly summarizatus. Existing theory explains some aspects of the discharge; but as pointed out by Redhead, classical theory f

mobility of electrons cannot explain the nonlinearity of ion current with pressure. In a very helpful paper, Knauiscussed some of the complex phenomena of the crossed field discharge, including dynamic effects that generequencies. Figure 6.49, from Peacock, Peacock, and Hauschulz [143], shows, greatly simplified, electron andajectories in the inverted magnetron discharge. In uniform crossed electric and magnetic fields, charged partic

n cycloidal jumps. In the cylindrical geometry of the inverted magnetron the electrons circle the anode in a sermall jumps,







Fig. 6.45HPS inverted magnetron gauge. Reprinted with permissionfrom R. N. Peacock, N. T. Peacock, and D. S. Hauschulz, J.

Vac. Sci. Technol. A 9, 1977 (1991) [Ref. 143].Copyright 1991 American Vacuum Society.



Fig. 6.46Circuit for operation of a cold-cathode gauge.Reprinted with permission from N. T. Peacockand R. N. Peacock, J. Vac. Sci. Technol. A 6,

1141 (1988) [Ref 173]. Copyright 1988American Vacuum Society.





Fig. 6.47A calibration of the inverted magnetron gauge of Fig. 6.45. The

anode supply was 4.0 kV, and the field was 0.12 T. Reprinted with permission from N. T. Peacock and R. N. Peacock, J. Vac. Sci.

Technol. A 6, 1141 (1988) [Ref. 173]. Copyright 1988American Vacuum Society.



Fig. 6.48Schematic diagram of a cold-cathode magnetron gauge.Reprinted with permission from P. A. Redhead,Can.

J. Phys . 37, 1260 (1959) [Ref. 175].Copyright 1959 Canadian Journal of Physics.





Fig. 6.49Ion and electron trajectories in the inverted magnetron.Reprinted with permission from R. N. Peacock, N. T.Peacock, and D. S. Hauschulz, J. Vac. Sci. Technol.

A 9, 1977 (1991) [Ref. 143]. Copyright 1991 AmericanVacuum Society.

able 6.4. Electron transit and Collision Parameters for a Penning Dischargea

ressure (Pa) τe τi v vi N Ni

011.2 µs 0.6 µs 21 MHz 1.7 MHz

25 2

041.2 ms 0.6 ms 21 kHz 1.7 kHz

25 2

071.2 s 0.6 s 21 Hz 1.7 Hz

25 2

01020 min 10 min 21 mHz 1.7 mHz

25 2

The columns are: average electron transit times,τe; average time between ionizing collisions,τi; electron collision frequency,v;ectron ionizing-collision frequency,vi; total number of collisions during transit, N ; total number of ionizing collisions during transit,i. Calculated for a Penning cell with anode voltage 5 kV, cell diameter 30 mm, and magnetic field 0.1 T. From Redhead [175].

petitively stopping, accelerating, and returning to rest. To maintain a discharge the peak energy must be adequate to create ions duringelastic collisions. As the magnetic field increases, the peak energy will decrease until ionization is not possible. In this simple model tectrons can move inward only as a result of inelastic collisions. Not only do electrons enter the discharge from ionizing collisions, butcondary electrons ejected from the cathode by ions may also participate. At low pressures it can take a long time for an electron to traom cathode to anode. Table 6.4, from Redhead [176], gives some interesting numbers for a CCG, including transit times.





he resulting circulating current can reach about 0.1 A. The space charge is large enough to depress the electroeld. With sufficient depression of the potential, electrons from the cathode are no longer able to enter into theirculating current. It is this effect that stabilizes the current, and causes the gauge to have a constant sensitivity178] measured the space charge in a Penning cell using a microwave probe method and found a space charge early independent of pressure between 104 and 108 Pa. From their curves, for a potential of 2500 V and magnf 0.19 T the electron density was 4 × 1015/m3. Their plots usually show a sudden change in density at about 3a.

Hobson and Redhead [113] and Feakes and Torney [179] proved the ability of the cold-cathode gauge to measuowest laboratory pressures then available. Special Redhead CCGs were left on the lunar surface to monitor thetmosphere. Some accelerator storage rings operating at XHV use CCGs. Gauges similar to that shown in Fig. vailable commercially [180], and there are other manufacturers [181, 182] also.

When the high voltage is applied to a CCG, there is a delay before the discharge starts. This is called the "strikiis only a few seconds at pressures greater than 104 Pa and is not noticeable. At pressures of 108 Pa and less w

ource of initial ionization is present, it can be hours or days [143]. If the gauge cannot be turned on at a pressuhe striking time is short, then supplying a source of initial ionization will overcome the problem. Including aadioactive source within the gauge has been suggested and tried with varying success [183187]. Another mean

nitiating the discharge is a source of UV light. Peacock and Peacock [188] showed a convenient way to introdght source.

.9.10onization Gauge Accuracy

Accuracy of measurement with ionization gauges is a complex topic. Calibration of either HCGs or CCGs is nomatter of determining the gauge constant by comparison with a standard in the range 104 to 103 Pa. Many userccept the manufacturer's catalog value. Whether calibrated or not, the application of the gauge may be at presseveral decades lower than the direct calibration interval of 104 to 103 Pa. Linearity must be assumed if the gae used at lower pressures.

inearity of ion current with pressure was first verified for the BAG by Alpert and Buritz [189] using a valvingrrangement designed to produce a quadratic change of pressure with time. To the accuracy of the method, the was linear from 107 to 101 Pa. Redhead [127], in a paper on factors influencing the gauge constant, plotted theonstant against pressure from approximately 104 to 101 Pa. It peaked sharply near 101 Pa. Peacock and Peacoomparing a BAG to a SRG, found the same peaking at emission currents of 1 mA, but at low emission curreneak in the gauge constant disappeared and it simply decreased above the linear region. Filippelli and Dittmannearched for pressure dependence of the gauge constant between 108 and 105 Pa and concluded that there was vidence for pressure dependence down to 5 × 108 Pa. Thus, as long as the calibration to determine the gauge c done at pressures verified to be in the linear region for an individual gauge, the extrapolation is acceptable.





catter of calibrations for new gauges has been examined at NIST (National Institute for Standards and TechnoGaithersburg, MD). The premise, as stated by Tilford [191], is "that gauge types that show small unit to unit van spite of manufacturing tolerances, would be more stable and predictable with time and use." Tilford [191] cois results for the calibrations of the gauge constant for six types of HCG to the manufacturers' specified valuesesult is reproduced as Fig. 6.50. The range of the gauge constants for 24 filaments of 12 conventional BAGs wpposed (tungsten) filaments was + 20 to 10%. For 10 filaments of conventional BAGs with thoria cathodes, itreater: + 13 to 38%. The UHV nude gauges had the greatest dispersion: For the sample of 15 cathodes the ran2 to 65%. The same figure also lists results for conventional triodes, BAGs with side-by-side filaments, and wange BAGs with small grids.

tability of calibration over long operating times is very important. Filippelli and Abbot [192], comparing repealibrations of 20 gauges returned to NIST, concluded that for gauges with tungsten cathodes the standard devihe maximum difference between successive calibrations was 3.1%, and for gauges with thoria cathodes it wasoulter and Sutton [193] at the National Physical Laboratory, Teddington, United Kingdom, operated five triodauges and six BAGs for periods of about 1000 hours, making up to 100 calibrations on each. The BAGs had acatter of initial gauge constants, and for one gauge they decreased at an average rate of 1.4% per 100 hours. Fiode gauges the changes were 0.08% and 0.45% per hundred hours. BAGs exposed to atmosphere, but not triauges, showed changes as large as 25%.

Fig. 6.50Average offset from the specified nitrogen gauge constants,standard deviation, and range of gauge constants for sixdifferent types of ionization gauge. The gauge types are

designated at the bottom of the figure and explained in the text.The numbers at the bottom are the number of filaments tested.The mean offset is indicated by the asterisk (*), ± one standarddeviation by the wider box, and the range of gauge constants isindicated by the narrower box. Reprinted with permission fromC. R. Tilford, J. Vac. Sci. Technol. A 3, 546 (1985) [Ref. 191].







here are many more papers on the reliability of HCG measurements made under the conditions of a standardsaboratory. An excellent summary was given by Tilford, Filippelli, and Abbott [194]. The papers cited above heferences, and they provide access to earlier literature.

ess is known about the accuracy, repeatibility, and stability of CCGs. Peacock, Peacock, and Hauschulz [143]hat early production records for one group of 159 gauges as in Fig. 6.45 show that 80% were within ± 20% of alibration at 103 Pa. An individual gauge, on the calibration system for more than a year with several exposuretmosphere, was compared frequently to an SRG. The scatter of the calibrations was about ± 5%. Filippelli [19eported that NIST had examined a group of several commercial CCGs and that they exhibited reproducible be

within ± 10%. There may, however, be many situations in the normal use of high vacuum gauging where CCGar more accurate results. Peacock, Peacock, and Hauschulz [143] describe an experiment comparing readings nd cold-cathode gauges during and after a pumpdown. They noted that when their UHV comparison system, e

with both HCGs and CCGs, was pumped down following a calibration experiment the CCGs consistently indicower pressures. Measurements showed that the pumping speed of the CCGs was about 3 × 105 m3·s1, and thaAGs was about 2 × 105 m3·s1. These numbers are similar, and in any case much too small to explain the diffuring pumpdown. This suggested comparing both types of ionization gauge during a simulated pumpdown. Tre shown in Fig. 6.51. Att = 0 the system was at base pressure, and all gauges had been calibrated previously. At =

min the system pressure was increased stepwise by admitting nitrogen. The gauges were compared to the SRG

s 103 Pa. With all ionization gauges off, the pressure was increased to 1 Pa. The pumpdown started att = 107 min.urves show the nitrogen equivalent pressures measured by the various gauges during the pumpdown. The caliwere also verified at the end of the experiment. At 200 min, there is a difference of more than a decade in the nquivalent pressures given by BAGs and CCGs. The difference is due to higher pressures within the HCGs cauegassing of material adsorbed during the exposure to nitrogen at 1.3 Pa. The extractor gauge, which has the loower input of the HCGs, shows the best agreement with the CCG. This experiment was repeated many times ame results. If the system is simply allowed to pump, the readings of the HCGs drift downward toward the CCowly, further indicating that the HCGs are in error. Degassing the HCGs reduces their outgassing, and they coetter agreement with the CCG.

Gauge constants change with time under the conditions of a standards laboratory. Industrial systems with residund vapors that contaminate the electrodes are much worse. However, there is little written on the effects ofontamination. Young [196] described the results of operating a gauge in methane. An insulating film, removaby electron bombardment, formed on the ion collector. Traces of oil in industrial systems frequently cause the cfficiency to go to zero. The situation with CCGs and contamination is identical to that of HCGs.

xternal magnetic fields have large effects upon ionization gauge calibration. Unfortunately, small fringing fielon pumps or cold-cathode gauges are often present. Gauges used around nuclear accelerators may experience elds of the





Fig. 6.51Differing behavior of a nude BAG ( ) a glass BAG , an extractor gauge (×),and a CCG ( ) in monitoring a pumpdown. The BAGs were at 1 mA emission.At t = 0 the system was at a base pressure of about 2×1010 Torr. Reprinted

with permission from R. N. Peacock, N. T. Peacock, and D. S. Hauschulz, J. Vac. Sci.Technol. A 9, 1977 (1991) [Ref. 143]. Copyright 1991 American Vacuum Society.

rder of 1 T, and frequently pulsed fields. There are a number of papers on the effect of fields on gauges [1972

Hseuh [197] studied a BAG in fields up to 6 × 103 T. For a field of 6 × 103 T perpendicular to the axis of the ghanges of gauge constant were as large as 140% depending upon the angle of rotation of the field about the axauge. Effects of about 10% occurred at fields as small as 1 × 103 T. Filippelli [198] used fields up to 0.16 T. Has much detail regarding direction of the field and also regarding ionizing electron, collector, and wall currentnd Hung [199] were interested in operating a gauge in fields up to 0.7 T. With proper orientation they succeed

200] considered both hot- and cold-cathode gauges used near magnetic fusion devices. Martin [201] had similnterests. These papers confirm that operation of a BAG in a magnetic field is possible with suitable orientationltered gauge constant.

.9.11Gauge Constant Ratios for Different Gases

would be desirable to have ionization gauges calibrated for all the gases of interest. The user would then havonstants, Kg , for use as needed. There is an imperfect alternate. In principle, if the ratios of the gauge constants Rg





efined by

were known for various gases, unknown gauge constants could be estimated by multiplying the known constaneference gas (here nitrogen) by the value of Rg from a table. There are tables of these ratios, such as Holanda's [2he problem is that the ratios as measured at different times with different gauges and operating conditions scaadly. This technique for estimating a gauge constant is at best only approximate. Figure 6.52 from Tilford [20auge constant ratios plotted against pressure for a number of common gases. Curves are given for both conveniode and for BAGs.

.9.12onization Gauge Controllers

he HCG controller supplies the grid and cathode bias voltages and the filament heating power, and it usually n electrometer for measuring the collector current. It is customary to operate with the cathode off ground so thurrent can be measured to ground.

he grid and cathode supplies should be well regulated, and particularly for laboratory use these voltages shoudjustable over the full range of commonly used values. Adjustable grid current from 10 µA to 10 mA is almosecessity. Filament heating can be by dc with series transistors, or ac with SCR control. The bias situation diffeomewhat with these methods, and dc is less likely to cause problems. Abbott and Looney [204] found that SCmission control with glass gauges without internal shield caused erratic gauge calibration. This effect is due tohanging wall potentials.

ailure modes of a controller should be considered. An ionization gauge is a vacuum tube operated at vacuum oltages. Interfacing with solid-state circuits that may be damaged by transients is not simple. If the grid circuitpen loop, the filament will go full on, perhaps burning it out. A control to set the maximum filament current crevent this. Most modern controllers turn the filament off if the pressure reaches some maximum value such ahis may help to prevent filament burnout or damage and electrode contamination.

ong gauge cables can be a problem with HCGs. Filament currents can be as large as 5 A, so voltage drop alonable may be significant.

Accurate measurements with a BAG are never possible until the gauge has been processed by some combinatioaking and degassing until normal operation of the gauge does not cause a pressure increase. The type of degasither by electron bombardment or resistive heating, demands careful thought. Electron bombardment degassinffective and can be used on all gauges. Resistive heating requires that the grid be a continuous wire in the formelix or double helix. Electron bombardment degassing requires a supply providing 600700 V, with current adjo 70 mA. A supply of this type can be lethal. Morrison [205] describes the problems and grounding precautionbserve when using an electron bombardment degas supply. Resistive heating requires voltages less than 10 V urrents of several amperes. The hazard is negligible. The pressure rises in the gauge during degas with either t

eating. But if it rises to pressures above 102 Pa with electron bombardment





Fig. 6.52Gauge constant ratios for several gases as a function

of pressure. Reprinted with permission from C. R. Tilford, J. Vac. Sci. Technol. A 1, 152 (1983) [Ref.203].




egas when using oxide cathodes, the cathode emitting material can be stripped in minutes by ion bombardmen

lectrometer stability and range must be compatible with the requirements. Electrometers are usually direct rearessure units. However, in the laboratory it is important to have the choice of reading the current directly.





he CCG controller supplies only the high voltage required by the gauge head, and it measures the current in thoop. Although CCGs require several kilovolts for operation, the current is limited to about 0.1 mA so the dangerious electric shock is reduced. Because the power requirements of the CCG are small (< 1 W), controllers caompact.

A wide range of vacuum equipment is available commercially. Little is fundamentally new, but it is smaller andonvenient to use. The trends toward miniaturization, lower pressures, and standard off-the-shelf equipment wirobably continue.

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artial Pressure Analysis

Robert E. Ellefson

Measurement of total pressure in a vacuum system is often not sufficient to characterize the vacuum for procesxperiments. The measurement of partial pressures of the components making up the total pressure is useful foiagnostics or process monitoring. A partial pressure analyzer consists of an ion source, a mass analyzer, an ionetection system, and the control electronics. A partial pressure analyzer used to measure the composition of thesidual gas in the vacuum system is usually a quadrupole mass spectrometer (QMS) with its ion source immeracuum system. Such a QMS is referred to as a residual gas analyzer (RGA). The measured ion currents from gpecies present are converted into partial pressures using a sensitivity for each gas species determined by a calirocess. When the total pressure of a vacuum processing system exceeds the operating pressure of the RGA, preduction methods are used which allow indirect measurement of partial pressures in the process or compositioas present. When pressure reduction is needed, a closed-ion-source mass spectrometer can be used which offe

mproved detection limits for small component partial pressures. The ions sources for partial pressure analyzersypically use electron impact ionization. Partial pressure analysis methods which measure optical absorption oran monitor certain components in a vacuum that have strong absorption or emission signatures.

1on Sources

he choice of ion source for a partial pressure analyzer depends on the pressure regime for the gases to be analhe accuracy and precision required for the






measurement application. To measure the residual gases in the medium to high vacuum pressure regime, an ionwith good conductance to the vacuum system is needed. If the vacuum system is evacuated to ultrahigh vacuumr extreme high vacuum (XHV), a high conductivity ion source similar to a total pressure ionization gauge is nhe residual gas composition measured by the RGA can include a significant contribution from the outgassinglectron stimulated desorption from a hot-cathode ionization source. Ion sources for UHV and XHV are design

minimize these effects. Process gas in the vacuum system is often analyzed for minor impurities. Low-level detmpurities can be achieved by using a closed ion source. Most ion sources for vacuum applications use a hot cahe formation of ions by electron impact ionization. This common ionization process and the different types of ources are described in the next paragraphs.

.1.1lectron-Impact Ionization Process

he electron-impact ionization process is an inelastic scattering process where the incident electron transfers enn electron in the target molecule or atom; the energy transferred is typically less than the kinetic energy (KE) oncident electron. The reaction can have a number of products with various probabilities (cross sections) for for

where M+ is termed the parent molecular ion where one electron is removed from the molecule. The product Moubly charged molecular ion formed when two electrons are removed from the molecule. The other examplesrocess are the formation of fragment ions, F+, and associated neutral fragment, N. The ionization process is shig. 7.1 as a potential energy diagram for the singly charged reaction products of Eq. (7.1). Electron-impact enansfer to an electron in the molecule is described by the FranckCondon principle [1], which states that ionizat

vertical transition" where little change in internuclear separation(s) occurs because the energy transfer occurs imuch shorter than a period of vibration of the molecule. Ionization proceeds from the ground state of the molec

ertically to a coordinate of the potential energy curve describing the resulting products such as parent molecullus escaping electrons or fragment ion with a neutral and electrons. The amount of energy just sufficient to prarent molecular ion, M+, and free an electron is defined as the ionization potential (IP) of the molecule. The mnergy to create a fragment ion or higher charge state of the ion is called an appearance potential (AP), which iharacteristic of the molecule related to its bond strengths. It is possible to produce an ion in an excited state wfter a few molecular vibrations, fall apart into other fragment ion and neutral species represented in Fig. 7.1 as

Energy deposited in the molecule can also lead to a repulsive state where the fragment ioneutral species have excess kinetic energy at the appearance potential, AP2. The energy dependence for the croection for production of parent molecular ions [2] is indicated in Fig. 7.2. Most electron-impact ionization mapectrometers use 70-eV electrons, which provide ample energy for





Fig. 7.1Potential curves for a molecule, M, and electron-impact

ionization products producing M+ parent ion and two fragmentions, when the incident electron has sufficient energy.

roduction of the parent molecular ion and fragment ions characteristic of the molecule. Ionization potentials oommon molecules and atoms are given in Table 7.1 from a detailed compilation [3] by the National Institute ocience and Technology. Characteristic fragment ions and their abundance for 70-eV energy ionization are givable 7.2 for common molecules [4]. Additional spectra and tables of characteristic fragment ions and their abure given in collections of mass spectral data [46].

.1.2Open Ion Source

he basic ion source for a residual gas analyzer is an open ion source similar to the structure of a BayardAlpertigure 7.3 shows various styles of open ion sources. The term "open" refers to a high conductance of the ion foegion to the surrounding vacuum region to ensure that the gas composition being analyzed reflects the composhe vacuum [7]. The conductance of some styles is restricted by solid support structures with the filament moun

within the structure (Fig. 7.3d,e ). Such styles can be used in medium- and high-vacuum applications. In a partialnclosed ion source, the hot cathode can induce local formation of various reaction products [8] (see Chapter 1

more open source, reaction surface areas are reduced and surface temperatures are lower so the filament reactio reduced (Fig. 7.3b,c,f ). For UHV and XHV applications, Watanabe [9, 10] has shown that outgassing of the io

ource due to the hot filament can be further reduced





Fig. 7.2Ion pairs/mbar-cm for various gases versus kinetic energy of incident electrons whichis directly proportional to the cross section for ionization for each species shown [2].

Table 7.1. Selected Ionization Potentials and Appearance Potentials of CommonMolecules and Atoms [3]







Table 7.2. Fragmentation Patterns for Common Molecules with 70-eV Electron Ionization [4]a

Fragmentation abundances in quadrupole mass spectrometers differ depending resolution and ion energy settingsused.



Fig. 7.3

Five variations on the design of open ion sources. Note the similarity of filament and gridstructures between an open ion source and a BA gauge.





y modifications of the ion source (Fig. 7.3 f ). A berylliumcopper ring around the source was used to reflect heat he filament and to shield the analyzer from filament heat by conducting the heat to the outside of the housing.

n open ion sources, different filaments geometries are used. Some ion sources have the filament located as a riutside the central cylindrical grid structure [7]. Another design has the filament located parallel to the axis on f the central grid, and a third design has the filament on the end of the ionization region in an axial ion sourcelectron emission current from the heated filament is established with the filament at a negative voltage (typica

with respect to the grid, thus defining the energy of ionizing electrons. The repeller (when present) is held at a fmore negative than the filament to repel electrons emitted outward back toward the grid. The grid is held at a p

otential with respect to the analyzer axis potential; the difference between the grid potential and analyzer axisefines the energy of ions that enter the analyzer. In a quadrupole mass spectrometer, this potential difference (nergy) is 515 V. In a magnetic sector mass spectrometer, this potential is 10010,000 V depending on the applind design of the mass spectrometer. The other electrodes labeled "focus plates" in Fig. 7.3 are adjusted to potehat focus the ion beam for maximum transmission through the mass analyzer. The operating pressure regime fpen ion source is from UHV to 102 Pa. Higher pressures are possible, but nonlinear response of the ion sourceue to three competing effects: (1) space charge (e and I+) buildup in the ionization region which alters the ionansmission out of the ion source into the analyzer compared with lower pressure operation [1114]; (2) spreadieam due to Coulomb repulsion of intense ion beams during transit from source to analyzer and for intense ion

he analyzer [15]; (3) collision losses during transit through the mass analyzer.he operational parameters that control the production of ions in the ion source of a mass spectrometer are iden

q. (7.2). The ion current, , for theith component is given by

where Ie is the electron emission current,σ i( E ) is the cross section for ionization at electron energy, E , and

is the ion transmission factor dependent on ion energy, mass, geometry of the grid structurhe electrostatic potentials extracting and focusing the ions from the source and the total pressure, Pi , and gas

omposition, Xi. The ratio of Pi , the source partial pressure, toT source( K ), the source temperature, gives the gas df the target component in the ionization region.

.1.3losed Ion Source

A closed ion source encloses the ionization region; the gas to be analyzed enters through a supply tube and exithe electron beam hole and the ion exit slit or hole. Figure 7.4 shows a closed ion source used in quadrupole mpectrometers [16, 17] and the Nier-type ion source [1821] used in magnetic sector mass spectrometers. An advf the closed ion source is that pressure in the ionization region is higher than in the analyzer region by a ratio onalyzer pumping speed to the closed ion source pumping speed. Typically, this ratio is 10100, which produces





Fig. 7.4Closed ion source designs for quadrupole and magnetic sector mass spectrometers.

ource pressures up to 101 Pa while the analyzer operates at 103 Pa. High source pressure allows measurementevel impurities while the analyzer pressure is maintained at a low enough pressure to minimize ion losses in thnalyzer section. Gas throughput needed for the analysis is also reduced by the ratio of the analyzer pumping she closed ion source pumping speed. Background components from outgassing or sample-induced desorption

mainly from the small surface area inside the ionization region and are small contributions to the gas sample. Tmall additions allows the measurement of low-level impurities in gas samples. The filament is located externaonization region, which minimizes filament surface reaction products from diffusing back into the ionization rnd contributing to the composition of the gas sample being analyzed.he QMS closed ion source uses a simple design with the filament located in front of a slit in the ionization chahe electrons are accelerated by applying 70 V (or other voltage to define electron energy) to the filament with

o the ionization chamber. A significant fraction (1020%) of the electrons from the filament go through the eleceam hole or slit terminating on the inside wall of the ionization chamber. In a Nier-type ion source, the electro focused with a grid and collimated by a small magnetic field parallel to the electron beam. The electron beam

hrough a hole on the opposite side of the ionization chamber into an electron trap electrode maintained at + 10lectron trap current is measured and used in an emission regulator circuit to produce a constant electron currenlectrons execute a helical motion in the source magnetic field creating a higher current density than without th

magnet. The narrow collimated beam also minimizes the energy spread in ions extracted and accelerated into thnalyzer. This is important for magnetic sector mass spectrometers because the resolving power is inverselyroportional to the energy spread of ions.

Variations on these basic designs for ion sources are used in commercial mass spectrometers. Evolution of ion sor specific applications has occurred especially with quadrupole mass spectrometers in recent years and will liontinue.





2on Detection

arly detection of positive ions was by observing the fluorescence of natural phosphors like glass, willemite (zlicate), and zincblende (a zinc sulfide) when positive rays were incident on the scintillators. By 1910, fluoresc

creens were replaced by photographic plates which gave a permanent record of spectra and intensity measuremom the opacity of the ion exposure [22].

.2.1araday Cup Ion Detection

y 1930, ion currents could be measured directly from a mass analyzer with an electrometer as ions strike a plaaraday cup [23]. This detection method is still preferred using modern electrometers and is generically termed Faradetection in honor of Michael Faraday, a nineteenth-century physicist who in his experiments collected electricaharges in a metal cup. Ion detection occurs when electron current flows to the plate to neutralize the charge ofhat arrive; the current is measured by an appropriate electrometer circuit. A "deep cup" detector is used in magector mass spectrometers to ensure that secondary electrons released by energetic incident ions do not escape up and thereby generate an apparent additional ion current when the electrons leave the plate. Other designs u

uppressor plates to repel secondary electrons back to the Faraday plate. Most quadrupole mass spectrometers enerate ions with enough energy to release secondary electrons at the detector plate. The time constant for a Fype of ion current measurement is dictated by the input resistance and the distributed capacitance of the curren

measurement circuit. A time constantτ = RC≈ 0.1 s are typical for Faraday cup/electrometer systems. The detectmit of a Faraday detector is typically the noise limit of 3 × 1016 A [104 ions/s] in modern field effect transistolectrometers. Faraday detection is the simplest and least expensive ion detection device and is often used in louadrupole mass spectrometers.

.2.2econdary Electron Multiplier Detection

mall partial pressures produce small ion currents that may be below the detection limit of a Faraday detectionhe use of a secondary electron multiplier (SEM) can convert the electrons released from a single ion incident etector surface into a larger electron current with a multistage amplification of the electron current. Early elec

multipliers used discrete dynodes (1012) with a 50- to 100-V accelerating potential between each stage to increlectron current. Later designs use a continuous dynode like that shown in Fig. 7.5. The gain of the multiplier,G, is o two factors: The first is the conversion of the incident ion to electrons at the first dynode or point of incidencontinuous dynode device. The number of electrons released in this primary event, p, is one to five depending on ionergy, mass, molecular structure, and even ionization potential. The second factor is the electron gain per stagecause the secondary electrons are accelerated between dynodes or through the continuous dynode structure. ummarized with the relation





Fig. 7.5A continuous dynode detector for ion detection by secondaryelectron multiplication (Galileo Electro-Optics Corporation).

wheren is the number of discrete dynodes orqn can be the overall electron amplification in a continuous dynoderucture. In Fig. 7.5, the continuous dynode film is formed on the inside of a glass horn-like structure with the lm (~ 108Ω) extending to the outside on both ends to provide connection points for the high voltage and groun

onconductive zone indicated in Fig. 7.5 is on the outside of the glass structure and electrically separates the enpplied voltage on the horn end is typically 2000 V with 20 µA of current through the film establishing the potradient inside the channel to transport and amplify secondary electrons from the first ion-to-electron conversioo the capture of the electrons by a collector plate connected to the electrometer/preamplifier. The output electrurrent of the SEM is 103 to 107 times the ion current at the first dynode, which is easily measured with an ele

with smaller input resistors than the Faraday detector and shorter time constant. Manufacturers recommend SEsed for ion currents less than 10 pA, which means less than 104 Pa (N2 equivalent) gas pressure in the ion souypical mass spectrometer. Higher currents are reported to degrade gain. SEM gain loss by a factor of 10 can ocotal transported electron charge of 4 mA·hr [24]; gain loss can occur from deposits, especially hydrocarbons, fon beam or from contamination. It is preferable to keep the SEM operating in a clean vacuum of 105 Pa or low

minimize contamination. Discrete dynodes are typically made of CuBe(2%) or AgMg(24%) "activated" in air table Be oxide (or Mg oxide) film on the surface which controls the secondary electron yield. This layer can bhemically altered or contaminated during use in a mass spectrometer, giving rise to changes in multiplier gainontinuous dynode 104 SEM replaces the discrete dynodes with a resistive layer on an insulator. The semicondlm on a continuous dynode SEM is chemically inert and adsorbed gases are desorbed by continued use, thus pmore stable gain over time than a discrete dynode SEM. Lifetime of an SEM is related to the total





lectron dose to the electrode surface. Some SEMs are designed specifically for use in pulse counting as an alteo analog measurement of low-level ion current. Typically, pulse counting detectors are limited to less than 106econd, which corresponds to an ion current of 2 × 1013 A.

he use of a SEM to measure small ion currents introduces a new calibration parameter due to the gain in the iurrent signal from a multiplier. The gain is adjustable by changing the voltage applied to the SEM. The gain applied voltage can degrade due to contamination of the multiplier surfaces and/or ion beam damage. The prac

matter of cross-calibrating the output of a Faraday detector with an SEM detector to give useful combined dataesolved by measuring an ion current from a peak where the intensity is on scale for both detectors. A measurehe SEM gain factorG can be defined:

on current data from the SEM can be divided byG to scale the value for use with Faraday detector data. Whenufficient ion current is present, the Faraday detector should be used for quantitative measurements to avoid mohe stability of the gain factor,G.

.2.3Microchannel Plate Detector

he gain of a continuous dynode SEM depends on the length-to-diameter ratio, which allows for miniaturizatioype of SEM [25]. The combination of a large number of small channels into a planar array results in a microchlate (MCP) where miniature continuous dynode SEMs in parallel form a compact multiplier-detector for ions.epresentation of the MCP array and the operation of an individual channel is shown in Fig. 7.6. The short leng

microchannels limits the applied voltage to about 1000 V producing a gain up to 25,000.

he multichannel plate detector output can be resolved spatially, which offers the possibility for ion current disn the array giving a "mass spectrograph"-like output. An example of a hybrid detector with MCP/phosphor/ph

rrays to convert dispersed ions into a spatial image is reported in the literature [26].3

Mass Analysis

Mass analysis of ions is achieved by various methods of acceleration and deflection by electric and magnetic fill the mass analysis methods, it is the mass-to-charge ratio of the ion, M/e , that is analyzed by the physical separaf ions in space or time. Thus ions like 40Ar++ and 20Ne+ will be analyzed with the same nominal M/e of 20.

.3.1Quadrupole Mass Analyzer

he quadrupole mass spectrometer (QMS) is the most popular mass analyzer used for vacuum partial pressuremeasurements because of its rapid scanning capability,





Fig. 7.6A microchannel plate detector array and electron

multiplication in a single channel(Galileo Electro-Optics Corporation).

ompact size, linear mass scale and relatively low cost. The QMS uses a mass filter that consists of four paralleonductive rods arranged in a square array with opposite rods connected electrically in parallel [27] as shown i.7. Ions from a source enter an end of the quadrupole mass filter near the axis drifting parallel to the rods (defihe z -axis) with a kinetic energy of 315 eV. The combination of a direct-current (dc) potential and radio-frequenotential applied to the rods accelerates the ions perpendicular to the z -axis; transmission through the quadrupoleotential field of the rod assembly occurs for ions in a narrow mass range. Low M/e ions move nearly in phase withpplied RF voltage and are accelerated to large x and y displacements. These light ions collide with the rods and aeutralized and lost from the beam. High M/e ions do not gather sufficient x or y velocity during the rf cycle to ach

much displacement, but the dc potentials give a constant acceleration that centers the ions between the rods witositive potential and attracts the ions to the rods with negative potential where the ions collide with the rods aeutralized. Between the high mass and low mass extremes, there is a range of M/e ions that can oscillate with smamplitudes and drift through the rod structure without striking the rods. These ions are transmitted to the detecthe value of M/e







Fig. 7.7Quadrupole mass filter structures. Parabolic rodsgenerate a true quadrupole field; cylindrical rods

approximate the parabolic shape and are less costly tomanufacture. The rf circuit is tuned to resonate at the

driving frequency for optimum coupling tothe rod assembly.

hat is transmitted depends on the amplitude of the rf voltage; and the range of M/e values,∆ M/e , depends on theumber of oscillatory cycles the ion spends drifting through the rod assembly. The equations of ion motion in tuadrupole field were first given by Paul et al. [29] and are summarized as follows.



igure 7.7 shows the quadrupole rod assembly and applied constant potential and rf potentials. The potentials ahe rods is

whereU is the dc amplitude,V is the amplitude of the rf applied potential with angular frequencyω, x and y areoordinates perpendicular to the axis of the rod





ssembly, andr 0 is the radius of a circle tangent to the inside of the rods. The equations of motion for ions in thotential are given by the Mathieu equations [29, 30]:

quations (7.6) and (7.7) together describe an oscillating system with restoring force that is periodic in time wingular frequencyω as the ion drifts through the rod assembly in the z direction. Simplification of these equationsccurs by defining parametersa and q:

he practical operation of a QMS chooses values ofa and q within the lowest region of stable oscillatory solutionhe Mathieu equations. Normal operation is chosen for highest resolving power, M /∆ M . (In much of the QMS litera

M /∆ M is referred to as resolution.) Choices likeq = 0.706 anda = 0.233 toa = 0.236 produce 50 < M /∆ M < 500 [30he actual adjustment of resolving power is done electronically by adjusting the ratio ofU/V , which is related toa any the ratio of Eq. (7.9) to (7.10),

However, as resolving power increases, ion transmission decreases due to a reduction in radius of ion beam acche mass filter asU/V increases. Mass scanning relations are predicted by Eq. (7.10) for a given choice ofq and forxed values ofr 0 andω, which shows that M/e is directly proportional to the rf amplitudeV :

r for a practical quadrupole application withq = 0.706, the mass (in amu) transmitted is

whereV is the rf voltage,r 0 is the quadrupole radius in meters, and f is the rf frequency in Hz. The resolving powelso be limited by the length of the rod assembly and the ion energy,eVz from the ion source:





he coupling of the ion source to the rod assembly also affects transmission through the mass analyzer. Ions wiadial displacements and small radial velocity components have the greatest chance of traversing the mass analeing detected. Also, off-axis location of the source or misalignment of the source or rods can degrade the peak

with notches or shoulders, making algorithms for quantitation of ion current more difficult. A common mode operation is to produce mass peaks with nearly constant∆ M of less than 1 amu for all M/e over the mass range of thnstrument. This enables measurement of small peaks at a mass adjacent to an intense peak even for high mass.M can be produced by maintaining a relationship between the dc voltage,U , applied to the rods and the rf maximoltage,V , given byU = KV + U offset, where K is a constant fraction andU offset is a negative offset voltage indicn Fig. 7.8. In Fig. 7.8, the shaded areas describing stable trajectories for two particular masses come from the aalues ofa and q of the Mathieu equations that produce stable ion trajectories [30]. By solving Eq. (7.9) and (7. and V , respectively, the scaling of thea and q parameters by mass M is indicated for the applied voltagesU and V

hown on the axes of Fig. 7.8. Useful mass separation is indicated whenU offset lowers the operating line to allow arrow range of rf voltages (dotted lines) centered aroundVM 1 and VM 2 that transmits masses M 1 and M 2,espectively, producing the observed near-constant width,∆ M , for each peak [31]. The constant∆ M mode of operatesults in ion transmission decreasing with mass as M 1, which limits useful sensitivity at high mass. However, thendependence of ion transmission from ion energy means that changes in ion energy by collisions does not resuarge loss in transmission, so a QMS can operate at a relatively high analyzer pressure [32]. This makes the QMspecially useful for residual gas analysis applications.

.3.2Magnetic Sector Analyzer

A magnetic sector analyzer achieves mass separation by deflection of ions of the same energy by a uniform maeld oriented perpendicular to the motion of the ion.

Fig. 7.8QMS operating line for producing a constant∆ M peak width over the

mass range of the instrument [31]. The mass scale is directly proportional to the applied RF peak voltage.





ons formed in the source are accelerated by applying a voltage,V , to the source. Each ion achieves an energy give

where z is the charge state on the ion of mass, M . When the ion enters a uniform magnetic field, it experiences aentripetal force

which traces an arc with radius, R. By eliminatingv from these equations, the radius of the path of an ion of mass M

r, by rearrangement,

he mass separation that occurs is shown in Fig. 7.9, which is a 60° magnetic analyzer used for residual gas an33]. Light M/e ions (small circles) have the smallest radius path in the magnet and exit the magnet with greateseflection from the original ion path before entering the magnet. The heavy M/e ions (large circles) have the largesadius within the magnet, as predicted by Eq. (7.18), and experience the smallest deflection. In a practical instrxed radius of curvature is defined by the source slit, analyzer baffle, and collector slit. This allows a narrow ra

mass to

Fig. 7.9A small commercial 60° magnetic sector mass spectrometer used for

residual gas analysis. Non-normal entry of ions into a 92° magnetshortens the focal length of magnet making a more compact analyzer [33].







e measured for a given magnetic field, B, and accelerating voltage,V . By scanningV or B, different values of M/z ce brought into focus.

An early method for measuring a mass spectrum was to measure the different radii [Eq. (7.18)] separating the iifferent mass on a focal plane exiting the magnetic field. Placing detectors or a photographic emulsion at the flane records the ion currents as a mass spectrograph. The first measurement of 20Ne and 22Ne isotopes andbundances was done by Aston [34] by building and using a mass spectrograph similar to this one. Modern verhe mass spectrograph locates detectors for selected masses to continuously monitor specific processes [34, 35]

An example of a 90° sector mass spectrometer is shown in Fig. 7.10 with ions entering and exiting the magneticormal to the pole face. The focusing of this geometry is simple: The distance from pole face to source and polollector slit is equal to the radius of magnetic deflection. Small adjustments to focal length is accomplished byhe magnet as needed radially to accomplish the best peak shape. The resolving power of a 90° magnetic sectorpectrometer with ion beam entering and exiting the magnet normal to the face is given approximately by

where R is the magnet radius,W collector is the collector slit width, andW source is the source slit width. To achievnattenuated ion transmission indicated by flat-topped



Fig. 7.10A 90° magnetic sector mass spectrometer. Note that the distance fromthe source and collector slits to magnet pole face is equal to the radius

in a 90° deflection sector, which is characteristic of a 90°magnetic sector with ion entry normal to magnetic field.





eaks in the mass spectrum, the collector slit width must be greater than the source slit, and often it is twice theit width to cover broadening or rotation of the ion beam before detection. The most common way to operate a

magnetic sector mass spectrometer is to fix the accelerating voltage and control the magnetic field to scan over Mf interest. This gives nearly constant sensitivity for ions as a function of mass, but the control of the magnetic ow compared with the rapid changes possible with a quadrupole mass spectrometer or with voltage scanning

magnetic sector mass spectrometer. Equation (7.19) shows that M/e depends on magnetic field squared. Thisompresses the range of magnetic field needed; however, it creates a nonlinear mass scale if the magnetic fieldcanned linearly. Figure 7.11 shows a voltage-scanned mass spectrum for the mass spectrometer in Fig. 7.9 whpermanent magnet. Note that the fixed resolving power of the magnetic sector analyzer produces peak widths∆ M/

hat are narrow at low mass and get wide at high mass.

Magnetic analyzers offer the advantage of a simple, fixed geometry that controls the resolving power and ionansmission of the analyzer. This results in very stable sensitivity over time which is needed for quantitative

measurements. Magnetic sector analyzers are not as popular as quadrupoles because the necessary magnetic fienterfere with the application; to achieve useful resolving power, the size of the analyzer can be large. Also, anycatters with a gas molecule in the analyzer loses enough energy to usually be lost from the mass resolved beamnalyzer pressure needs to be kept low for quantitative measurements.

Fig. 7.11A computer-controlled analog mass spectrum made by voltage scanning a

magnetic sector analyzer. The mass scale is linearized; evidence of near-constantresolving powerm/∆m of a magnetic sector analyzer is seen with the narrow peak

width (∆m) at low mass compared with the peak width at higher mass [33].





.3.3ime-of-Flight Mass Analyzer

he concept of time-of-flight (TOF) of ions as the basis for mass separation is attributed to Stephens [36], withrototype TOFMS developed by Wiley and McLaren [37]. A schematic of the operational features of a linear Thown in Fig. 7.12. Ions are formed in an open source region continuously or by (pulsed) electron impact folloxtraction of ions with a drawout pulse and acceleration with an applied voltage,V , resulting in a drift velocity of thons given by

he drift time for each ion M/z (referenced to the time that the drawout potential is applied) is

where D is the length of the flight tube. Arrival times at the electron multiplier detector vary with the square roo M

or a 1-m tube and 3-kV acceleration, the arrival times range from 1.9 µs to 13 µs for M/z = 2 and 100, respectivelyMeasurement of a mass spectra is accomplished by recording the ion current in a time window∆t recorded at a varime delay, t delay. By varying the time delay linearly,t delay = At + t 0, from 1 to 15 µs and recording the ion currerriving in a 10-ns time window, a mass spectrum covering mass 2100 is recorded (for a TOFMS with D = 1 m;V =V). The mass scale of this linear time base will be proportional to the square root of mass according to Eq. (7.

Multiple ion monitoring is achieved by setting multiple time delays with measurement windows,∆t , adjusted to caphe whole peak width. The time delays are set to measure selected masses. With the multiple delays, it is possib

measure ion currents of many species formed at a single ionization event. Repetition time for replicating the iorocess is limited by the longest drift time of ions being measured (clearing time) and the duration of the ionizarocess. With continuous ionization, ions are formed during the mass analysis of the previous pulse. With pulselectron impact, the electron beam is turned on for a desired time period followed by ion extraction. Repetitionary from 10 kHz to 100 kHz depending on mode of operation, mass

Fig. 7.12A linear time-of-flight analyzer mass spectrometer.





ange, and TOFMS design. The resolving power for a TOFMS is measurable on a time spectrum as

where t M is the time of flight for an ion M and ∆t FWHM is the full-width at half maximum spread in arrival timehe ions. The origin of the peak width,∆t FWHM, in the mass spectrum is mainly due to the variation in ion energ∆om the finite width of the electron beam forming the ions that are drawn out by the extracting field, E . An alternatxpression for resolving power is

where for ion accelerationV = 3 kV, extraction field, E = 150 V/cm, and the electron beam width in the source,∆d =m, a resolving power of 200 is predicted. The development of the TOFMS has been limited by this modest resower and the cost of fast measurement circuits to record and process microsecond time frame signals. Time-o

mass spectrometers were popular in the 1960s for many applications including monitoring of fast reaction kineRecent developments have resulted in improvements in both aspects. Resolving power can be improved by em

nergy focusing methods like the ''reflectron" [38], where an electrostatic mirror is used to focus ions with slighifferent energies to arrive nearly simultaneously at the detector, thereby reducing the width of the peak,∆t FWHM.Availability of relatively inexpensive electronics with fast (ns) response and data storage electronics has reviventerest in time-of-flight mass spectrometry for a variety of applications including partial pressure analysis.

.3.4rochoidal (Cycloid) Mass Analyzer

he double-focusing properties of crossed electric and magnetic fields were first described by Bleakney and H39], with possible ion motions described as trochoidal paths. A commercial instrument shown schematically in.13 was developed by Robinson and Hall [40] where the path traced is a prolate cycloid with the spacing betwource slit and detector, D , equal to 2.7 cm. Ions are formed and analyzed within a region of electrostatic field, E , wi

magnetic field perpendicular to the plane of ion motion generating a mass-dependent cycloidal motion given by

Mass analysis can occur by scanning the magnetic field, B, or by changing the electric field, E , due to the appliedoltageV 2 V 1 shown in Fig. 7.13 on the electric field plates in the figure. The excellent focusing of this design ability and high sensitivity for ion detection with resolving power up to 400 in a very short ion path, making i

or quantitative measurement of partial pressures [41]. Permanent magnet versions of this instrument were madelatively) open ion source for residual gas analysis and in closed ion source versions for analytical measuremeas samples. For RGA applications the source within the magnetic field region limits use to an appendage mou

Also, the electrode structure is complex and has a lot





Fig. 7.13A cycloidal mass spectrometer.

f surface area for outgassing, which limits its usefulness for UHV applications. The location of the ion detectoot allow a traditional electron multipler detector to be used, although a microchannel plate detector might nowycloidal mass spectrometers have not been made since the early 1970s because of some of these limitations;

nstrument companies have instead focused on quadrupole mass spectrometers as a more flexible design.

.3.5Omegatron

he omegatron was developed by Sommer, Thomas, and Hipple for measuring atomic constants [42] and has by Alpert and Buritz [43] as a mass spectrometer for measurement of partial pressures in an ultrahigh-vacuum

A schematic diagram of the omegatron developed by Alpert and Buritz is shown in Fig. 7.14. The operation of

megatron is similar to a cyclotron. Ions are formed by electron impact ionization in the center of a uniform maeld. A resonant ion traces a spiral path as the ion of mass-to-charge ratio M/e gains energy from an rf field with earbit within the magnetic field. The condition for cyclotron resonance of an ion is

where B is in gauss and M/e is in amu. The resolving power of the omegatron is







Fig. 7.14Schematic diagram of a simplified version of the omegatron

developed by Alpert and Buritz [43].

where R0 is the distance from the ionization center to the detector (cm), and E 0 is the magnitude of the rf field (V/cn the Alpert and Buritz omegatron, the mass range from 1 to 40 amu was covered with a frequency range of 3o 81 KHz, respectively, with a magnetic field of 2100 gauss. With an rf electric field of E 0 = 1 V/cm and R0 = 1 cm

maximum resolving power of 212 at M/e = 1 is achieved and 5.3 at M/e = 40. The resolving power of an omegatrolearly favors measurement of low mass ions. Recent use of an omegatron is seen in the measurement of compof hydrogen and helium isotopes for fusion-related applications.

4ptical Measurement of Partial Pressures

Optical measurements of partial pressures of selected gases in a vacuum system have been employed in specifipplications where a noninvasive measurement is needed. The advantages of optical measurement methods are

measurement is speciesspecific and does not introduce reaction species like hot-filament measurement devicesAdvances in laser technology that have produced high-intensity laser beams with a wide range of wavelengths llowed the development of multiphoton photoionization processes to produce ions and resonant absorption me

measurement of impurity species in process gases and in vacuum systems.





.4.1hotoionization Measurement of Partial Pressure

he use of laser multiphoton ionization with mass analysis to detect low-pressure gas species had been reportedmany researchers [44, 45]. A quantitative study on measurement of CO partial pressures using resonance-enhanmultiphoton ionization with a time-of-flight mass spectrometer (Fig. 7.15) has been reported by Looney [46, 47

O partial pressure is measured by resonance excitation of the CO molecule with two 230-nm photons followengle-photon ionization of excited-state CO molecules. The ionization process is shown schematically in Fig. near formation of CO+ ions with CO partial pressure has been demonstrated over the pressure range 107 to 10

with uncertainties of ± 1015% limited by repeatability of laser pulse energy [47]. This method has also directlymeasured the production of CO by hot filaments of ionization gauges and RGAs. Reduction of CO in the vacuumeasured when gauges were sequentially turned off. The photoionization-based measurements where the beamhrough the chamber do not induce reaction products but are currently limited to selected molecules with a dipo

moment (CO, NO). Nonresonant photoionization with multiphoton absorption using 248-nm photons from a Kximer laser has been demonstrated for numerous species [45] with demonstration of linear production of ions

Kr, and Xe over the pressure range 106 to 103 Pa for fixed laser power [44, 45]. Data indicate an ion current prelation of the form

where is the ion current of theith component formed with cross sectionσi from a laser intensity I Laser foromponent partial pressure, Pi . The exponent of laser

Fig. 7.15Schematic for a resonance-enhanced multiphoton ionization apparatus.







Fig. 7.16A schematic energy diagram for three-photonionization of CO. Hereλ is the two-photonresonance absorption probability,β is the

probability for single photon ionization fromthe n* excited state, and A is the probability

for radiative decay from then* state.

ntensity, n, is 2 or 3 depending on laser power and accidental occurrence of wavelength combinations, giving aesonant excitation. As high-power UV lasers become more cost effective, the use of nonresonant photoionizatartial pressure measurement will probably increase.

.4.2nfrared Absorption Measurement of Partial Pressure

nfrared (IR) absorption has been extensively used to measure part-per-billion levels of H2O, CO, CO2, CH4, NN2O, NO2, NH3, and SO2 impurities in N2, Ar, He, and H2 process gases and in air [4850]. The method requihe impurity to be measured must have IR absorption at a different wavelength than any absorption by the matrariety of gas-phase IR spectroscopies have been used for measuring impurities in matrix gases [48]. The ppb dmits of these methods suggest at least 104 Pa detection capability for partial pressures in a vacuum by IR absohe infrared transmitted through an absorber is described by a Beer's law expression:

where I 0 is the incident intensity,ai (v) is the absorbance (Pa1·cm1) at frequencyv, L is the path length in cm, Pi is tartial pressure of the component being measured. Measurement of partial pressure of a species has been done

modulating the frequency of a tunable diode laser and phase detecting the Ii(v). From the signal and a calibratedbsorbance and cell path length, component partial pressures are measured [49, 50].







Fig. 7.17Schematic of a cavity ring-down measurement system for measurement of partial

pressure of H2O.Application of IR absorbance measurements to vacuum systems has produced commercial instruments for meaf H2O, organics, and metal organic vapors for chemical vapor deposition for thin films [51, 52]. The measure

water vapor partial pressure in a vacuum system with an RGA has uncertainties caused by induced desorption blament or H2O production from filament reactions [8]. Water vapor has a strong IR absorption band such thatpectroscopy is a inviting technique to use. Standard IR absorption spectroscopy for gases uses a gas cell and ream to measure absorbance. However, with the high level of water vapor in the atmosphere, fluctuations of wapor in the reference beam and sample beam paths can cause measurement errors that are difficult to compens

method termed cavity ringdown spectroscopy (CRDS) has been developed which measures the rate of IR absorwater vapor in the sample chamber only [5355].

A schematic of CRDS apparatus for measuring partial pressure in a vacuum system is shown in Fig. 7.17. The lement is the mirrored cavity with reflectance≥ 0.9999 for each mirror. A pulsed laser source of light is used to he measurement process. A fraction of the incident IR light enters the cavity and is multiply reflected. A smallaction exits to the detector, which allows monitoring of the decrease in the internally reflected signal. Byifferentiating Beer's law [Eq. (7.29)] with respect to path length (number of round trip reflections), a relationshe defined between the decrease of monitored signal with time (number of round trips) to the partial pressure oapor present. The beauty of the method is that the measurement of water vapor in the cavity (and vacuum systndependent of the initial laser pulse intensity and external water vapor and depends only on absorption within avity.

5omputer Control, Data Acquisition, and Presentation

Most mass spectrometers used for residual gas analysis or process monitoring are controlled by a computer witoftware provided by the manufacturer or developed by the user. Methods for data acquisition, intensity measulgorithms, and display of mass spectra are often proprietary by the manufacturer or, if developed by an instrumeflect the particular needs of the user. The fundamental data





rovided by a mass spectrometer is an analog scan of the mass spectrum. This records the raw ion current versund displays it on a computer screen or chart recorder. An example of the analog mode is shown in Fig. 7.11 fo

magnetic sector RGA. The bar graph display mode gives a software-interpreted intensity of ions at an M/e which isisplayed at the mass as a vertical line whose height represents the ion current as shown in Fig. 7.18. Data for seaks in a mass range can also be displayed in a table mode. The single intensity number for each M/e detectedepresents the ion current correctly only if the mass scale is well calibrated, and the algorithm for measuring peurrent covers all shapes of peaks that can be encountered in the mass spectrum that the software interprets. Thntensity versus M/e data can also be printed out or used in spreadsheets. Many RGA manufacturers produce cooint outputs or switches where the switch status is controlled by a user-selected ion current level or range for a

M/e . This allows process changes to be made based on the measured ion current of the selected M/e . The third commoftware mode of software control for RGAs is multiple-ion monitoring. This is an extension of the bar graph m

where the ion current of selected M/e components are monitored periodically and their ion current displayed as aunction of time to record trends in composition. This multiple ion monitoring mode is especially useful for pro

monitoring and control.

6esidual Gas Analysis

he dominant use of partial pressure analyzers (PPAs) is for measuring residual gas composition in a vacuum shis mode, a PPA with an open ion source is used

Fig. 7.18Multiple modes of computer-controlled data display: (1) Multiple ion detection showingselected ion currents as a function of time. (2) Bar-graph display of mass and associated

maximum ion current determined by peak measurement algorithm. (3) Table of data givingmass and associated maximum ion currents for all peaks found in a mass

range (Leybold-Inficon, Inc.).





with the ion source immersed directly into the vacuum system in a manner and location similar to the use of anonization gauge.

n mounting the PPA on a vacuum system, the port used must have good conductance to the vacuum system bemeasured, and its location should minimize interference with other gauges. Simple on/off tests with other gaugdentifies any interference problems. A primary function of this mode of operation is to diagnose the condition acuum system by identifying the components of the residual gas as a pumpdown progresses or to diagnose leaontamination problems. In Fig. 7.19, there are three spectra, measured with a QMS using a Faraday detector, te used to determine the components of the total pressure. Note that the display is logarithmic in ion current fro 109 A to more visually display all components detected. The top spectrum shows a pattern of peak groups w

mass of each group spaced 14 amu from the next group. This is characteristic of hydrocarbon oils where fragmroups differ by a mass corresponding to the mass of CH2. The source of this hydrocarbon contamination isackstreaming of forepump oil perhaps during a long period of foreline pumping without adequate traps. A secpectrum in the middle of Fig. 7.19 shows evidence of an air leak in the vacuum system. The largest peak is at nd is probably N2 since there are other air components like O2 at mass 32, argon at mass 40, and carbon diox

mass 44. The significant isotopes 15N and 18O are evident as 15N14N+(29), 16O18O+(34); however, the spec

mass 30 has an abundance too large to be and is probably NO+ generated as an artifact of the ionization

here is also evidence of water vapor at mass 18 with many fragment ions nearby and at lower masses:Ar2+(20), F+(19), OH+(17), O+(16), 15N+(15), N+(14), C+(12), O2+(8), N2+(7), He+(4), H+(1). Thpectrum in Fig. 7.19 shows a clean vacuum system with a base pressure of 2 × 107 Pa. This spectrum is domin

H2O+(18) with an associated OH+ fragment ion at mass 17 and CO+ at mass 28. The remaining peaks are

which are characteristic of a clean stainless steel vacuum system.

election of a filament for an RGA depends on the application and dominant gas present during use. Common materials for PPAs are thoria- or yttria-coated iridium (ThO2/Ir or Y2O3/Ir), tungsten (W), and rhenium (Re). Ahese filament materials are compatible with inert gases and N2. The thoria (yttria)-coated iridium are all "burnesistant" because they are already oxidized and produce electrons while operating at low temperatures (see Ch1). Because of the low operating temperature of these oxide coated filaments, reactions with gases are minimihe filaments have a long lifetime. However, the thoria (yttria)-coated iridium can become a source of oxygen froduction of water vapor, CO, and CO2 in the presence of hydrogen [8]. The oxide layer may also entrain watungsten works best in a reducing atmosphere or for UHV applications. When oxygen is present, the tungsten ormed are volatile compounds which leave the filament, causing thinning and eventual burnout of the filamen

Rhenium at







Fig. 7.19

Mass spectra showing (top) hydrocarbon contamination of a vacuum system, (middle)an air leak into a vacuum system, and (bottom) a clean vacuum system operating at5 × 107 Pa total pressure (Balzers-Pfeiffer, Leybold Inficon).





s normal electron-emission operating temperature evaporates Re atoms and ions, which causes thinning of thelament. Rhenium can also catalyze chemical reactions on its surface. The lifetime of an Re filament in continu a few months, whereas a W filament in a high vacuum or reducing atmosphere can last for years.

7ressure Reduction Sampling Methods for Vacuum Process Analysis

A common use of RGA and closed-source mass spectrometers is measurement of partial pressures or gas compn a vacuum process where the process gas pressure exceeds the normal operating pressure of the mass spectromor these applications, a pressure reduction apparatus is needed to accomplish the transition. For convenience, ansition is often done with a variable leak valve. This is suitable for pressure reduction to allow qualitative vi

he composition of the gas in the higher-pressure region. However, the mass dependence of the flow through thariable leak valve depends on the smallest "critical" dimension of the leak. Figure 7.20 shows the type of flowmolecular, transition, or viscous) for a given critical dimension as a function of the upstream pressure [56]. Foimension, the flow can be molecular, transition, or viscous depending on the upstream pressure. It is desirablestablish molecular flow into the mass spectrometer ionization region where exit flow is normally molecular. Tesults in a simple, mass independent pressure reduction expression between process pressure and ion source pr

Fig. 7.20Diagram to indicate the flow regime of gas in a process by position of thecoordinate of the pressure and critical dimension that limits the flow rate

in the process.





where Ain is the area of the inlet orifice. For a closed ion source, Asource is the sum of the area of the electron entort and are of the ion exit hole. For an RGA whose housing is pumped to reduce the ion source operating pressource is an effective area related to the pumping speed of a RGA housing. By calibration of the ion source toartial pressures, process pressures can be inferred knowing the ratio of conductances into and out of the ion soas in molecular flow. Equation (7.30) becomes more complicated if the flow into the ion source is not molecuequires process-specific calibration. The use of fixed conductances defines a fixed factor relating the pressureshe use of a variable leak requires remeasurement with each setting. Some common fixed-conductance reductio

methods include: (1) molecular flow orifice reduction used for the pressure regime from 103 Pa to 100 Pa for mases, (2) long, narrow-bore capillary tubes used as a viscous flow restrictive element for pressures near an atmr greater, and (3) a capillary tube for viscous flow to a pumped interstage region where the reduced-pressure gampled by molecular flow through an orifice into the mass spectrometer. In the latter method, the compositionow-pressure interstage reflects the composition of the process gas, and the introduction into the mass spectromives a mass independence flow for species as predicted by Eq. (7.30).

8alibration of Partial Pressure Analyzers

alibration of a mass spectrometer consists of establishing a correspondence between the change in a represent

urrent due to a change in partial pressure of the gas which produces the ion [57]. Also see Section 12.3.4, whiiscusses calibration of mass spectrometers. It is useful to define a sensitivity for each gas species to quantify thalibration. Sensitivity is defined as the ratio of the change in ion current ( Ii Ii0) due to an addition of a known parressure ( Pi ) for the particular gas species, where Ii0 is background ion current at the mass of interest:

inear response of the mass spectrometer occurs ifSi is a constant. A measure of deviation from linearity is definhe largest percent deviation from the average sensitivity over a specified range. In Fig. 7.21, the sensitivity of alotted for measurements from 105 Pa to nearly 1 Pa [57]. The linearity is less than 30% for 3 eV ion energy anor 8 eV ion energy for source pressures less than or equal to 3 × 102 Pa. Above this pressure, deviations in senccur due to changes in ion transmission efficiency from the ion source through the rod assembly to the detectohe definition of sensitivity in Eq. (7.31) and the relation for production of ions in Eq. (7.2), the sensitivity of a pectrometer depends on the following physical parameters:

mission current, Ie , electron energy, E , and source temperature,T source (K) can be kept constant as the sourceressure changes and the ionization cross section,σi( E ), is a constant for the species being ionized. This leaves thxpression for ion





Fig. 7.21Relative sensitivity versus ion source pressure for a QMS with differing nonlinearresponse depending on ion energy [12]. Linearity for 3-eV ion energy () is 30%,

and for 8-eV ion energy (×) it is 15%, for pressure less than 3 × 102 Pa.

ansmission, F , as the term that varies above 102 Pa in Fig. 7.21. For the example of low ionnergy, E ion = 3 eV, space charge (ions and electrons) builds in the ion source region at higher source pressureseads to an increase in sensitivity, reaching a maximum at about 2 × 102 Pa followed by a sharp decrease in sens the pressure is increased. This variation of ion transmission with pressure has been the subject of numerousnvestigations [1115]. At the higher gas pressures (1021 Pa), ion space charge can exceed the electron space chlter the electric fields in the ion source and in the entrance to the mass analyzer, as well as within the mass anahanges in effective ion energy can change the extraction of ions from the source and coupling to the analyzer

Repulsion of ions and gas scattering can also occur at high ion current densities and at high gas pressures wher

ee paths of ions become of the order of the dimensions of the analyzer structure. In Fig. 7.21, the sensitivity fperation with 8-eV ion energy, a larger fraction of ions are extracted from the source than for the 3-eV ion enes pressure is increased, there is a gradual decrease in sensitivity. For quantitative measurements, the nonlinearegions should be avoided by keeping the ion source pressure low, electron emission low, and ion energy relativonsistent with good resolution of peaks [1215].

ensitivities for each gas of interest should be determined by introducing a known partial pressure of the gas my a calibrated gauge. For example, pure gas introduced and measured by a calibrated total pressure gauge andorresponding





measurement of ion current can be used to establish the sensitivity [Eq. (7.31)]. Gas introduction needs to be lonough in pressure to be in a linear operating range yet high enough pressure to get good measurements of bothurrent and partial pressure gas addition. Once a set of sensitivities,Si, are determined for the gases of interest, parressures, Pi , present in the ion source can be calculated from the ion currents measured:

he correction term,Σ jRijIj , subtracts fragmentation contributions to theith ion of interest from all higher massed , that contribute a peak. Often there are no fragment interferences; however, the formalism raises the question

nterferences at each mass. The fragmentation ratio, Rij, is the ratio of the observed fragment ion abundance to thebundant peak measured from a mass spectrum of the pure gas that produces the pattern. Examples of abundaniven in Table 7.2; however, the values are typically different for each mass spectrometer. In complicated spects hydrocarbon mixtures, the interferences become significant and the calculation of partial pressures is best ha

with a matrix formalism. For closed ion source mass spectrometers, it is difficult to measure the pressure in theonization region directly such that sensitivities can be referenced to the higher process pressure typically meascapacitance diaphragm gauge. This type of calibration calculates directly the partial pressure in the process frurrents. Care must be taken to differentiate between ion currents generated from the background of the mass

pectrometer and ion currents from species in the process gas especially when measuring small impurity compohis is done by modifying Eq. (7.33) to subtract the background ion currents, Ii0 (when no process gas is flowing),sing sensitivitiesSi(process) referenced to process pressures for gas addition in Eq. (7.31):

rom the partial pressure measurements, gas composition can be calculated relative to the partial pressures mea

his definition of composition ignores peaks that are not in the summation, so it is important to include appropeaks into the summation. A check for a reasonable inclusion of all components is made by comparing the sumalculated partial pressures (ΣiPi ) with a total pressure gauge reading of the sample.

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eak Detection and Leak Detectors

Werner Grosse Bley

n setting up vacuum systems, one of the most important requirements to fulfill is the leak tightness of the vessDepending on the intended experiment or process, different levels of leak testing have to be applied. These ranhe simple observation of the achievable pressure to the use of tracer gases detected with highly sophisticated mpectrometer leak detectors.

Many of these methods, though developed for vacuum science, have now been extended to the nondestructive variety of components reaching from big barrels with leakage rates of about 103 mbar·liter·s1 to cardiac pace

with less than 109 mbar·liter·s1. An overview of all relevant leak testing methods can be found in handbooks oondestructive testing [1].

he following sections deal with all the different aspects of modern leak detection methods of vacuum systemsomponents. It is important to distinguish between vacuum systems, consisting of a vacuum vessel with appropigh-vacuum pumps and components such as tubes, valves and fittings without pumping equipment. In systemetection is often possible with the built-in pressure sensors, whereas for component testing a complete leak de

with a pumping system is needed. Different gases and pressure ranges have to be dealt with; thus even with moutomatic test equipment, basic knowledge of the vacuum physics involved is indispensable for reliable results






1rinciples of Vacuum Leak Detection

.1.1ypes of Leaks and Leak Rate Units

At first sight a leak is always a kind of hole in the wall of a vacuum vessel. However, there can also be porous ermeable areas permitting an undesired flow of gas, usually air, into a vacuum chamber. Depending on the sizeak, the amount of gas flow ranges from less than 1011 mbar·liter·s1 up to more than 1 mbar·liter·s1, which re

more than 11 orders of magnitude. The gas species and mode of flow influence the amount of gas flowing throiven leak, so the characteristics of leaks should be known for a prediction of leakage rates under different opeonditions of a component or system. The pressure-volume units used above were meant to indicate the quantitow. This is most convenient in vacuum leak detection, but other units are also used [2].

Gas flow is normally given in units of particle flow (s1), mass flow (kg·s1), or molar flow (mole·s1). All these escribe the amount of substance moving per unit time through a given cross section. For leak detection in vacystems, the pV throughput of a leak, given in pressure times volume per unit time, is a more convenient unit. Lot the equation of state of the ideal gas, written for molar gas flowdn/dt ,

wheren is the number of moles, R the universal gas constant,T the absolute temperature, p the pressure, andV theolume, it is clear that the gas flow described by pV throughput is only defined for a given absolute referenceemperatureT , often chosen as 296 K (23°C). In practical cases, when leaks have to be found and repaired (not

measured), temperature effects can be neglected. (There is, however, an additional temperature effect in practicetection when dealing with permeation gas flow; see below.)

f required, pV throughput can be readily converted into the amount of particles, mass, or moles passing throughy using the above gas equation of state, Eq. (8.1). Different units of pV throughput are given in Table 8.1.

ike gas flow in general, leak gas flow can be viscous or molecular in nature. As has been described before in , the Knudsen number, being the ratio of mean free path of the gas particles and the typical diameter of the leahannel, determines the type of gas flow. For viscous flow the dynamic viscosity and mean pressure of the gas

mixture determine the flow conductance whereas in molecular flow molar mass alone is important. Gas flow isiven by the product of flow conductance and pressure differential. This leads to a relation quadratic in pressuriscous case and linear for molecular flow:




< previous page page_483 next page >Pag

Table 8.1. Conversion Factorsn for Leakage Rate Units





whereQ is the gas flow,η is the dynamic viscosity, M is the molar mass, and p1 and p2 are the pressures at either sf the leak.

Normally, in vacuum leak detection, the pressures on either side of a leak are atmospheric pressure and ''zero" espectively. Leakage rates under such conditions are callednormalized leakage rates . The above formulae are usehe acceptance level of leakage in a test is given as a normalized leakage rate but different pressure conditions uring the actual test. In this case, one has to make an assumption about the mode of flow. If in doubt, both forhould be tried and, to stay on the safe side, the bigger leakage rate taken as the result of the test.

A special kind of leakage can occur through permeable materials such as rubber, plastics or glues present in gaoints. These are often not recognized as leakage but may contribute a considerable amount of gas flow into thehamber. Permeation gas flow is similar to molecular flow in that it is following a linear pressure law:

where A is the cross-sectional area andd is the thickness of the permeable wall.

he permeability is described by a constant P depending on the material and gas species involved. P is the product ohe solubility and diffusion constant of the gas in the permeable material. It is therefore exponentially temperatuependent. Numbers for P for various gases and elastomers may be found in Yasuda and Stannett [3] and Laurennd Dennis [4].

2otal Pressure Measurements

he simplest way of finding out whether a vacuum system is leaky is by using the built-in total pressure gaugeinds of tests can be distinguished:

Ultimate pressure test (lowest achievable pressure in the system)Isolated pressure test (pressure rise without pumping)

Gas spray test with gas-dependent gauge (for leak localization).

All these tests are only useful for large leaks to be found in systems with pumps and gauges, not for the test ofomponents. During the setup or service of a vacuum system, they are most helpful, especially when no specifietection equipment is at hand.

f the achievable ultimate pressure of a vacuum system is not reached, one can assume a leak. It should be consowever, that increased gas desorption from the walls of the vessel (especially from newly inserted componentlso produce an ultimate pressure higher than normal. If the achievable pressure pe is known from experience and iumping speedS has not changed, the gas flow through the leak can be estimated by the following equation:





where p is the ultimate pressure actually reached in the system, pe is the achievable pressure,Qleak is the leakage rnd S is the pumping speed at the position of the pressure gauge.

f the achievable pressure or the pumping speed is not known, isolation of the vacuum chamber from the pumpystem can help decide whether a leak exists. In a system with volumeV and leakage rateQleak, the pressure rise isiven by

After closing the pump valve, the rise in pressure should be recorded for a suitable period of time. Because therlways be an initial pressure rise due to gas desorption, one will have to wait for some time until desorption hasn equilibrium with the vapor pressure in the gas phase [5]. Then a further pressure rise due to leaks can beistinguished. Figure 8.1 shows the three possible cases. Only leaks with gas flows much higher than desorptioound in this way.

o find gross leaks in a vacuum system, one may take advantage of the fact that the indication of many vacuumepends on the gas species present. This is true for heat conduction gauges as well as ionization gauges becaus

ressure itself but a gas-dependent quantity that is measured in these gauges. For historic reasons the halogen salkali ion sensor) should be mentioned which is able to detect very small amounts of gaseous halogen compouefrigerant gases such as Freon, Frigen, etc.).

f a leak is sprayed with a gas different from air, the air flowing through the leak is replaced by this gas. This rehange of gauge indication according to the different gas heat conductance or ionization probability or, in the che halogen sensor, an increased amount of alkali ions emitted from a heated platinum wire. Helium or methaneas) are very suitable for use with heat conductance or ionization gauges because (a) they have much higher heonductivity than N2 and (b) their ionization probability is much different from N2 (for helium lower by a factor methane higher by a factor of about 2).

Fig. 8.1Pressure rise versus time in a closed vesselafter pumpdown. (a) Pure gas desorption,

(b) pure leakage, (c) leakage and gas desorption.





n practice, the change of gauge indication is rather small since only the leak gas flow is replaced. For systems esorption flow and high pumping speed the resulting change of indication is often difficult to see. A zero suppunction or differential indication is provided by some gauge controllers to support leak detection.

3artial Pressure Measurements

f a vacuum system is equipped with a partial pressure gauge, leak detection is possible in a much more eleganmore reliable way than with total pressure gauges alone. In vacuum systems, normally a quadrupole mass spectead is used as a partial pressure gauge. The halogen sensor with alkali ion emission is also a type of partial prauge, though a very unstable and nonlinear one. For overpressure tests on refrigeration systems ("sniffing"), itstablished itself as a cost-effective instrument.

he type of instrument used most in vacuum systems is a quadrupole mass spectrometer with a mass range staror 2 amu and ending at 100 amu. This enables the experimenter to use nearly every available tracer gas from

ver helium, methane, or argon to krypton or halogen compounds [6]. Each of these gases has a prominent peaange between 1 and 100 amu. If the gas is applied to the outer surface of the vacuum chamber with a concentrTG, atm, a certain partial pressure depending on the leak size and the pumping speed for that gas (at the positi

uadrupole) can be measured inside. A quantitative measure of the total gas leakage rateQleak is given similar to E8.5) for the achievable total pressure:

with the index TG characterizing the tracer gas used. (The tracer gas partial pressure pTG, meas in the vacuum cha

measured by the quadrupole sensor head according to pTG, meas = sM TG is the measuron current on mass M for the tracer gas and sM , TG is the sensitivity for that gas on mass M ).

n most cases, simply the ambient air can be used as the tracer gas: In case of a leak, two peaks on masses 28 aespectively, show up with the characteristic height ratio of approximately 4:1 corresponding to the concentratiitrogen and oxygen in natural air. A typical spectrum of a leaky vessel is shown in Fig. 8.2. The partial pressu also a very powerful instrument for further residual gas analysis. For example, a clear distinction between "v

eaks" (i.e., water vapor desorption) and real leaks can be made which would not be possible by watching the tressure alone.

4Measurement of Leakage Rates with Helium Leak Detectors

he most convenient way of detecting and measuring leaks is with dedicated instruments such as helium leak dn principle, these are stand-alone vacuum





Fig. 8.2Mass spectrum of a leaky vacuum chamber.

ystems with a mass spectrometer, of either magnetic sector or quadrupole type measuring the partial pressure or hydrogen as a tracer gas.

ince mass spectrometer leak detectors include a pumping system of definite pumping speed, a calibration of thncoming helium gas flow in units of pV throughput is possible with suitable reference leaks. Basically, themeasurement of a leakage then follows Eq. (8.7). (In practice, there are different types of pumping and detectioystems in modern helium leak detectors leading to slightly different expressions; see Section 8.8). Helium leaketectors are simply coupled to a vacuum chamber with their inlet port (for the best measurement position see .6). Leak detection of components is also possible because a pumping system is provided in the leak detector.escribed in more detail in the following paragraph.

5elium Leak Detection of Vacuum Components

Generally, leak detection of components should start with an overall (or integral) test in order to minimize the tme. Localization and repair can be very time-consuming and difficult, especially if leaks are not directly acceecause of complicated design of the component. Only if the integral test has shown that the component is leakocalization of leaks can be tried if it seems worthwhile.

n an integral test a definite concentration of helium is applied on the outside surface of the component to be tewhile it is coupled to the leak detector. Except for industrial tests, where a great number of identical parts have ested, in the laboratory a simple plastic bag is most suitable as a hood for such a test.

he test is started by pumping down the component and noticing the background indication of the leak detectomay be set to zero, if possible). Then the hood is put over the component, filled with pure helium, and fixed widhesive tape in such







way that no gas can escape in short terms. (It is important to keep the coupling flange to the leak detector freeood because it is not to be tested). By keeping the hood slack, the applied helium pressure is rather precisely kar, which is important for determining normalized leakage rates (see Section 8.1). For smaller objects a compnclosure is made. On big components it may be convenient to cover only those areas where leaks are suspectespecially welds and flanges.

he leakage rate indication of the leak detector is watched for a short period of time (usually some seconds). Thalue is then taken as the overall leakage rate. An increasing indication over some minutes is usually due to heermeation through rubber gaskets or other permeable elements. Helium permeation gas flow is normally not rs a leakage rate. Because the permeation of air is much lower than that of helium, the resulting leakage rate unperating conditions can normally be neglected in rubber-sealed systems.

Once a component has been shown to be leaky in the integral test, repair of the leaks is normally necessary excery inexpensive parts. Hence, leak localization is the next step. To find the leaks, after removal of the hood a fure helium is directed on the object's walls while its inner volume is still coupled to the leak detector. If a leakhe helium jet, the leak gas flow is replaced by helium which is pumped away and detected by the leak detector

ecause flow conditions in the component's volume are normally molecular, a very quick response within a few

econds or even less can be expected. This enables the tester to get a definite correlation between his spraying nd the leak response, so the position of the spray gun will be very close to the leak when an indication is noticner the helium jet, the more precise the leak localization.

o find small leaks in the vicinity of big ones, it is sometimes necessary to mask or close the big leaks. Maskinone by covering leaky areas with some foil or sticky tape. Temporary closing of leaks is best done by applyinlcohol with a syringe that clogs the leaks. After the evaporation of the alcohol the leak opens again without anamage to the system.

o perform a leak test within reasonable time, some understanding of the time aspects of a test is necessary. Pumme and response time are the crucial parameters.

n component testing, a certain pumpdown time is necessary until the pressure in the test object is low enough eak detector is ready for measurement. This time depends very much on the surface conditions of the test objehe type of leak detector involved. In general, the maximum inlet pressure of the leak detector has to be reacheumping the component down before any leak indication is possible. As gas desorption from the test object's warts below about 0.1 mbar, the pumpdown curve flattens appreciably below that pressure. The time law of preecrease for volume gas only (i.e., without desorption) is

where p0 is the starting pressure,V is the object's volume, andS is the pumping speed of the leak detector pumpinest object. If the pressure is only governed by gas desorption from metal walls, the pressure decrease after desoas started can





pproximately be described by the expression

whereQ0, des is the initial desorption gas flow at timet 0 and S is the leak detector pumping speed.

Although a fast pumping speed of the leak detector accelerates the pump process, the slope of the pumpdown cmuch less steep with the same pump once the desorption regime has started below 0.1 mbar (see Fig. 8.3). In ineak detection pumping time is lost time. Leak detectors with maximum inlet pressures above 0.1 mbar have andvantage when rapid cycle testing is required.

When trying to localize leaks by spraying helium, a rapid signal response is important for unambiguous resultsmple exponential processes, response time is expressed as a time constant (rise to 63% of the equilibrium leve

espective decay of signal). The overall response time is dependent on both (a) the properties of the leak detectnd (b) the test object. This means that in most cases it cannot simply be expressed by one time constant alone.ehavior can be described by three parameters:

The electrical response time needed to measure and average the signal, described by a time constantt e of the leaketector's signal processing unit



Fig. 8.3Pumpdown curves for three different pumping speeds.





The volume response time needed to pump away gas from the object's volume, described by a vacuum time cV

The diffusion response time needed by the tracer gas to traverse regions of high total pressure, described by aiffusion time constantτD.

he first time constant is dependent on the leak detector's preamplifier and the averaging by the internal softwaecond time constant depends on both (a) the basic principle and actual mode of operation of the leak detector ection 8.9) and (b) the test object's internal volume. The third is mainly a property of the vessel's dimensions a

otal pressure conditions under test. The electrical and volume response time can be shortened by sacrificing loetection limit. Avoiding the most sensitive amplifier range by looking only at leakage rates above a certain lev

much shorter electrical signal response can be achieved.

f a big test volume is involved, an additional roughing pump will reduce the vacuum time constant, but it will educe the detection sensitivity for the tracer gas, because of operation in a partial flow mode (see Section 8.6).

he diffusion time constant is important mainly in big vessels with high total pressure. In such cases there is anptimum total pressure for minimum response time [7]. It should be noted that in such cases helium is a very gacer gas because of its high diffusion velocity.

6elium Leak Detection of Vacuum Systems

Vacuum systems basically differ from components in that they incorporate a roughing or high-vacuum pumpingometimes big components have to be treated as a system because an additional vacuum pump is necessary to own the volume in a reasonable time. The principal tests, integral tightness and leak localization, are quite theor simple components, but the sensitivity of the test will be appreciably lower because a portion of the incominas is pumped away through the auxiliary pumping system without producing a signal in the leak detector. Thiavorable when rather big leaks are expected and the leak detector would be driven into overflow nearly all theareful consideration of the partial-flow sensitivity is necessary, and the connection position of the leak detecto

acuum system is of great importance for both sensitivity and response time.he general partial-flow arrangement found in every vacuum system leak test situation is shown in Fig. 8.4. Be

eak detector always shows a signal proportional to the incoming flow of tracer gas, the ratio of the total leakagow QL to the gas flow portion into the leak detectorQLD has to be calculated. With a system pumping speedS systnd a leak detector with inlet pumping speedS LD, this is given by

f a partial-flow factorγ = S syst/S LD is defined, the indicated leakage rateQLD is correlated to the true leakage rat





Fig. 8.4Partial-flow configuration in the leak test of a vacuum system.

o estimate an order of magnitude in practical cases, 1 +γ can be replaced byγ with good accuracy. The reductionensitivity can be several orders of magnitude if the leak detector is connected to a vessel pumped by a high-vaump. This problem can be avoided by choosing a more suitable position to connect the leak detector.

n principle, a leak detector can be connected to a vacuum system in two ways: in place of the pumping systemow through leak detector) or in parallel with it (partial flow). The full-flow connection gives the best sensitiviue quantitative measurement because all the gas must pass through the leak detector. However, this is only po

he total gas flow out of the system can be pumped by the leak detector's built-in pumps. Often this is only possome time is spent in degassing. In addition, some valving is necessary to shut off the pumps of the system undll other cases, the leak detector has to be connected in a partial flow manner.

hree different locations for the partial flow connection of a leak detector to a high vacuum system are possibleo the high vacuum chamber, between the high vacuum and backing pump, and at the exhaust of the backing puhese are shown in Fig. 8.5. In principle, true leakage rate measurements can be made at all three positions aftppropriate calibration. There are, however, certain peculiarities of the system that have to be known to achieveasonable results.

Although the most obvious, a direct connection to the high-vacuum chamber is normally not the most effectivese a leak detector. Because the pumping speed of the high-vacuum pump is very high compared to the leak denlet pumping speed, the sensitivity is reduced by some orders of magnitude (large partial-flow factorγ ). This meanhat the detection limit for leaks is less by the same amount. This is normally unacceptable for leak detection onacuum chamber.here are situations where one has no choice but to connect the leak detector directly to the high vacuum, usuadsorbing or gettering pumps such as cryo or sputter ion pumps are installed in an ultrahigh-vacuum (UHV) chhese cases, however, there is the risk of contaminating a clean UHV chamber by hydrocarbons diffusing backwom the leak detector inlet port into the vacuum





Fig. 8.5Positions for the connection of a leak detector to a high-vacuum system:(a) directly to high-vacuum chamber, (b) between high vacuum and

backing pump, (c) at exhaust of backing pump.

nder test. Only "oil-free" or "dry" leak detectors (see Section 8.8.5) can avoid this problem. The best solution ases is to install a quadrupole mass spectrometer on the system and use it not only for residual gas analysis bueak detection (see Section 8.3).

Normally the pumping system of a vacuum chamber consists of several pumping stages or separate pumps. Thpossible to use the optimum connecting position for the leak detector. With a two-stage pumping system, the

osition is between the high vacuum and the backing pump. Here, the pumping speed of the backing pump is mmoderate partial flow factorγ ) and the intermediate volume between the pumps is small enough to keep sufficieensitivity at a reasonable time constant. Additionally, the high-vacuum system cannot be contaminated byackstreaming oil because the high-vacuum pump's compression ratio will prevent that.

f there is no appropriate access either to the high-vacuum chamber or between the high-vacuum pump and theump, the leak detector has to be connected at the exhaust of the backing pump. Because the exhaust pressure tmospheric, a sniffing device has to be used for that purpose. In the simplest case, this is a capillary of appropength and diameter in order to reduce the pressure from atmospheric to the maximum inlet pressure of the leaketector. The sensitivity is greatly reduced by the partial-flow factor given by the ratio of the flow of the snifferhe total gas flow.





7pecial Methods and Other Tracer Gases

racer gas leak detection with mass spectrometer leak detectors is such a versatile and sensitive method that it ot only for vacuum systems or components but also in nondestructive testing of gas pressurized or hermeticallarts in modern production processes. A short description of such test methods will be given in the following.

Hermetically sealed parts such as electronic packages or relays cannot be connected to a leak detector and testepraying them with tracer gas. In some cases they can be filled with tracer gas (especially helium) during the

manufacturing process, but even this is not possible for integrated circuit packages. To test such devices for tighe so-called "bombing test" was developed. The parts are placed in a chamber where they are pressurized withor several hours. If a leak exists, a certain amount of helium will enter the inner volume of the test object. Aftehe part is taken out of the pressure chamber; and after some waiting time, necessary for desorbing helium fromuter surfaces, the part is placed in a vacuum chamber connected to a leak detector. Now the escaping helium cetected, and even a quantitative measurement is possible with some computation and calibration [8]. The detemit is somewhere in the 108 mbar·liter·s1 region.

Many industrial systems have to be leak-tight under pressure. Often these parts cannot be evacuated or have no

ppropriate connection flanges for a leak detector. To test such objects, sniffing devices were developed for heletectors. As mentioned earlier, the simplest way to make a sniffer for a helium leak detector is to use a capillaose with a fine opening at one end and connect it to the inlet port of a leak detector. To achieve maximum senhe gas flow through the hose should produce the maximum tolerable inlet pressure for the leak detector. If the his device is slowly moved across the surface of the pressurized object, escaping tracer gas will be detected anndicated by the leak detector. Detection limits of 1 × 106 mbar·liter·s1 and even lower can be achieved.

ecause pressurized objects are often filled with gases different from helium, one would like to perform leak tey using the filling gas itself. Recently, the introduction of new refrigerant fluids has accelerated the developm

mass spectrometer sniffing leak detectors for those gases. In principle, they do not differ from the helium sniffietectors except that gases with higher masses can be detected only with quadrupole mass spectrometers. Therevere problems in sensitivity or mutual interaction of peaks, so each gas species has to be treated separately.

or vacuum leak detection, tracer gases different from helium are not very convenient because either they are phe ambient atmosphere in rather high concentrations or their properties (toxicity, inflammability, etc.) do not mhem very suitable for spraying into the environment. Gases such as methane, CO2, argon, or other noble gasessed for leak detection of vacuum systems if a quadrupole mass spectrometer is present and no helium is availa

8Mass Spectrometer Leak Detectors

Mass spectrometer leak detectors are units containing a mass spectrometer and a high-vacuum pumping systemroducing the necessary vacuum for the mass





pectrometer (below 104 mbar) and pumping the tracer gas in a stable and reproducible way. Although masspectrometers have been known since the beginning of this century, the early ones were big and expensive systequiring a vacuum pressure below 106 mbar.

he solution to many problems came about with the invention of the helium leak detector based on a small mapectrometer. The need for the detection of really small leaks in an industrial plant was motivated by the requiref the uranium enrichment technique necessary for producing the atomic bomb in the United States in the 1940

he next sections dealing with different types and specifications of helium leak detectors will discuss problemsesign of a leak detector vacuum system and the state of the art today.

.8.1Mass Spectrometer System for Helium Leak Detection

Dedicated magnetic sector mass spectrometers with a mass range from 2 to 4 amu are used in helium leak detecmost frequently. These spectrometers are designed to be of high sensitivity and good resolution even at high prup to 103 mbar) and under rather dirty vacuum conditions (oils and vapors from pumps and test objects).

he first helium mass spectrometer for industrial use was designed by Nier [10]. It was an all-metal magnetic sf reasonable small size that could really be used under industrial conditions. The mass spectrometer itself had asic features known about modern helium spectrometers. It was connected to the test object by means of a lea

while the object was pumped by an auxiliary pump. The response time in such a topology was rather long becawas nearly no pumping speed at the inlet port of the arrangement. Nevertheless, a response ''within a few seconhat time was judged to be "a rapid response."

.8.2Direct-Flow Helium Leak Detectors

or some time, helium leak detectors were operated in a partial flow mode. In this mode a portion of the tracer ot reach the detection system (the mass spectrometer plus its pump system) and the sensitivity is limited. On tand, the total pressure in the test object can be rather high, resulting in short pumpdown times.

he introduction of a liquid nitrogen (LN2) trap made it possible to open the inlet valve wider without having too long for water vapor desorption to become low. Now a "crossover" from roughing to full-flow measuring wossible. This means that the total gas flow including all tracer gas from the test object flows through the leak digh-vacuum system and is measured by the mass spectrometer. The unit is a "direct-flow" leak detector. The vchematic of a modern direct-flow leak detector is shown in Fig. 8.6. In such an arrangement the partial pressurelium in the mass spectrometer, pMS, He, generated by a given leakage rateQHe flowing into the leak detector isiven by

whereS HV, He, is the high-vacuum pump's speed for helium.





Fig. 8.6Vacuum schematic of a modern direct-flow leak detector (Leybold model UL400).

To find out the crossover point, first the bypass valve is opened to check for pressurerise in the mass spectrometer. Only if the pressure rise keeps below a certain level,

the inlet valve is opened for direct-flow operation.

he intrinsic sensitivity sDF of a direct-flow leak detector, defined as the ratio of the partial pressure of tracer gagenerated in the mass spectrometer) to a given leakage rate [11], can therefore be expressed by the equation

n order to achieve enough sensitivity in a direct-flow unit, the high-vacuum pumping speed for helium,S HV, He, ishrottled to typically 1050 liter·s1 and can even be throttled by another factor of 10 to achieve ultimate sensitiv"throttle valve" in Fig. 8.6).

he overall sensitivity (defined as the ratio of output voltage to input leakage rate) is the product of several term sD only one of these (see Section 8.9).



he "crossover"that is, the change in pumping conditions from roughing to measurementis always the most critroblem to be dealt with in a direct-flow leak detector. That is why numerous solutions were developed to makasy as possible for the user. In early units, the user had to manually open an inlet throttling valve while carefulbserving the pressure in the mass spectrometer to keep it below 104 mbar. This procedure works best with LNap, but there is no protection for the filament if a sudden air inrush takes place. That is why solenoid valves w





ntroduced which are automatically opened at the crossover point (expressed either as pumping time or as inletnd closed rapidly if the pressure rises. Now a new problem arises: Depending on the amount of water vapor onnner surfaces of the test object, the crossover point is not known in advance. For production testing of the samuick cycles, the crossover point can be found and set by trial and error. For a variety of objects exceeding a ceolume, this method is not practicable either with or without LN2 because the crossover pressure will vary withifferent rates of water vapor desorption.

o overcome those crossover problems, pressure-controlled piezo- or motor-driven inlet valves allowing continow control are used in the latest direct-flow leak detectors. The leak detector in Fig. 8.6 uses the bypass valvehecking the pressure before crossover. Although, after these developments, direct-flow leak detectors are reliaheir reliability is very much dependent on the treatment they get from the operator. Frequent use without LN2,f "dirty" (i.e., oily) objects, and switch-off without obeying the proper warming-up procedure of the LN2 trapo high service expenses. So there was more and more demand for leak detectors that can really operate withou

.8.3imple Counterflow Helium Leak Detectors

he solution of LN2 problems came about when the so-called "counterflow" of helium was developed [1214].

Counterflow" is based on the property of all molecular pumps, diffusion and turbomolecular pumps, to have aompression ratio for the gases pumped. This means that if a certain gas species with a given partial pressure pFV isresent on the fore-vacuum side, there will be also a definite partial pressure pHV of that gas on the high-vacuum she relation of these partial pressures is given by the zero-flow compression ratio K 0 of the molecular pump

wheren is the rotational speed of the pump (or the vapor jet speed in a diffusion pump),α is a proportionality constontaining the geometrical data of the pump, and M is the molar mass of the gas involved.

As Eq. (8.14) shows, K 0 depends exponentially on the square root of the molecular weight. This means that for as like helium the compression ratio is orders of magnitude smaller than for nitrogen or water vapor emergingest object. Connecting the test object to the fore-vacuum line of a leak detector therefore results in a measurabgnal in the mass spectrometer, whereas the total pressure in the spectrometer is kept sufficiently low. The senf the leak detector can be adjusted by the parameternthat is, the rotational speed of a turbomolecular pump or theating power of a diffusion pump, respectively.

he basic vacuum schematic of a simple counterflow leak detector is shown in Fig. 8.7. In such an arrangemenartial pressure of helium pMS, He in the mass spectrometer generated by a given leakage rateQHe flowing into theak detector is given by

whereS FV, He is the fore-vacuum pump's speed for helium.





Fig. 8.7Basic vacuum schematic of a counterflow leak detector

with turbomolecular pump.

he intrinsic sensitivity sCF of a counterflow leak detector, expressed by the relation of the partial pressure of trenerated in the mass spectrometer by a given leakage rate, may therefore be expressed analogous to Eq. (8.13

omparing this equation with Eq. (8.13) for the direct-flow leak detector, it is obvious that a counterflow leak dwith the same intrinsic sensitivity as a direct-flow one can be built by making (S FV, He· K 0) in the counterflow macqual to sHV, He in the direct-flow one. As a typical example a fore-vacuum pump of 0.3 liter·s1 is combined wurbomolecular pump with reduced speed to yield a helium compression ratio of 100. In this case we have (S FV, He

30, which is the same as for a typical direct-flow leak detector. If the follow-up detection system is also the sotal sensitivity (see Section 8.9) is equal.

When the test object is connected to the fore-vacuum line no "crossover" problems arise. Once the pressure haselow the tolerable limit of the high-vacuum pump, the fore-vacuum valve is opened and measurement is posslong with no need for an LN2 trap, made possible a completely new generation of helium leak detectors whiche fully automated because of the ease of the pumping cycle. This makes them simple and rugged enough to benly by scientists but by everybody in industry.

ike all technical systems, the counterflow leak detector is not free of disadvantages. The weakest point is the facuum pump now pumping the test object determining the signal stability and the response time for the heliumecause its pumping speed is low, only small test objects can be tested in the reasonable time of some





econds. The detection limit, given by the signal stability, is also limited to some extent (see details in Section 8pecial fore-vacuum pumps with high pumping stability are therefore necessary to build a good counterflow leetector.

n the direct-flow leak detector the high-vacuum pump with much higher speed is pumping on the object after rossover. Instabilities of the fore-vacuum pump are not contributing to output signal stability because of the hiompression ratio of the high-vacuum pump. That is why for very low detection limits (below some 1011 mbarstrongly throttled direct-flow unit with an LN2 trap is still unbeatable.

o combine the simplicity and ruggedness of the counterflow principle with the speed and sensitivity of the dirrinciple, advanced counterflow leak detectors were developed. They involve a more complicated pumping anystem.

.8.4Advanced Counterflow Helium Leak Detectors

One of the first advanced counterflow helium leak detectors was the cabinet model UL500 (Leybold AG, Germwhose vacuum diagram is shown in Fig. [8.8]. The heart of this system is a twofold turbomolecular pump [15].ncorporates two pumps in one housing pumping in opposite directions and backed by one fore-vacuum pump.ormer high-vacuum side is pumping the leak detector's inlet port, thus boosting the backing pump's speed. Thienerates an extraordinary high inlet pumping speed of about 12 liter·s1 for helium. The pumped helium is diffackwards through the other half-pump into the mass spectrometer in a counterflow

Fig. 8.8Vacuum schematic of advanced cabinet counterflow leak detector for big volume

testing (Leybold model UL500). The turbomolecular pump has two separate sets ofstages in one housing for high inlet pumping speed and counterflow, respectively.The roughing pump assists the measurement mode via a coupling valve opened to

the fore-vacuum pump when roughing is completed.







manner. The roughing pump fulfills an additional purpose after roughing is completed at about 0.1-mbar inlet pVia the coupling valve some speed is added to the backing pump to enable an easy crossover by keeping the foacuum pressure below 0.1 mbar. Otherwise, when the turbomolecular pump takes over the inlet pumping, the acuum gas flow would suddenly be much too high for the backing pump to keep the pressure below 0.1 mbarhis unit, volumes up to 100 liters can be tested down to 2 × 1010 mbar·liter·s1 with a response time of secondshe use of LN2.

Another version of a twofold turbomolecular pump was used in an advanced portable counterflow leak detectoHLT150/160 model of Balzers the turbomolecular pump rotor is divided into two stages of pumping in the samirection. The inlet is connected in between the two stages so that the lower stage works as a highly stable and acking pump for the counterflow procedure, for which the upper pump stage (connected to the mass spectrommployed. For dirty systems with higher pressure up to 0.5 mbar the complete turbomolecular rotor is used forounterflow, and the oil-sealed backing pump alone pumps the object. This portable unit can be used for servicurposes where clean components as well as dirty systems with higher pressure have to be tested down to som

mbar·liter·s1.

y replacing the lower half of the turbomolecular pump with a molecular drag type stage (see Chapter 4), it is po create leak detectors with a maximum allowable inlet pressure in the range of millibars or even tens of millib

elps to decrease the pumping time for components and allows the testing of systems in the low vacuum range sing partial flow and big roughing pumps.

.8.5Oil-Free and Dry Helium Leak Detectors

he presence of an oil-sealed rotary pump at the inlet port of a counterflow leak detector always produces a sliontamination of the test object depending on the pressure conditions and the testing time. Advanced counterfletectors avoid this problem by not roughing down to the low pressure rangethat is, at most only down to 0.1 mhis pressure region, viscous flow conditions prevent the oil from the fore pump backstreaming into the test objetectors of this kind are sometimes called "oil-free" because their inlet port is kept free of oil and thus the test ept reasonably clean for later use under UHV conditions.

here is always the risk of wrong operation producing oil contamination of test objects even with "oil-free" uniecause there are conditions of operation where oil backstreaming from the roughing pump cannot be avoidedompletelyfor example, for rather big leaks under low pressure, where the roughing pump is still at the inlet poperating in partial flow. To keep sensitive test objects completely hydrocarbon-free, especially for the semiconndustry, completely "dry" leak detector systems are required. The technical basis for "dry" counterflow leak dere molecular drag pumps with a very high fore-vacuum compatibility up to 10 mbar or more. These enable rouacking with diaphragm or scroll pumps, thus completely avoiding any oil in the system. Dry leak detectors arather expensive and bulky units because they are derived from existing counterflow models by replacing forepcroll pumps or a combination of diaphragm and small drag pumps.

he most important problem in dry leak detectors is the recovery time after having seen some helium from a leecause the dry fore-vacuum pumps are all operating





ery close to their ultimate pressure limit, their pumping speed is nearly zero. To overcome this problem, purgedmitted into the fore-vacuum line. Ideally, this gas must be free of helium. Such pure gas is difficult to supplyspecially for a portable unit. In practice, ambient air is used. The natural helium content of atmospheric air themit on the detection of small helium leaks.

ince the development of dry detectors has just started, one can expect that by lowering the detection limit andme as well as achieving a quick pumpdown, these will be inexpensive and simple solutions in the near future.

9pecifications of Mass Spectrometer Leak Detectors

Helium leak detectors are described by a set of specifications like all analytical instruments. The three most imharacterize the performance of a leak detector are sensitivity/detection limit, response time, and maximum allonlet pressure.

here is often confusion about the terms "sensitivity" and "detection limit" of a leak detector. The minimum deeakage rate (the detection limit) is determined mainly by the stability of the detection system. It is given by theetectable electrical signal that the preamplifier and processing unit can distinguish from noise and drift. Overaensitivity s0 of a unit is defined as the ratio of the output signal Si to the leakage rateQ. The following relation ho

his has to be distinguished from the intrinsic partial pressure sensitivity of a leak detector as described in Eqs.nd (8.16):

where s is the intrinsic sensitivity sDF or sCF of a direct or counterflow leak detector ( s has the unit (liter/s)1), sMS he mass spectrometer sensitivity (unit: A/mbar) and samp is the amplifier sensitivity (unit: V/A). The minimum

etectable leakage rate (detection limitQmin) is given by the overall sensitivity s0 of the unit and the minimumetectable signal Simin:

imin has to be defined by means of stability criteria such as signal noise and drift. Such a definition has been xample, in ISO 3530 (and the older AVS 2.1 standard) by stating that the minimum detectable signal is given o-peak noise and the amount of drift in a specified short time interval. As the noise can be severely influencedme constant of the signal amplifier or the follow-up averaging software, the time constant has always to be sta

ogether with the detection limit specification. For modern leak detectors having very low drift, the minimum dgnal is merely given by the peak-to-peak noise of the signal. The performance of a specific unit can be assessme constant it needs to achieve a given detection limit.





he shorter the response time of a leak detector, the better it is suitable for industrial testing in short cycles, espor leak localization. The required minimum detectable leakage rate normally puts a first limit to quick responsecause it requires a minimum time constant. The response time of a leak detector is, however, made up of sevompletely independent contributions, nearly all of which also have some influence on the detection limit:

Gas transport time constants are (a) diffusion time in high-pressure connection piping from the test object and (acer gas pumping speed at the inlet port of the leak detector (or the outlet port of the test object) together withbject's volume (or at least the leak detectors dead volume in its valve system). Whereas diffusion time in theonnection piping is not a property of the leak detector and can be avoided by an appropriate setup, the inlet pupeed is most important for the response time in a test. It depends mostly on the leak detector principle. It is smsimple counterflow, reasonable in a classical direct flow, and maximum in an advanced counterflow leak detebooster pump. Only in the latter can the inlet pumping speed be increased without a reduction in the intrinsic

ensitivity, which would have a negative effect on the detection limit according to Eq. (8.19).

he electrical time constants in a leak detector are (a) the preamplifier's time constant (the longer it is, the moreensitive it is) and (b) the time constant resulting from any averaging procedure in the software for smoothing toise. In order to generate a reasonable signal from the very small ion current produced in the mass spectrometertain gain of the preamplifier at the ion collector is necessary. The higher the gain, the more noise is produced

ome time constant is required to smooth the signal again. For low noise, one has to achieve high gain in the firf amplification. In order to measure larger signals with the same unit, switchable amplifiers are used. These gedditional noise, so optimization is necessary.

here have been numerous solutions to the problem of optimizing the time constant, noise, and sensitivity.Microprocessors combined with advanced analog semiconductor devices enable still new ways of preamplifierModern leak detector amplifiers are capable of quantitative measurement of 1 × 1015 A with a time constant ofhan a second.

A leak detector is different from an electrical measurement instrument in that not only does it have to measure uantities of tracer gas, but the measurement of the tracer gas should be independent of other gases such as air apor flowing from the test object into the leak detector. For a leak detector to be most useful, the pumpdown oreparation time should be as short as possible. This means that the test object should be tested at the highest pressure, resulting in a high amount of air and water vapor escaping from the object and flowing through the leetection system. On the other hand, a mass spectrometer has specific limits of linearity and sensitivity dependotal pressure (see Chapter 7, "Partial Pressure Analysis"). Therefore, the spectrometer has to be protected againd vapors different from the tracer gas.

Dealing with mass spectrometer leak detectors, depending on the test specimen, two different concepts to descrandling have to be used. When connected to systems with their own pumps that generate a certain total pressueak detector has to tolerate this as its inlet pressure. The limit of "maximum tolerable inlet pressure" has to bepecified, and the leak detector with the highest value will be most useful. In testing components, the leak deteumps down the object. Now the





hortest pumpdown time until the detector is ready for a leak measurement will characterize the best unit. Theumpdown time is given both by the maximum tolerable inlet pressure and by the pumping speed for air at thether words, it is given by the "maximum tolerable total gas flow" that the leak detector vacuum system can be

measurement conditions. The actual total gas flow from the test object will decrease exponentially with time abpproximately 0.1 mbar (volume gas flow), but only inversely with time below that pressure (desorption gas flo

maximum tolerable inlet pressure of more than 0.1 mbar indicates extremely short pumpdown times because thesorption time regime is completely avoided.

10uantitative Leakage Rate Measurements

n recent times, the demand for quantitative leakage tests has increased sharply. This is due to the standardizatiouality systems by the ISO 9000 series of standards. Each quantity in a production process has to be measured andards traceable to a national standard. For quantitative measurements of leakage rates, such traceable stand

eference leaks calibrated against transfer standard leaks from the respective national laboratory.

Helium leak detectors are not fundamental measurement instruments because the measurement of leakage rate n instrument is based on a set of parameters that are not precisely known. The most important of these are the

peed of each vacuum pump at the respective total pressure, the sensitivity of the mass spectrometer, and the sef the preamplifier. Even when a leak detector is once adjusted to yield the "true" value of leakage rate, its longability is normally not sufficient to use the leak detector itself as a standard.

herefore, a helium leak detector needs frequent recalibration with a standard leak to ensure precise measuremractice, such a calibration is often done with only one leak in the 108 mbar·liter·s1 range because of the difficet a leak calibrated in different leakage rate ranges. Because the measurement range of a modern leak detectoreaches from some 1010 mbar·liter·s1 up to some 102 mbar·liter·s1 or even more, the accuracy of measurementanges far away from the calibration point is not really known. In other words, the linearity of the leak detectornown. In fact, because no traceable leaks with sufficient accuracy are available in the whole range, the uncertig or small leakage rates can only be estimated from the uncertainty of the components involved. This is normufficient for acceptance tests of industrial parts, but the operator should be aware of the limited accuracy if mealues get close to acceptable leakage rates. Safety margins should be used.

alibration leaks are leak artifacts that produce a definite amount of tracer gas flow under definite pressure connd with a good long-term stability. In principle, both permeation or conductance (capillary)-type leak artifactssed for that purpose. Because of the risk of clogging, however, permeation leaks are used if possible [16].

At present, traceability of the leakage rate is only achieved in the main European countries and the United Stathe national laboratories have established primary leakage rate standards and a calibration service for helium leeakage





ates in a certain range [17]. Primary standards for helium leakage rates exist in the range of some 106 mbar·litown to some 109 mbar·liter·s1. Helium transfer leaks are normally made in the form of a quartz permeation turessurized by several atmospheres of pure helium which is kept in a pressurized reservoir. Such an arrangemeompletely safe against clogging and has a long-term drift (depending on the volume and pressure of the reservhe leakage rate) in the order of 0.5% per year. Such transfer standards are used by national calibration servicesenerate calibrated standard leaks which in turn are used to calibrate and adjust helium leak detectors [18].

Having a leak traceable to a primary standard in hand, this may be used to calibrate leaks for everyday work. Tmethods are available:

Method A : Calibration by comparison using a mass spectrometer (normally built in a leak detector for measurineaks) as the transfer device

Method B : Calibration by direct volumetric measurement of gas flow using a calibrated capillary and a timer

Method A is the easiest way to do a calibration, especially when a leak detector can be employed (as for heliumis, however, limited to the range of linear measurement of the leak detector and the available standard leaksa

eakage rates below 1 × 106 mbar·liter·s1. One can use either one or two standard leaks for comparison. The lehe unknown leak has to be in between the values of the two standard leaks. This allows an estimation of uncerncluding linearity errors of the leak detector used. Using one leak is only reasonable if its value is at least in thecade as the "unknown" leak because otherwise the (normally unknown) linearity error of the leak detector mmpossible to state any uncertainty of the measurement. If, however, the leak is very close to the reference leaknearity error can be neglected.

f both the reference and the "unknown" leak are of the same type and hence have the same temperature dependemperature correction is necessary if both leaks have been stored at this temperature for a sufficiently long tim

Method B is only applicable to leaks greater than 1 × 106 mbar·liter·s1 because of possible temperature effects measurement capillary. It requires a skilled worker capable of handling a calibrated capillary with a water or oimoving under the action of the escaping tracer gas from the leak. Leaks discharging to vacuum and atmospherealibrated in this way. The uncertainty of measurement is mainly determined by the accuracy of reading the capow constant the temperature can be kept, and the duration of the measurement.

is often required to convert leakage rates measured with a given tracer gas into leakage rates for a different gven a liquid present under actual process conditions. Because the different modes of flow depend strongly on nd pressure which may not be constant in the leak channel, an analytical computation is rather difficult when esults are required. There are rather precise numerical predictions possible for different gases, if a set of characor a given leak have been measured with one gas specie [19].

o determine rejection levels for a tracer gas test, first acceptable leakage rates for the process fluid have to bestablished from process considerations (lifetime,





nvironmental aspects, cost, etc.). The following formulae can then be used to determine rejection limits for a tpecific tracer gas different from the process fluid. Much experience in calculating such limits has been accumuhe packaging of radioactive materials [20].

or the conversion of leakage rates when gas species, temperature, or pressure differential are different during tperation of a system, the following equation gives the relations in the case of molecular flow:

whereT are absolute temperatures, M are molar masses of the flowing gases, and∆ p are the pressure differentialsuring test and process, respectively.

or viscous flow conditions, the conversion of leakages has to be done according to

where p1 and p2 are the upstream and downstream pressures for test and process, respectively, and theη are theynamic viscosities of the flowing gases. The effect of temperature is accounted for by the effect of temperaturiscosity, varying as the square root of temperature (see Section 1.10).

o apply the above equations, the conditions of flow have to be stated. Having atmospheric pressure on one sidacuum of less than 1 mbar on the other side, it is practical to assume molecular flow (flow dependent on pressifferential) for leakage rates below 107 mbar·liter·s1. Viscous flow (flow dependent on difference of squaredressures) can be assumed for leakage rates above 104 mbar·liter·s1. Intermediate leakage rates have to be convpplication of both flow considerations and a conservative determination of the resulting rejection level.

11Mass Spectrometer Leak Detectors for Other Tracer Gases and Future Developments in Leak Detection

he technique of mass spectrometer leak detection is becoming more and more a standard method of nondestruesting in industry. This means that although the operation of the mass spectrometer as the heart of the leak deteased on a high-vacuum system, the test objects are increasingly parts of systems such as valves, cans, gas supnd so onthat is, systems normally operating under atmospheric or overpressure. Some of these systems alreadyspecific gas or liquid that can be used for leak detection purposes. So there is a demand for tracer gas leak deapable of detecting gases different from helium.

A specific application in this field was generated by the introduction of new refrigerant fluids caused by the pro

zone layer damage by the old ones. Very sensitive, but at the same time selective, leak detection on closed preefrigerator systems became necessary. Although this is not a vacuum application, it took only a short time formanufacturers to modify the existing helium leak detectors and





evelop powerful tools for the testing of such systems. The sniffing technique (see Section 8.7) and the quadrumass spectrometer well known from residual gas analysis in vacuum vessels were combined to produce a new mass spectrometer tracer gas leak detector. Very compact, transducer-like quadrupole mass spectrometers desigecent times made this development possible.

n principle, this new kind of leak detector could easily be modified to operate in a vacuum testing mode. Howases different from helium or hydrogen cannot easily be separated from desorbing water by traps or counterfloperation, the detection limit can be expected to be very poor or the pumpdown time long. So it seems that ligh

will remain the best choice as tracer fluids in vacuum leak detection for the time being.

or the future of tracer gas leak detection, one can expect that new, less complicated yet well-performing detecystems will be developed to replace the mass spectrometer and high-vacuum systems of present units.

References

. R. C. McMaster, ed., Nondestructive Testing Handbook , 2nd ed., Vol. 1. American Society for Nondestructiveesting and the American Society for Metals, 1982.

. C. D. Ehrlich, A note on flow rate and leak rate units. J. Vac. Sci. Technol. A 4(5), 2384 (1986).

. H. Yasuda and V. Stannett, Polymer Handbook . Wiley, New York, 1975.

. L. Laurenson and N. T. M. Dennis, Permeability of common elastomers for gases over a range of temperatur J.ac. Sci. Technol. A 3(3), 1707 (1985).

. H. E. Nuss and I. Streuff, Leak rate measurements for large vacuum chambers.Vacuum 46, 845 (1995).

. L. C. Beavis, Real leaks and real leak detection.Vacuum 20, 233 (1970).

. M. Moraw and H. Prasol, Leak detection in large vessels.Vacuum 28, 63 (1977).

. D. A. Howl and C. A. Mann, The back pressurizing method of leak testing.Vacuum 15, 347 (1965).

. A. Nerken, History of helium leak detection. J. Vac. Sci. Technol. A 9(3), 2036 (1991).

0. A. O. Nier, C. M. Stevens, A. Hustrulid, and T. A. Abbott, Mass spectrometer for leak detection. J. Appl. Phys . 10 (1947).

1. G. Reich, Leak detection with tracer gases: Sensitivity and relevant limiting factors.Vacuum 37, 691 (1987).

2. W. Becker, Erhöhung der Empfindlichkeit des Heliumlecksuchers durch Verwendung einer Turbomolekulaesonderer Konstruktion.Vak.-Tech . 8, 203 (1968).

3. M. H. Hablanian and W. E. Briggs, New technical developments in helium leak detection. Proc. Int. Vac. Congr.,th , Vienna,1977 , p. 199 (1977).

4. W. Becker and W. K. Huber, A novel leak detector with turbomolecular pump. Proc. Int. Vac. Congr., 7th , Vien977 , p. 203 (1977).

5. G. Reich, The principle of He enrichment in a counterflow leak detector with a turbomolecular pump with nlets. J. Vac. Sci. Technol. A 5(4), 2641 (1987).

6. W. Jitschin, G. Grosse, and D. Wandrey, Diffusion leak artifacts as a secondary standard for gas flow.Vacuum 383 (1988).







7. K. Jousten, G. Messer, and D. Wandrey, A precision gas flowmeter for vacuum metrology.Vacuum 44, 135 (19

8. G. Grosse, G. Messer, and U. D. Wandrey, Summary abstract: Calibration and long-term characteristics of heference leaks. J. Vac. Sci. Technol. A 5(4), 2661 (1987).

9. J. L. Chamberlin, The modeling of standard gas leaks. J. Vac. Sci. Technol. A 7(3), 2408 (1989).

0. J. Higson, C. Vallepin, and H. Kowalewsky, A review of information on flow equations for the assessment on radioactive transport containers. Proc. The 9th Int. Symp. Packag. Transp. Radioact. Mater . (PATRAM '89), June116, 1989, Washington, DC, USA, Vol. I, pp. 195205.





High-Vacuum System Design

Wolfgang Schwarz

High-vacuum systems cover a wide range of size and complexity from simple bell jar chambers for laboratory ophisticated industrial production systems and large-size research equipment. Most of these systems operate inressure range from atmospheric down to 106 mbar or less.

Designing vacuum systems comprises a number of tasks from different engineering disciplines such as mechanngineering, electrical and electronic design, software engineering, and vacuum engineering. The main tasks inacuum engineering step are the selection of appropriate types and sizes of pump sets, sizing of pipework, valvther components influencing pressure or flow distributions in the system according to the process requirement

n this chapter the design equations for the pumpdown process and for process operations are given. Together wffective pumping speed of the pump set and the gas loads in the system, they yield predictions of the system's erformance. Appropriate analytical and numerical calculation techniques are reviewed.

1alculations of Vacuum Systems

he pump set on a vacuum system has to perform two tasks. It has to evacuate the system starting from atmospressure down to a specified pressure within a certain time, and it must be able to maintain a specified pressurehe vacuum






Fig. 9.1Schematic diagram of a basic vacuum system.

rocess operation. Since, in general, these process requirements result in completely different requirements on umps, it is advisable to consider both tasks separately in the first step and in a second step to evaluate the resuoth tasks with respect to pump types and sizes.

A schematic diagram of a basic vacuum system is shown in Fig. 9.1.

.1.1asic Pumpdown Equations

n order to derive basic design equations an elementary idealized vacuum system is considered. A chamber of vt a uniform pressure p is connected to a pump set through a component (e.g., a tube) of conductanceC . The pump sas a pumping speed

t its inlet. Since we are interested in the pumping action at the system, we define the effective pumping speed

sing the pressure p in the system instead of the pressure p0 at the pumps inlet. The effective pumping speed can balculated from a steady-state flux balance of the flow entering the component and the flow into the pump and ressure drop across the component determined from its conductance:







Fig. 9.2Relative effective pumping speed as a function of the relative

conductance between system and pump set.

he effective pumping speed is always smaller than the installed pumping speedS 0. The fraction of the speed of thump set

which is available at the system is illustrated in Fig. 9.2. In order to obtain an effective pumping speed of 90% S 0more the conductance between the system and the pump set has to be larger than nine times the pumping speed

ump set. This emphasizes the importance of high conductances between the pump set and the system.

or all further considerations the effective pumping speed will be used instead ofS 0, and it is implied thatS has beeerived from the known conductance or pressure across the component (e.g., determined as outlined in Chaptehe intrinsic pumping speedS 0 of the pump.

n Fig. 9.1 a gas flow into the system is shown schematically. This flow can be caused by gas entering theom the ambient by a purposely fitted gas inlet, by leaks or permeation through seals or chamber walls. It can,

owever, also be caused by gas sources physically within the system like outgassing from materials.rom the basic quantities volume of the system, effective pumping speed, and flow into the system the time-def the pressure in the system can be calculated. If we apply the ideal gas law with the assumption of constant gemperature, a flux balance yields the basic differential equation:





where is the flow the pump system removes from the chamber:

n order to solve the differential equation the pressure-dependence and time-dependence of the effective pumpind the flow into the system have to be known.

n real systems the pumping speed is markedly pressure-dependent. In some cases, even its time-dependence honsidered (e.g., during start-up of a pump set). The flow is generally a function of time and it can be a functioressure as in the case of outgassing. The simplest assumptions, although not necessarily realistic, are pressureme-independent constant pumping speed and flow. This yields a simple expression for the pressure in the syst

igure 9.3 gives an example of a pumpdown curve of a system with a volume of 200 liters pumped by a pump S0 liter·s1. The flow into the system is 0.75 mbar·liter·s1.

he pressure versus time curve clearly shows two ranges. Starting from atmosphere, the pressure drops exponewith time (range I):

During this time the gas flow into the system can be neglected since p·S is large compared to . Hence practica

nly gas is pumped which has been contained in



Fig. 9.3Pumpdown curve for a system withS = const = 10 liter·s1,

a volume of 200 liters, and a flow into the system of= const = 0.75 mbar liter·s1. In range I the gas flow

from the volume determines p(t ); in range II the

pressure is only a function of .





he volume. The pressure drop in range I is characterized by the vacuum time constant:

which is only a function of the system volume and the effective pumping speed. It is independent of . In thange the pressure is practically constant:

n this range, only the gas flow together with the pumping speed determine the pressure, but not the system vol

ecause has been assumed to be not time-dependent, Eq. (9.10) yields the minimum attainable pressure inystem under these conditions. The pressure pB is often calledbase pressure or ultimate pressure .

olving Eq. (9.7) fort yields the pumpdown time from p0 to p:

rom Eq. (9.11) as well as from Fig. 9.2 it is obvious that as p approaches pB the pumpdown time diverges. Small n the (in general predicted) pB can result in huge errors in the pumpdown time.

n the above example, pumpdown started at atmospheric pressure. It should be noted, however, that none of thequations or assumption makes explicit or implicit use of pressure or flow ranges. Therefore, the solutions derivalid for all pressures from UHV to above atmospheric pressure as long as the conditions of constant gas tempeonstant flow, and constant pumping speed are fulfilled.

.1.2rocess Pressure

With a few exceptions, vacuum processes are started after the system has been evacuated and the pressure has felow a defined value. Typically the system then operates in range II of Fig. 9.3, that is, in the flow-controlled ange. Therefore in order to calculate the pressure the flow into the system and its time-dependence have to be

ince can exhibit arbitrarily complex behavior, no general expression can be derived. Instead the limitingowly varying and rapid step-like changing flow are considered.





n range II for a slowly varying flow a quasi-steady-state pressure is to be expected. Neglecting the gas storagehe volume compared to the flow removed by the pumping system, we obtain

quation (9.5) yields a quasi-steady-state pressure:

he condition (9.12) can be rewritten as

r as a condition for the rate of flow change:

or both, the relative change of pressure and the relative change of flow the rate of change has to be small com/τ to allow the use of the approximation in Eq. (9.13). It is interesting to note that the volume, while not expliceeded for the determination of the quasi-steady-state pressure, shows up implicitly in the conditions in form oacuum time constant.

he other limiting case of the time-dependence of the flow is a rapid change from one flow level to an other. Function change of the flow:

he pressure follows an exponential relaxation:

where are the equilibrium pressures before and after the flow change, respectively

he characteristic time for the relaxation is again the vacuum time constantτ = V/S . It is the same for rising and falressure, and it is independent of the equilibrium pressure as long as the effective pumping speed remains unchrom Eqs. (9.13) and (9.9) the necessary pumping speedS for a defined gas load and a required time constant canirectly calculated.







Applying these equations to practical systems, however, poses a number of problems. Neither the condition forndependent effective pumping speed nor that for constant gas flow are hardly ever fulfilled in practical systemll pumps exhibit a pronounced pressure-dependence of their pumping speedS 0. Furthermore, the conductance oflements such as tubes, valves, or baffles is also markedly pressure-dependent as shown in Chapter 2. The gas he system is, in general, not constant but is a function of time, especially when outgassing dominates.

n order to calculate realistic pumpdown curves it is therefore necessary to determine the time-dependence of thSection 9.2) and to calculate the effective pumping speedS ( p) at the system (Section 9.3).

2as Loads in High-Vacuum Systems

n every vacuum system a number of gas sources is usually present. Chamber walls and the components withinhamber release gas which was adsorbed at the surfaces or entrapped in the volume of the material. Air and wanter the system through leaks or permeate through seals. Finally the process performed in the vacuum system elease gas from the material being processed or it may require gas from an external source. In order to size theet the gas loads from the different sources have to be known.

.2.1Outgassing

One major gas source is the outgassing of the vacuum system itself and the material to be processed. Although esearch has been done in the field of the theory of desorption from surfaces and diffusive outgassing of bulk m not possible to predict the outgassing behavior from basic material properties. The main reason is that the sur

eal materials is an ill-defined mixture of different microscopic structures with different geometrical and desorproperties (for details see Chapter 10). Therefore outgassing measurements have to be performed on the materinterest.

igure 9.4 illustrates some examples of the time-dependence of the outgassing rate at constant temperature. Thiagram suggests that at least for a limited time interval the outgassing rate can be fitted to

with the geometrical surface A and the fit parametersa1h and α . The parametera1h can be identified as specificutgassing rate after 1 h of pumping. The decay exponentα is the negative slope of the outgassing curve in a loglFig. 9.4).

he specific outgassing rates cover a range over several decades depending not only on material type but also oreparation, cleaning steps, exposure times to atmosphere, and relative humidity. The decay exponent ranges fr

.2 to 1.2. Its value hints to the type of outgassing mechanism. Desorption from surfaces with





Fig. 9.4Time-dependence of the outgassing flow rate for different materials.

nly negligible contribution from the bulk yield values close to 1, and diffusion-controlled outgassing from thehe material yields values of about 0.5. At room temperature the main contribution to the outgassing flow from

which have been exposed to ambient air is water vapor (≥80%) with small amounts of N2 and CO2.

Metals, glasses, and ceramics yield outgassing rates which are well fitted with a single set ofa1h and α values forutgassing times from about 1 s to more than 100 h. The decay exponent for these materials is close to 1. Espec

metals, details of the preparation and cleaning steps have a larger influence on the specific outgassing rate thanifferences between different types of materials.

olymer materials generally show higher outgassing rates compared to metals and decay constants in the range.8, indicating contributions from diffusion from the bulk. In many cases, however, a single-parameter set is noufficient for an adequate fit over the time interval of interest. In these cases either two fits of Eq. (9.17) for diffme intervals or other fit functions should be used. Apart from water, some polymer materials contain volatile ubstances which are released during the outgassing process. In contrast to water vapor, these substances cannoeadsorbed during exposure to ambient air, resulting in reduced outgassing rates for repeated pumpdowns.

or an entire vacuum system the gas load due to outgassing is obtained from the summation over the contributiurfaces. With Eq. (9.17) the time-dependence of the gas load is





Fig. 9.5Time-dependence of the total outgassing flow rate of asystem consisting of 4.5 m2 steel surface and 0.25 m2

polymer surface.

should be noted that due to the small decay constants even small surface areas of polymer or rubber material ause significant contributions to the total gas load for long pump times as shown in Fig. 9.5. Therefore use of

materials should be minimized in high-vacuum systems.

Although this analytic approach for the calculation of the gas load for a vacuum system is scientifically correctome practical limitations. Outgassing measurements are typically performed on small samples of simple-geomhaped plates, which are easy to clean and easy to handle. Due to practical constraints, however, components fo

acuum systems cannot always be treated like outgassing samples. As a consequence, this results in outgassingharacteristics with increased outgassing rates and smaller decay constants compared to samples. Furthermore,omplex components it may be difficult to access the geometric surface and the outgassing parameters of all ki

materials involved.

ome of the problems can be circumvented by measuring the outgassing characteristic of a similar system and caling the results to the system under consideration. In order to measure the outgassing flow rate of a system,

vacuated and the time-dependence of the pressure p(t ) in regime II is recorded. The flow rate is then calculom p(t ) and the measured or calculated effective pumping speedS ( p):

Assuming negligible leak and permeation rates is the outgassing rate of the system. The flow rate for th

nder consideration is then obtained by scaling with the ratio of the surface areas of the two systems:



Obviously this scaling approach is only valid for systems which are comparable with respect to materials,manufacturing, and cleaning procedures and similar ambient conditions.





As suggested by the curve for the total flow in Fig. 9.5, effective outgassing rates and decay constants can alsoor entire systems using Eq. (9.17), although several fits for different time ranges may be necessary for good ac

.2.2eaks

eaks are unintended and undesired paths for gases and vapors into a vacuum system. Obviously the flow rate eaks, the leak rate, cannot be predicted since no information about the geometry of the leak channel exist a pri

he smaller the leaks that need to be detected, the more time-consuming and the more expensive the leak checkystems and components become (see Chapter 8). It is therefore desirable to have criteria for necessary leak chensitivities derived from the systems requirements.

or most systems, leaks are sufficiently small if they do not contribute more than 10% to the base pressure; thaeak rate has to be no higher than 10% of the total flow rate, with the remaining more than 90% being due to ound permeation. The tolerable leak rate is therefore

Assuming that this leak rate is due to a number ofnleak of undetected leaks of equal leak rate, the detection sensihould be

On high-vacuum systems the effective pumping speed ranges from 10 liter·s1 on small load lock chambers to meveral 10,000 liter·s1 on large systems. The number of undetected leaks should be not more than 10 on small cnd less than 100 on large systems. With these rough estimates the necessary leak detection sensitivity for sings a function of the base pressure are plotted in Fig. 9.6.should be kept in mind that these are only crude guidelines. Process requirements may well put more stringen

equirements on leak detection sensitivities.

.2.3ermeation

All materials exhibit a certain permeability for gases. This process involves three steps: the adsorption of a molhe high-pressure side of the material, the diffusion through the material, and the desorption on the low-pressur

Depending on the details of the kinetics, the permeation flow rate at constant temperature is





Fig. 9.6Estimated leak detection sensitivity for single leaks as a function

of the base pressure of systems in order to keep the leak flowrate smaller than 10% of the total gas load at base pressure.

Fig. 9.7Gas permeation through metals.

Here A is the cross-sectional area through which permeation takes place,d is the thickness of the material, and p1 an2 are the pressures on both sides of the material. For most of the gases like H2O, N2, and O2 which permeatehe material as a molecule, Eq. (9.23) applies. Hydrogen, however, is dissociated during adsorption and therefoccording to the law of mass action, Eq. (9.24) has to be used.



he permeation conductivityk perm is a gas-type-dependent and material-dependent parameter which strongly inwith increasing temperature. Figure 9.7 and





Fig. 9.8Gas permeation through polymer materials.

ig. 9.8 give examples of the permeation conductivity of some metalgas and polymergas systems. At room temhe permeation rates through metals are very small and can be neglected. Permeation through polymers used, foxample, for seals have to be taken into consideration in systems where base pressures of some 107 mbar or lese achieved.

.2.4rocess Gas

Vacuum processes involve a wide range of physical and chemical mechanisms. In some processes, such as vacnnealing to modify crystal structures, vacuum is only needed to avoid contamination of the material being pro

Gas is neither released nor needed for the process. Other processes, such as degassing of liquid metals, can relemounts of gas. Table 9.1 summarizes examples of typical process gas loads.

Due to this wide range, no general rules exist for the process gas load of vacuum systems. For the design of a dacuum system it is therefore necessary in most cases to scale experimental data on process gas loads from sim

ystems. The scaling factors have to be chosen carefully, considering the basic reaction mechanisms and the kinhe process. Degassing processes, for instance, can be limited by the transport mechanisms within the material, esorption step at the surface, or by kinetics in the gas phase. Accordingly, the geometrical dimensions of the ms surface area, or partial and total pressures should primarily be used for scaling. However, as geometric relatihange, the relative importance of the limiting mechanisms may change. It is therefore advisable to recheck the

mechanisms after scaling.





Table 9.1. Typical Ranges of Process Gas Loads in Industrial Vacuum SystemsProcess Typical

Process Gas Load(mbar·liter·s1)

Evaporation of optical layers0.11

Semiconductor processing110

Large-area sputter coating of architectural glass520

Precision casting0.110

nduction melting 101000Steel degassing 5000100,000

3esign of High-Vacuum Pump Sets

ump sets for high-vacuum systems have to operate in the pressure range from atmospheric to the system base pressuray be as low as 108 mbar. This pressure range is covered by a combination of high-vacuum pumps which operate ty

elow 102 mbar and fore-vacuum pumps which pump from atmospheric to the ''changeover pressure" of the high-vacumps. In most cases the forepumps also serve as backing pumps for the high-vacuum pumps. Details on the differentumps and their pumping mechanisms can be found in Chapters 35. In this section the combination of different pumpe discussed.

3.1orepump Sets

3.1.1ore-Vacuum Pumps

n practically all high-vacuum systems, oil-sealed or dry compression pumps are used as forepumps often in combinatoots blowers. The pumping speed characteristics of the forepumps are published in the manufacturer's data sheets. Fesign calculations, however, these data need some interpretation. Published pumping speed curves are measured accoSO standards under well-defined conditions. These conditions, however, are not necessarily representative of the appnvironment. Speed curves and base pressures of oil-sealed pumps, for example, are measured excluding condensableacuum systems, however, water vapor is the dominant gas at low pressures. Therefore the water vapor pumping speee needed. Furthermore, the oil in forepumps is often contaminated with water, which increases the base pressure of th values much higher than the data obtained under standard measuring procedures.

or design calculations it is therefore desirable to have a method to generate pumping speed curves of forepumps withdjustable ultimate pressure (see Fig. 9.9). A simple but surprisingly accurate approximation of the pumping speed is om the model of an ideal pump with pressure-independent pumping speedS max and a constant internal backstreamingt the base pressure pu the backstreaming balances the throughput puS max; that is, the net pumping speedS ( p) vanishes. F





Fig. 9.9Pumping speed of forepumps with different base pressures.

flux balance the net pumping speed is

At high pressures, Eq. (9.25) yields a pumping speed ofS max which can be taken from the manufacturer's data shhis approximation allows one to set the base pressure pu according to the application conditions of the pump, yie

ealistic speed and throughput close to pu .3.1.2oots Combinations

n order to increase the pumping speed of a forepump set or to attain lower ultimate pressures, Roots blowers cdded in series with the forepumps. This approach is often more economical than using more or larger-size forer multistage pumps, respectively.

A Roots blower can be considered to consist of a perfect pump with a theoretical displacementS th plus an internalackstreaming. The backstreaming is due to clearances between the rotors and gas adsorbed on the rotors at theacuum side and subsequently desorbed at the high-vacuum side of the blower. Using this model the net throug

net = p . S can be determined from the blower's theoretical throughput and the internal backstre

:

Assuming that the internal backstreaming is proportional to the pressure difference across the blower, cxpressed as a function of the maximum compression ratio at zero throughputk 0( pF):







where pF is the fore-vacuum pressure. From the flux balance equation [Eq. (9.26)] with , the net pumpin obtained:

ince for a given high-vacuum pressure p the corresponding fore-vacuum pressure pF is not known a priori, thealculation starts with an assumed fore-vacuum pressure for whichS is obtained from Eq. (9.28) usingk 0( pF ) and SFpF ). The corresponding high-vacuum pressure is then determined by the continuity equation for the flow throuump set:

ssuming the same gas temperatures at the inlet and the outlet of the blower. The efficiency of the blower (i.e., f the net speed and its theoretical speed),

only a function of the staging ratio of the blower speed and fore-vacuum pumping speedS th/SF and the maximumompression ratiok 0. The maximum compression ratio of a blower mainly depends on the shape of the rotors anlearances between the rotors and the housing. Figure 9.10 shows a typicalk 0 curve for air. Blower efficiency of m

han 70% is achieved withk 0≥ 15 and staging ratios of 10 or less (Fig. 9.11). It only weakly depends on the absoalue of the maximum

Fig. 9.10Maximum compression ratio of a Roots blower as

a function of the fore-vacuum pressure.







Fig. 9.11Roots blower efficiency as a function of compressionratio at zero throughput for different staging ratios.

ompression ratio but tends to decrease significantly for staging ratios above 10. Therefore in order to achieve fficiencies in the entire operating range of the blower, the staging ratio should not exceed 10.

Although relatively high compression ratios are possible at high fore-vacuum pressures, the pressure difference∆ p which can be safely achieved is limited by mechanical forces on the rotors and the temperature rise of the gas ixhaust area of the pump. Therefore pump manufacturers specify a maximum pressure difference∆ pmax for continperation for blowers without integrated bypass valves. This pressure difference also determines the pressure pc, R a

which the blower can be cut in.

n order to calculate pc, R the continuity equation is rearranged, yielding

quation (9.31) can be iterated with respect tok 0. Considering that pc, R only slightly decreases with increasingk 0, afe value for the cut in pressure can be calculated withk 0 = 15. Typically, the cut in pressure ranges from about 1bout 100 mbar depending on staging ratio and tolerable pressure difference.

he net pumping speed of Roots blower/fore-vacuum pump combinations, using the compression ratio accordi.10, is shown in Fig. 9.12. The pumping speed curve of the combination begins at a considerably lower ultimaressure than that of the forepump alone. It then steeply rises to a nearly constant speed plateau. At higher preslower speed decreases due to the diminishingk 0.

As to be expected, the ultimate pressure is approximately that of the forepump divided by the compression ratiressure. Therefore the combination's ultimate pressure is typically a factor of 2030 lower than that of the forephis would suggest an operating range extended by the same amount. However, the net







Fig. 9.12Pumping speed of Roots blower forepump combinationswith a maximum fore-vacuum pumping speed of 100

m3/h and a theoretical blower speed of 500 m3/h.

peed close to the ultimate pressure is very sensitive to small changes in the ultimate pressure of the forepump o variations ink 0 which might be induced by contamination of the rotors. Therefore the lowest operating presshe combination should be about four to five times the calculated ultimate pressure.

At the high-pressure end of the operating range of the blower, thermal aspects have to be taken into consideratiompression performed by the blower is

his power heats the exhaust gas and the blower. For example, a blower with a theoretical speed of 1000 m3/h y a 200-m3/h forepump yields a compression power of about 2 kW when operating at an intake pressure of 25art of this heat load is transferred to the ambient through the housing of the blower and the pipe work betweenlower and the forepump. A considerable amount, however, is transferred into the forepump by the hot exhausansient operations such as evacuating a system, the heat load to the forepump is usually not a problem, but foate operations at high intake pressures a gas cooler may be necessary between blower and forepump in order verheating the forepump.

or applications where high pumping speeds are needed in the pressure range between 102 and some 10 mbarmultistage blower systems with a comparatively small fore-vacuum pump can be used. The calculation of the n

umping speedS 2 of the entire pump set is analogous to that ofS 1, the speed of the forepump and blower 1. FirstS 1p1) is obtained from Eq. (9.28), then the combination of forepump and blower 1 are considered as forepump fand the same algorithm is applied to this blower. Figure 9.13 gives an example of such a pump set. Valve V1

he pump set from the vacuum system, and V2 is an optional valve in case the forepump has no integrated inlethe cut in pressures of the blowers are sensed by the pressure switches PS1 and PS2. These can be either two

membrane-type pressure switches or trigger signals derived from a suitable gauge with gauge controller.





Fig. 9.13Schematic diagram of a

forepump set with two Roots blowers. The pressure switchesPS1 and PS2 start the blowers

at their appropriate cut in pressures.

n most installations, due to space restrictions, the forepump set has to be placed some distance away from the ystem. Often V1 is then installed at the chamber. With V1 closed and the forepump operating, the blowers andubes between the pump set and the chamber are evacuated and the blowers are started. The entire volume fromhe inlet of the forepump quickly reaches pressures well below 1 mbar. Opening V1 to start evacuation of the syauses a rapid expansion of the air in the system into the evacuated volume of the pump set. Although the preswitches will immediately turn off the blowers because of their inertia, they will generate a pressure peak at theorepump. The high air speed associated with the expansion may transport dust and particles from the chamberorepump, and the pressure peak may damage exhaust filters in the forepump.

n order to avoid these problems, V1 should be located close to the pump set and the blowers should be switchllowed to spin down for a few seconds before opening V1. An alternative would be a bypass valve with flow rcross V1.

.3.2High-Vacuum Pump Sets

he majority of high-vacuum pump sets today are equipped with turbomolecular pumps, turbomolecular pumpombination with cryo-surfaces, or cryo-pumps. Diffusion pumps are applied mainly in systems, where high pupeeds are needed and where considerable amounts of debris from the processes are to be expected.

Although it applies totally different pumping principles, the pumping speed of all these pumps can be describedchematically by three regions as illustrated in Fig. 9.14. The operating range is characterized by a constant-speumping plateau. At low pressures, pumping is limited either by the maximum compression of the transfer







Fig. 9.14Schematic sketch of the three ranges of the

pumping speed of high-vacuum pumps. Detailed behavior of the speed curve in the overload and

ultimate pressure range vary for different pump types.

umps (turbomolecular and diffusion pumps) or by the equilibrium vapor pressure in the entrapment pumps (crumps, cryo-surfaces). At high pressures, overload due to high gas load occurs. In turbomolecular pumps, gas etween rotor and stator blades causing unacceptable heating of the rotor yields an upper limit for the operatingressure. In diffusion pumps the jets become unstable when the collision rate between the oil vapor and the gasumped exceeds a certain value. Cryo-pumps and cryo-surfaces cease stable operation when the heat load on thondensing surfaces cause their temperatures to rise or when adsorbing surfaces become saturated. The actual lhe operating range of a particular pump of course depends on the pumping principle and its technical realizatio

or the design of a high-vacuum pump set, all three ranges have to be kept in mind: the ultimate pressure rangeespect to the planned ultimate system pressure, the operating range with respect to process pressure and througnd the overload range with respect to pumpdown and crossover from fore-vacuum to high-vacuum pumps. Re

which type of high-vacuum is actually used, a few general design rules apply to the three ranges.

At the planned ultimate pressure of the system, pu, s , a sufficiently large and repeatedly achievable pumping speeeeded. Therefore the high-vacuum pump and its ultimate pressure should be chosen so that the pumping speed pu at least 90% of the plateau pumping speed. In high-vacuum systems equipped with turbomolecular or cryo-p

his criterion is of no concern since their ultimate pressures are smaller than 109 mbar whereas pu, s ≥ 108 mbar. Foriffusion pumps and cryo-surfaces, this rule has to be considered in more detail as discussed later in this chapte

he pumping speed of all high-vacuum pumps as well as the conductances of the vacuum components betweenumps and the chamber are gas-type-dependent. However, the gas-type dependencies of pumping speed andonductance often show a tendency to counterbalance: Pumping speeds for light gases such as hydrogen or heln most cases smaller than those for heavier gases, whereas the molecular conductances show the opposite behaherefore in most cases it is sufficient to calculate the effective speed for nitrogen and use this result for other gomponents too. In systems with cryo-surfaces or cryo-pumps the differences in pumping speed for





Fig. 9.15Selection of the changeover pressure from

fore-vacuum to high-vacuum pumps.water vapor and all other gases is generally large so that a different approach has to be taken.

During normal operation of a vacuum system the overload range of the high-vacuum pumps should never be reut during pumpdown, short overload periods are hardly avoidable. In order to minimize the overload time theriteria for the change over pressure pco have to be met: (i) The effective pumping speed of the high-vacuum pum

must be at least as large as of that of the fore-vacuum pumps (Fig. 9.15), and (ii) the backing pump must be ablhe backing pressure below the maximum tolerable foreline pressure when the high-vacuum pump operates at thangeover pressure.

When criterion (i) is not met, switching from the fore-vacuum to the high-vacuum pumps decreases the effectivumping speed as illustrated at p2 in Fig. 9.15. As a result, the pressure in the system starts to rise. This may thenchange back to the fore-vacuum pump set again, thus starting a cycle of several changeovers.

n order to avoid this situation, a changeover pressure p1 < pco, max should be chosen. Obviously it takes more tieach p1; but during this additional fore-vacuum pump time the system continues to outgas, and the outgassing ecreases. Switching then from the small fore-vacuum speed to the larger high-vacuum pumping speed causes rop in the chamber pressure and shortens the overload time of the high-vacuum pump considerably.

During changeover the high-vacuum pump has to handle the largest throughput. The backing pump must be abmaintain the foreline pressure below the critical foreline pressure under these circumstances. Otherwise the higacuum pumps will cease pumping; this may result in cycling between fore- and high-vacuum pump, similar totuation at too-high changeover pressures.

3.2.1urbomolecular Pump Sets

urbomolecular pump (TMP) sets are usually configured according to one of the schematics shown in Fig. 9.16ystems where the spin-up time of the turbomolecular pump of several minutes can be tolerated, no high-vacuuetween system and pump set is needed, thus reducing cost and avoiding pumping speed losses in the high-vacalve.

he system is pumped down by starting the backing pump set and opening V2. The chamber is evacuated throuMP. Usually the internal conductance of the







Fig. 9.16Schematic diagram of turbomolecular pump

sets (a) without and (b) with high-vacuum valve between system and pump set. The bypass

valve V3 in (a) is optional.

MP is large enough so that it does not limit the roughing of the chamber. A few minutes before the backing pulone would reach the maximum tolerable backing pressure pB, max of the TMP (typically 0.10.5 mbar for standa

MPs, 510 mbar for pumps with molecular drag stages), the spin-up of the TMP can be started. When the TMPeached its operational speed, the backing pressure is then below pB, max.

n systems where debris from the chamber is expected to move during roughing, it is advisable to bypass the Talve (V3 in Fig. 9.16). This avoids particle deposition in the TMP during roughing.

hambers which require short pumpdown times or which are cycled continuously from atmosphere to high vacave to be equipped with a high-vacuum valve V1 and a bypass valve V3. Before the pumpdown of the chambhe TMP is evacuated via V2 and ramped up to speed with V3 closed. For roughing, V2 is closed and V3 openhis time the TMP operates without backing pump. Its fore-vacuum pressure is monitored, however. In case it eB, max, roughing is interrupted by closing V3. Opening V2 then allows the system to pump below pB, max. Propeming of the valves has to make sure that before opening V2 the pressure in the fore-vacuum line between V2 maller than the maximum backing pressure.

alculation of the effective high-vacuum pumping speed of a TMP pump set is in principle straightforward. Aco Eq. (9.3), the speed of the TMP as published by its manufacturer and the conductances of all the vacuum cometween the TMP and the chamber are needed for the calculation. For most of these components, molecularonductances either are published or can be calculated. However, in some of the components such as valves or ansitional flow may occur. This would suggest that the pressure-dependence of the conductance has to be kno

which is rarely the case for complex components. Since the speed of the TMP decreases with increasing pressuonductances play a less important role at higher pressures.





Fig. 9.17Effective speed of a 150 liter · s1 TMP with a 100-mm-

diameter, 300-mm-long tube using the pressure-dependentconductance and a pressure-independent approximation.

herefore for most applications, using the molecular conductance in the transitional flow regime yields a sufficccurate approximation of the effective pumping speed. Figure 9.17 gives an example.

Although the pumping speed of TMPs decreases above about 1 × 103 mbar, this is no indication of overload, beduction in pumping speed is due to the pumping mechanism. Most TMPs can continuously operate at inlet prp to 102 mbar and provide very stable pumping speeds.

he backing pump set has to be designed so that the maximum tolerable fore-vacuum pressure pF , max as specifiedhe TMP is not exceeded except for a few minutes during pumpdown. From the maximum expected operation

op, max, the throughput of the pump is obtained using the effective TMP pumping speedS . When the T equipped with a purge gas system, the purge gas flow has to be added, yielding a backing speed of

should be noted thatSF is the pumping speed required at the fore-vacuum flange of the TMP and that it is a lomit for the pumping speed. Larger fore-vacuum pumping speed may be necessary due to, for example, pumpdequirements.

3.2.2iffusion Pump Sets

he schematic diagram of the diffusion pump set is shown in Fig. 9.18. For start-up of the diffusion pump, V1 re closed and the pump is evacuated by the forepump through V2. When the foreline pressure reaches the maxore-vacuum pressure of the diffusion pump pF , max the heaters are started. After the diffusion pump has reachedperating temperature pumpdown of the system can be started in the usual way be closing V2 and opening V3.dvisable to monitor the backing pressure of the diffusion pump during pumpdown with V1 and V2 closed. Thacking pump, shown as option in Fig. 9.18, will







Fig. 9.18Schematic diagram of adiffusion pump set. The

baffle and the additional backing pump are optional.

maintain sufficiently low backing pressures even in the presence of small leaksfor example, due to particles onf V1. Without this additional pump, when the backing pressure rises, the roughing has to be interrupted for a sy closing V3 and reopening V2 until an acceptable backing pressure is reached again.

rossover from the fore-vacuum to the diffusion pump should be performed according to the rules outlined in S.3.2. During crossover and high throughput operation the backing pressures of the diffusion pump needs specittention. Maximum foreline pressures of diffusion pumps as published in the data sheets are usually measuredhroughput. In order to run a pump at high throughput, a lower backing pressure is needed for stable operation,ne-half to two-thirds of the pressure for zero throughput. Therefore the necessary effective backing pump spee

he operating pressure range of diffusion pumps extends from about 10 times the ultimate pressure up to the mnlet pressure pmax where the overload range with nearly constant flow begins (Fig. 9.19). pmax ranges from a few

mbar for large pumps with inlet diameters of 1 m to a few 103 mbar for small pumps. The effective pumping spalculation has to include the conductance of V1 and eventually that of the baffle. Although the conductance oalve is pressure-dependent in the upper operating and the overload range, for approximate calculation this caneglected. Typically the conductance of angle valves for diffusion pumps as well as the baffle conductance are arge as the nominal pumping speed. Therefore as a rule of thumb the effective pumping speed of a diffusion p





Fig. 9.19Operating pressure range for diffusion pumps.

Fig. 9.20Inlet pressure changes caused by flow changes in

the operation and overload range in a diffusion pump.

alve is about half of the nominal speed. With valve and baffle it is about one-third ofS 0.



Without special measures, stable operation at pressures above the maximum inlet pressure is hardly possible. Selative changes in the flow which are reflected in proportional pressure changes at low pressure yield large pre

xcursions above pmax due to the flat curve (Fig. 9.20). To enable stable operation at pressures in the sysbove pmax, the pump is throttled by a suitable throttle valve. Figure 9.21 illustrates the operating principle. Fo

ow and no conductance losses





Fig. 9.21Extension of the operating range of a diffusion pump

by throttling.etween the system and the pump, the pressure pP at the inlet of the pump and the pressure in the system pS are theame. Throttling the pumpthat is, purposely introducing conductance losses between chamber and pump yields

ffective pumping speed in the system. For the same flow a higher chamber pressure results while at the sahe pressure at the pump remains at pP , thus ensuring stable operation.

3.2.3ump Sets with Cryosurfaces

n high-vacuum systems most of the outgassing flow of the chamber consists of water vapor. This suggest the uump sets with high water vapor pumping speed. Cryo-cooled surfaces are able to provide large water vapor pupeeds at reasonable cost. Cryosurfaces are used in many different forms such as cooled tubes or panels within ystem or cryo-cooled baffles in front of pumps. Cooling is provided either by boiling liquid nitrogen or by aefrigerator recirculating a cooling mixture.

umping Speed of Cryosurfaces . The pumping speed for a condensable gas of a cold surface of surface area A isetermined by the surface temperatureTs , the saturation pressure ps at Ts , and vapor pressure pg and temperatureTg

or water vapor at room temperature with Mg = 18 g/mol and a sticking coefficientσc = 1, Eq. (9.35) yields a pumpeed of

he water vapor saturation pressure can be approximated by







Fig. 9.22Water vapor pumping speed of cryosurfaces at constant

surface temperature.

n the temperature range from 150°C to 0°C with sufficient accuracy for pumping speed calculations. With Eq. nd Eq. (9.37) the pumping speed can be calculated explicitly from pH2O in front of the condensing surface and thurface temperatureTs . Figure 9.22 illustrates the strong influence of the cryo-surface temperature on the pumpipeed at low pressures.

he heat load on the cryo-surface consists of the heat of condensation and the thermal radiation from the ambie

he contribution of thermal radiation is nearly independent of the surface temperature, but strongly dependent mbient temperature. At room temperature the radiative heat load is approximately 400 W/m2, in an environmn ambient temperature of 80°C the load more than doubles to about 850 W/m2. This underlines the importanchielding cryo-surfaces and cryo-pumps against high temperature radiation.

he condensation rate is proportional to pumping speed and gas pressure:

or water vapor at room temperature and a pressure of 103 mbar the maximum possible condensation rate is ab/(m2·s).

Due to the thermal load by thermal radiation and the heat of condensation, the surface temperature of the condeurfaceTs is higher than the temperatureT liq of the coolant because of the temperature jump between coolant anryopanel wall∆Twliq, the temperature drops across the wall∆Tw, and the temperature drops





Fig. 9.23Temperatures on a liquid-cooled cryopanel.

cross the frost∆Tf on the surface (Fig. 9.23):

ven when water vapor is pumped at pressures above 103 mbar and heat loads of a few kilowatts per square mryosurface have to be removed, the total temperature drop normally does not exceed 20°C. With liquid nitrogeoolant the surface temperature stay below 180°C, so a constant pumping speed of the cryosurface from UHV

medium vacuum is obtained.

Refrigerators do not provide the low temperatures or the power handling capacity achievable with liquid nitrogefrigerators have a cooling power characteristic starting at a temperatureTR,0, the minimum coolant temperature

without heat load and increasing nearly linear with increasing thermal load:

he parameter AR characterizes the power handling capability of the refrigerator. Just asTR,0, the minimum coolanemperature, AR, depends on the refrigerator type and its coolant mixture.

rom the combination of Eqs. (9.36) to (9.41) the pumping speed of a refrigerator-cooled cryosurface can be casing appropriate refrigerator parameters and estimates for the temperature drops between condensing surface aoolant. Figure 9.24 gives an example of a 0.5-m2 cryosurface operated with a refrigerator with AR = 50 W/K andifferent minimum coolant temperatures. For the design of a pumping system with a cryosurface, Fig. 9.24 sughoosing the minimum coolant temperature so that the ultimate pressure of the cryosurface is at least one decadhan the planned ultimate pressure of the system.

he overload range for this refrigerator cryosurface combination starts at about 102 mbar water vapor pressureperating range can be extended to higher pressures either by reducing the cryosurface with the same refrigeratsing a more powerful refrigerator with the size of the cryosurface unchanged. It should be kept in mind that theats up as it travels through the cryocoil. In order to avoid redistribution effects from the hotter to the cooler phe cryosurface, the





Fig. 9.24Water vapor pumping speed of a 0.5-m2 cryosurface for a

refrigerator with AR = 50 W/K and different minimumcoolant temperatures.

esign of the cryosurface should be based on its maximum temperaturethat is, on the outlet temperature of the

ump Combinations with Cryo-surfaces . In high-vacuum systems, cryosurfaces with surface temperatures above0 K (193°C) can only be used to pump water vapor. For the noncondensable ''permanent" gases, other pumps equired. In order to size the water vapor pumping speedS H2O relative to pumping speed for permanent gasSp, weonsider the total and partial pressures:

Obviously, as soon as the water vapor partial pressure is small compared to the permanent gas partial pressure, ncrease in water vapor pumping speed will not significantly reduce the total pressure. For the calculation of thressure it is convenient to define a total pumping speed,

nd express the water vapor flow rate as a fraction f H2O of the total flow rate,

ielding the following for the total pumping speed:







Fig. 9.25Gain of total pumping speed as a function of water

vapor pumping speed for different water vapor fractions.

or the fraction of water vapor in the gas of a vacuum system, no general rules exist. Mass spectrometer measun high-vacuum systems taken during pumpdown and close to the base pressure resulted in f H2O valves for betwee0% and 95%. Figure 9.25 illustrates the gain in total pumping speed with respect to the permanent gas pumpins a function of the relative water vapor pumping speed. As suggested by the diagram, water vapor pumping sp

which are 10 to 15 times the permanent gas pumping speed are probably an optimum for water vapor fractionsr less.

3.2.4ryopump Sets

oday, high-vacuum cryopump sets nearly exclusively make use of refrigerator-type pumps. Therefore the discryopump set design will focus on this pump type. As an entrapment-type pump, cryopumps show design char

which are not found in transfer pumps. In contrast to, for example, turbomolecular or diffusion pumps, cryopumlimited storage capacity for pumped gas and therefore require regeneration at periodic intervals.

ike all other high-vacuum pumps, cryopumps exhibitin principlepumping speed characteristics as illustratedchematically in Fig. 9.14. Published pumping speed data, however, only show the operating range with pressundependent speed.

or the overload range a pumping speed curve similar to that of cryosurfaces (Fig. 9.24) would be expected. W

ryopumps, however, this range is not accessible. In contrast to cryosurfaces, overload in a cryopump usually complete breakdown of the pumping action. As soon as the temperature on the low-temperature stage rises marbove 20 K, pumped gas is released from the adsorbing surfaces, resulting in a pressure rise within the cryopumn turn by conduction through the gas increases the heat load from the pump housing at room temperature to thryopanels. Further temperature rise of the adsorber and gas release then usually require a shutdown and regenhe pump. Therefore overload of cryopumps, even for short times, has to be avoided.

he operating range of most cryopumps begins at about 103 mbar and extends to the UHV range. In vacuum sywhere operating pressures higher than the





maximum inlet pressure of the cryopump are required, a throttle valve has to be added between the system andump. The function is the same as discussed for throttled diffusion pumps (see Section 9.3.2.2).

he water vapor pumping speed of cryopumps is typically 3 to 4 times larger than the pumping speed for nitrorgon. In order to calculate the pressure achievable with a cryopump, either the total pumping speed approach 9.44)] or explicit partial pressure calculations analogous to Eq. (9.42) should be taken.

he maximum operating timet max before regeneration is necessary is limited by the amount of gas which can bn the pump without noticeably degrading its performance.t max can be calculated from the pump capacityQmax as

ublished by the manufacturer and the average flow

or hydrogen the capacity is typically between 10 and 40 bar·liter, whereas for all heavier gases the capacity isrder of 1000 bar·liter. Hydrogen is therefore the critical gas in many cases. It should be noted that in some prouch as plasma processesalthough not purposely introducedhydrogen may be produced by dissociation of watehe ultimate pressure attainable with a cryopump is not only a parameter of the design of the pump. Instead, it n the type and amount of gas which has been already stored in the pump. For operation in high vacuum systemowever, the ultimate pressure is usually low enough as long as the pump has not yet reached its capacity. In orttain ultimate pressures below 108 mbar cryopumps have to be well-regenerated and operated not too close toapacity limits.

hangeover from the fore-vacuum pump to the cryo-pump imposes a peak heat load on the cryo-surface since om the systems volume has to be pumped in a short time. In order to maintain the cryopanels at sufficient low

emperatures the changeover pressure pco has to be chosen according to

he changeover valueQco depends on the cooling capacity of the refrigerator and is specified by the pumpmanufacturers. For a cryo-pump with an inlet flange of 200 mm, typicallyQco ranges from 50 to 200 mbar·liter.

or regeneration of cryo-pumps, different procedures are applied for warming up and removal of the pumped ghapter 5).

At the end of the regeneration cycle the cryopump has to be evacuated below 5 × 102 mbar before the refrigeraarted. Since the adsorber panels are very sensitive to oil contamination, oil backstreaming from the pump set voided. As illustrated in Fig. 9.26, this can be achieved either by an adsorber trap or alternatively by purge ga

ntroduced in the pump line between cryopump and forepump. The adsorber should be isolated by V4 duringumpdown in order to avoid loading the adsorber material with water vapor. For the purge gas to be efficient invoiding oil backstreaming, the flow should be adjusted so that the pressure at the





Fig. 9.26

Schematic diagram of acryopump set V4 is onlyneeded in combinationwith the adsorber trap.

Alternatively to theadsorber purge, gas can be introduced via V5.

nlet of the forepump is 0.1 to 0.2 mbar and the gas inlet should be located near the cryopump fore-vacuum por

4alculation Methods for Vacuum Systems

n order to derive solutions to the basic design equations in Section 9.1, highly simplifying assumptions have bmade. Conditions such as constant pumping speed or time-independent flow are hardly ever met in real system

herefore these solutions can provide approximations for real systems; but for sufficiently accurate predictionsacuum performance, calculations have to be based on realistic data of pumps, conductances, and gas flows.

n principle there are two ways to include real data in the design calculations: (i) Model all relevant data such aumping speeds and flows in an analytical form and solve the basic equations analytically or (ii) use the data ahe equations by numerical methods. Both approaches have their advantages and their limitations. Analytical mield closed-form solutions which provide insight into the dependencies of different parameters. However, analolutions are only available for simple approximations of, for example, pumping speed curves. Numerical methhe other hand are very powerful in including the most complex dependencies and system structures, but they rppropriate software tools and they do not show dependencies directly.



n this section, analytical approximations and numerical methods are discussed.





.4.1Analytical Approximations

olutions for the basic differential equation [Eq. (9.5)] have been derived assuming constant pumping speed anonstant gas flow. In real systems these conditions are certainly not fulfilled for the entire pressure range. For lianges, however, these assumptions are often well-approximated. Combining analytical solutions with appropripproximations can therefore provide useful practical solutions.

or the approximation of the pumping speed as discussed in Section 9.3.1, we obtained

nd constant gas flow the basic differential equation has the solution

or the pumpdown of a system. During pumpdown the major gas load is due to outgassing. Since the outgassingas a slow time-dependence compared to typical vacuum time constants, Eq. (9.47) also yields a reasonablepproximation for the pumpdown of a system with outgassing. Using Eq. (9.17) for the outgassing flow rate theressure during pumpdown is

o check the accuracy of this approximation, it has been compared with numerical solutions using the same pupeed and gas flow formulae. The largest differences occur in the transition range between volume-gas-controlow-controlled pumpingthat is, between range I and range II in Fig. 9.3. Here the deviations in the calculated pre less than 20%. In range I as well as in range II the deviations between the approximate and the numerical sore typically less than 5%.

quation (9.48) provides an explicit pressure versus time curve. Although pumpdown times to specified pressue extracted from calculated p(t ) data, often it is desirable to have an explicit expression for the pumpdown timeq. (9.48) cannot be solved fort explicitly, an alternate approach is needed. An estimate for the pumpdown timebtained considering the evacuation of the volume (range I) and pumping of outgassing flows (range II) indepeor both steps a separate pumping time is calculated and the results are added to obtain the total pumpdown tim





or a pumping speed according to Eq. (9.25) and an outgassing flow according to Eq. (9.17) the times are

his approach yields an estimate for the pump time which is larger than the actual pump time. As to be expecteargest errors occur in the transition region between range I and II. Here the estimated times can be too large byf 1.7. In range I the deviations are a few percent at most. In range II the time is less than 30% too large. Althoery precise, this estimate makes it immediately obvious whether the pumpdown process is dominated by rangange II pumping by comparingt I and t II.

Up till now, only constant pumping speeds and ultimate pressure-limited pumping speeds have been consideredump sets with Roots blowers or with high-vacuum pumps, at least step changes in the pumping speed have tonto account. The calculation of the pumpdown curve using a step function speed is straightforward in principleressure range is subdivided into constant pumping speed ranges as illustrated in Fig. 9.27. Then p(t ) is calculated fach range separately from Eq. (9.48) using appropriate matching conditions.

rom atmosphere to the cut in pressure pc,R the pressure is

As the pressure reaches the cut in pressure att = tc,R the pumping speed increases toS 2:

inally after the changeover to the high-vacuum pump we obtain

is important to note that the time argument in the exponential function and the associated starting pressure hadopted to the different pumpdown ranges





Fig. 9.27(a) Step function approximation of the pumping speed.

(b) Calculated pumpdown curve. Note the change in theslope of p(t ) caused by the change of the pumping speed.

while the time argument for the outgassing flow remains unchanged. Although Eqs. (9.50) yield p(t ) explicitly, the tmatching conditions for switching from one pumping speed to the next have to be iterated numerically. The acchis approximation is mainly determined by the choice of the constant pumping speed representing the real spe

During the changeover from one pumping speed to the other, transient errors are to be expected. In reality thehangeover is not an instantaneous process, but it takes some time to activate valves and to run blowers up to surthermore, during crossover the high-vacuum pump has to cross its overload range. Depending on the overloandling capability, this can take some time. Fortunately these transient errors do not noticeably influence the pn the long run.



Analogous to the pressuretime curve the estimate of pumpdown time, Eq. (9.49), can be applied to step functioumping speeds. The volume gas pump times in the





ifferent speed ranges are added to the outgassing pump time. For the pumpdown to a pressure below the crossressure to the high-vacuum pump the estimated pump time is

or this estimate, about the same errors as for Eq. (9.49) are to be expected. On top of these intrinsic errors thencertainties inS 1 to S 3 have to be considered.

or pumpdown calculations Eqs. (9.50) and (9.51) constitute about the maximum complexity of analyticalpproximation which can be handled with reasonable effort. Better approximations of pumping speeds or gas flhould be analyzed using numerical methods.

.4.2Numerical Methods

he analytical methods outlined in Section 9.4.1although powerful and easy to usereach their limitations whenredictions of vacuum system performance are required or when multiple interacting vacuum chambers have toonsidered. In these cases, numerical methods have to be used which can handle the complexities involved in talculations.

wo different approaches have been taken for the numerical solution of vacuum calculation problems: Dedicatacuum system design software has been developed and general simulation software has been adapted to vacuuroblems.

4.2.1edicated Software

acing the challenge of precise pumping speed and pumpdown predictions the vacuum industry developed nummethods and dedicated programs for vacuum system calculations.

or the calculation of the pumping speed, approximate approaches are usually not precise enough when accura0% or better are required. Instead, measured pumping speed data have to be used whenever possible. From a noint of view, pumps can be classified into two categories: (1) pumps whose pumping speed is







irectly available from measured data and (2) pumps where the pumping speed has to be calculated from charaata of the pump and from properties of the remaining pump set. Typical examples for the first group are fore piffusion pumps, and turbomolecular pumps, while Roots blowers and cryo-surfaces belong to the second categ

or pumps for which measured pumping speed data are directly available the construction of theS ( p) curve israightforward. The pumping speed is interpolated on a logS log p basis as required by the pumpdown calculationlgorithm.

he basic calculation steps for pumps of the second category have been outlined in Section 9.3. In order to preacuum performance of Roots blowers and cryo-surfaces accurately, their individual characteristic data have tonown. For instance, the maximum compression ratio of Roots blowers is influenced by the detailed internal gf the pump, resulting in differentk 0 curves for blowers of different size. Furthermore, not onlyS th but alsok 0 for aiven machine depends on its rotational speed.

n order to obtain accurate effective pumping speed data the pressure-dependent conductance of all flow restricetween the pump set and the system has to be considered. In some pump sets there are noticeable flow resista

within the pump set which have to be taken into account: tubes of considerable length or filters installed betweifferent pump stages. Furthermore, purge gas may be needed at different points within the pump set, which als

nfluences the effective pumping speed.With the so determined effective pumping speed and appropriate gas load data the basic differential equation [Eas to be solved. Considering the large pressure range to be coveredin most cases more than nine decadesand thhanges in pumping speed or gas flow, stable numerical methods are needed. One proven approach is the use onsatz function similar to Eq. (9.47) for small time steps. For the limiting cases of constant speed and gas flow,he exact solution independent of the size of the time steps. For all other caseswhich are by far the majorityin ahe ansatz function a suitable predictorcorrector scheme has been implemented. This method results in high nuability. It handles sudden changes of speed or flow without any problem, and it also handles the complete pumom atmospheric pressure to the system base pressure.

uch programs, which include all the pump and conductance aspects, measured gas flow versus time data, and olution strategies, are able to predict the pumpdown with accuracies of better than 10% over the entire pressurom atmospheric to high-vacuum. Besides providing reliable predictions for new systems, the accuracies allowf the results of the simulation as an analytical tool for existing vacuum equipment. By comparing measured analculated pressure versus time data, pump problems or hidden flow restrictions can be identified.

4.2.2etwork Approach

All systems considered so far are based on the schematic diagram in Fig. 9.1that is, a chamber with one pump sifferent gas sources assumed to be at a uniform pressure. This model requires that the pressure drop within theue to the conductanceC system between the gas sources and the pump port be small compared to the absolute phat is, C system must be much larger than the effective pumping speed.

While adequate for typical single-chamber systems the model fails in most multichamber systems and in extendystems, where distributed pumps and gas sources





Fig. 9.28Schematic diagram of avacuum system with twochambers coupled by a

conductanceC 12.

ave to be taken into account. Figure 9.28 gives an example for a two-chamber system. Through the conductanetween the chambers, gas flow between the chambers is possible. The straightforward but tedious approach wo set up a system of coupled differential equations for both chambers and solve it for p1 and p2; but for networks olements, other methods already exist.

has long been known that an analogy exists between vacuum systems and electrical networks. For electrical nalysis, sophisticated software tools are available. This suggests that we should apply these tools to vacuum syalculations.

he relation between vacuum metrics and electrical metrics are found by comparing terms in similar equationsaw relates an electrical current I with the voltage drop V across an electrical conductance G by

he corresponding equation for the gas flow is

whereC is the conductance of the element and p is the pressure drop acrossC . Charging and discharging an electriapacitor of capacitance C is described by

whereas the change of the gas content in a volumeV follows:



is important to note that the symbols V andV and C andC have completely different meaning in electrical andacuum context and they should not be confused.





able 9.2. Correspondence Between Electrical and Vacuum Metricslectrical Metric Electrical Symbol Electrical

UnitVacuum Metric Vacuum Symbol Vacuum Units

oltage V V Pressure p mbar Pa

urrent I A Gas flow mbar·liter·s1 Pa·m3·s1onductance G 1/Ω Conductance C liter·s1

m3·s1

apacitance C F Volume V liter m3

atching terms in these four equations yields a correspondence table between vacuum metrics and electrical metrics (Table 9.2). Althouectrical units a single standard is established for engineering purposes in vacuum technology, different systems are in use. Any of thesstems can be used with circuit simulation software as long as self consistency is maintained within the units. Table 9.2 gives two examts of units. With the correspondence table, vacuum components can be translated into electrical circuit elements (Figure 9.29). A volupresented by a capacitor with one side connected to ground potential. In vacuum metrics this ground potential corresponds to zero absessure, the reference level relative to which the pressures are measured.

ow resistances without internal volume, such as orifices, are modeled by a simple resistor. Tubes, where not only the conductance bute volume has to be considered, are represented by resistorcapacitorresistor networks. The resistors have to be chosen so that their serinnection yields the total conductance of the tube, whereas the capacitor represents the entire volume. For long tubes and in cases wheessure distributions along tubes are to be investigated, several of these networks can be connected in series.

mps with constant pumping speed can be represented by a conductance to the zero-pressure reference nodethat is, to ground potentiases where the ultimate pressure of the pump shall be included according to Eq. (9.25), the equivalent circuit consists of a conductancerresponding toS max in series with a constant voltage source, which is to be set to voltage corresponding to pu .

ost gas loads can be approximated by current sources injecting currents irrespective of the pressure.

r the vacuum system shown in Fig. 9.28, the equivalent electrical circuit is illustrated in Fig. 9.30. With this network, many aspects ocuum performance of the system can be studied. Starting the simulation with the volumes ''charged" to atmospheric pressure and imp

propriate time-dependent outgassing flows 1 and 2 yields the pumpdown curve. Similarly, process operation can be simulated bocess gas flow where necessary. Propagation of pressure changes from one chamber to the other are easily investigated and even openosing of a valve between the two chambers can be simulated by varying the conductanceC 12 from zero (i.e., valve closed) to the conductathe open valve. This great flexibility has turned circuit simulation into an indispensable tool for calculations in complex vacuum syst

here are, however, some requirements on the circuit simulation software in order to be useable for vacuum system simulation. The prenge to be covered in





Fig. 9.29Translation of vacuum elements to equivalent circuits.



Fig. 9.30Electrical equivalent circuit of the two-chamber vacuum system in Fig. 9.28.

vacuum simulation often extends over more than nine decadesfor example, from atmospheric pressure to lessmbar. The software must be able to handle this large range with sufficient accuracy. Vacuum elements such asonductances and pumps usually exhibit considerable nonlinear behavior. Therefore for an adequate





mulation it must be possible to use nonlinear elements defined by tabulated data or formulae. Finally, arbitrarefinable time functions for the current sources are needed to simulate gas loads.

General References

D. Degras, Le Vide 64, 155 (1956).. Dushman, inScientific Foundations of Vacuum Technique (J. M. Lafferty, ed.), 2nd ed. Wiley, New York, 1962

Elsley, Vacuum 25, 229 (1975).

Elsley, Vacuum 25, 347 (1975).

h. Gebele and W. Buschbeck, LEYBOLD SYSTEMS, private communication.

A. Haefer, Kryo-Vakuumtechnik, Grundlagen und Anwendungen . Springer, Berlin, 1981.

G. Horikoshi, J. Vac. Sci. Technol. A 5, 2501 (1987).K. Kanazawa, J. Vac. Sci. Technol. A 7, 3361 (1989).

F. O'Hanlon, A User's Guide to Vacuum Technology , 2nd ed. Wiley, New York, 1989.

Santeler, J. Vac. Sci. Technol. A 5, 2472 (1987).

W. Schwarz, J. Vac. Sci. Technol. A 5, 2568 (1987).

. R. Wilson, J. Vac. Sci. Technol. A 5, 2479 (1987).

M. Wutz, H. Adam, and W. Walcher, eds,Theorie und Praxis der Vakuumtechnik , 3rd ed. Vieweg Verlagsges.,raunschweig, 1986.





0Gas-Surface Interactions and Diffusion

ohn B. Hudson

At the pressures encountered in typical vacuum systems, the mean free path of gas molecules is very long comphe dimensions of the apparatus. Consequently, the behavior of the gas is dominated by gassurface collisions. Iases, the energetic interactions between the gas molecules and surfaces within the system are sufficiently stronhe gas molecules will be trapped at the surface, or sorbed, for a period ranging from nanoseconds to essentiallyhe magnitude of this surface lifetime is a critical factor in a number of the processes involved in vacuum systeperation. Pumping processes such as sorption or cryopumping depend on the trapping of gases on cold surfachysical adsorption. Getter pumping depends on the uptake of active gases by a combination of chemisorption bsorption into the bulk of the getter material. The gas load that must be handled by the system pumps consistsor a brief period at the beginning of the pumpdown cycle, of gases leaving the surface by a combination of (a)ermeation through the surface from the bulk of the material exposed to the vacuum and (b) desorption from ad

ayers present on the surfaces themselves.n the material that follows, these processes of sorption and desorption will be discussed in detail, with emphasffect that these phenomena have on the performance of vacuum systems and on the operations carried out withystems. In this discussion the interplay of four processes will be seen to control the net rate of uptake or emissas from the surfaces of materials exposed to the vacuum environment.






Fig. 10.1Processes involved in the overallrate of sorption or desorption of

a gas at a surface.

he sorption of gases on surfaces, either as adsorption on the free surface or as solution into the bulk below thean be treated by either a thermodynamic or a kinetic approach. In most processes of interest in vacuum techno

ates of adsorption and desorption phenomena will be of greater importance than the equilibrium amounts of gadsorbed on, or dissolved in, the surfaces of the system. Moreover, it will be shown that the equilibrium conditilways be obtained by equating the rates of all sorption processes to the rates of the corresponding desorption por any set of system conditions. Consequently, the kinetic approach to these processes will be emphasized here

he rates of the surface-related processes that may occur, in the most general case, may be represented as show0.1. This figure shows, schematically, the rates of the competing surface processes such as adsorption into thea , and dissolution into the bulk, Rs, which remove material from the gas phase, and processes such as permeati

he solid, Rp, and desorption from the adlayer, Rd , which liberate material into the gas phase. For any set of systeperating conditions, the net rate of pumping or outgassing associated with the surface will be set by the balanchese rates.

0.1dsorption

0.1.1asic Equations

n many cases, the rates of one or more of the processes described above will be either negligible or extremely he behavior of the system can be characterized completely in terms of one or two of these rates. Adsorptiondehenomena can be described, in the absence of effects due to bulk processes, in terms of the parameters that coates of adsorption and desorption. These are the molecular impingement rate, I , which was defined in Section 1.4

which sets an upper limit on the rate at which material can accumulate on the surface; the desorption frequencyvd ,which is the probability of desorption per adsorbed species per unit time and which will depend upon (1) the nahe gassurface interaction in any specific system and (2) the temperature and the amount of the gas adsorbed; thnstantaneous surface coverage,na ; and the probability that a molecule striking the surface will be accommodatehe adsorbed layer,S , which may be a function of the amount adsorbed.





he amount adsorbed at equilibrium,neq (molecules/unit area), is related to these parameters through the equatio

wheren represents the order of the desorption process and is usually a small integer, and the subscript eq indicaand vd are the values appropriate to equilibrium coverage. It must be borne in mind that becausen may differ fromnity and becausevd and S may depend on the adlayer coverage, a linear relation betweenneq and pressure will bebserved only in the simplest of adsorption systems.

he temperature dependence of the equilibrium coverage is contained invd . The physical significance ofvd can be

escribed in terms of the energetic interaction between the adsorbed species and the surface. In the simplest casnteraction can be represented in terms of a one-dimensional potential energy well, as shown in Fig. 10.2. This hows the change in system potential energy that takes place as a molecule from the gas phase approaches an ate on the surface. Once the molecule is trapped in this potential well, the probability of escape is given by abs

eaction rate theory as



Fig. 10.2One-dimensional potential well for a gas molecule approaching a solid

surface.





where ν '0 is an attempt frequency, on the order of the vibrational frequency of the adsorbed species (~ 1013 s1)

is the molar free energy of activation for the process. For a potential well of the form shown in Fig. 10.2atter term may be approximated as

where f and f * are the molecular partition functions of the system in the equilibrium and activated states, respechus

where ν0 is ν '0/( f*/f ).

Alternatively, rather than looking at the desorption frequency, it is often more useful to use the reciprocal of thiwhich is known as themean stay time for adsorption or mean surface lifetime . This is given by

Note that this implies that the deeper the potential wellthat is, the greater the magnitude of∆ Hd the longer will be thmean stay time. The values ofτ0 measured experimentally range from about 1016 to 109 s, implying that the rat f/anges between about 103 and 104. Equation (10.3) may be rewritten in terms of the mean stay time to yield

he existence of a finite value forτa means that a given molecule will spend a proportionally larger fraction of itear the surface than anywhere else in the system. Thus, the time-averaged concentration is going to be higher urface than in bulk of the gas phase. This is just the condition that is described classically as adsorption.





he value ofτa in any situation is a strong function of both∆ Hd and T . The value of∆ Hd is in turn a function of the type of attractirces present in the system. Systems in which the only attractive forces are of the van der Waals, or dispersion, type show valunge from 100 cal/mol to 5000 cal/mol. Customarily, adsorption processes involving forces of this magnitude are called physicalsorption or physisorption processes. Systems in which hydrogen bonding, covalent chemical bonding, or metallic bonding canace will show values of∆ Hd ranging from 5 kcal/mol to as high as 150 kcal/mol. Adsorption processes involving forces of thisferred to aschemisorption processes . The effect of this wide range of observed∆ Hd values on the stay time is summarized in Tab

0.1 [1], based on the assumption thatT = 300 K andτ0 = 1013 s. As can be seen from the table, the values ofτa cover a range from

mes essentially equal toτ0 at the low end, to inconceivably long times at the high end. Note, however, that there is a fairly wideHd values for whichτa is within a few orders of magnitude of 1 s, and that this range can be greatly extended by changing themperature. For example, if the temperature were 600 K instead of 300 K, the value ofτa associated with∆ Hd = 40,000 cal/mol woop from 1017 s, which is approximately the age of the earth, to 1 s, a readily conceivable and experimentally measurable valu

0.1.2dsorption Isotherms

onsider next a number of possible assumptions concerning the value ofn, the relation betweenS and na , and the form of the param, and also consider the effect of these assumptions on the form of the relation betweenneq and p at constant temperaturethat is, th

dsorption isotherm. The simplest set of assumptions that one can make are thatn = 1 and thatτa and S are independent ofna . The fo

able 10.1. Mean Stay Time for Adsorbed Molecules at 300 K for Various Values of the Adsorption Energy, Assumingτ0 =013 sa

Hd Typical Cases τa (s)00 cal/mol Helium

1.2 × 1013

.5 kcal/mol H2 physisorbed1.3 × 1012

.54 kcal/mol Ar, CO, N2, CO2 (physisorbed)1 × 1011

015 kcal/mol Weak chemisorptionOrganics physisorbed 3 × 106

2 × 102

0 kcal/mol H2 chemisorbed100

5 kcal/mol6 × 105(1 week)

0 kcal/mol CO chemisorbed on Ni4 × 109(> 100 yr)

0 kcal/mol1 × 1017(≈ age of the earth)

50 kcal/mol O chemisorbed on W101100

(≈ 101090 centuries)Adapted from DeBoer [1].





q. (10.3) in this case will be

which at constant temperature leads to

his behavior, which is known as Henry's law , predicts a linear increase ofneq with p, as shown in Fig. 10.3. Thebvious difficulty with this model is that it predicts an unlimited adlayer coverage as p increases, which is not obsen practice.

n order to account for the fact that many adsorption systems appear to show adsorption on specific surface sitehat adsorption is limited to one adsorbed species per site, we may introduce what is known as the Langmuir model ofhe adsorption process [2]. In this model it is assumed that the adspecies are bound to a fixed number,n0, of adsorptes per unit area, with no more than one adspecies per site, that the value of∆ Hd is independent of coverage and i

ame for all sites, and that the adsorption probability is finite for impingement on empty sites, but zero for impin occupied sites. This leads to

Fig. 10.3Henry's law isotherms showing equilibrium adlayer

coverage versus pressure for a range of temperatures.







nd to

Defining the fractional coverage,θ, as

nd dividing Eq. (10.13) byn0 yields

his may be solved to yield

his equation is known as the Langmuir adsorption isotherm and is plotted in Fig. 10.4. Note that at low pressure

where this relation reduces to the Henry's law relation

At high pressures, where the equation reduces to

nd all adsorption sites are filled.



he Langmuir model provides a good description of the adsorption process in many systems in which stronghemisorption occurs. It does not provide a very good description in systems involving relatively weak adsorptorces (physical adsorption), because it neglects lateral interactions among adspecies, surface mobility, surfaceeterogeneity, and the possibility of adlayers thicker than one monolayer.





Fig. 10.4The Langmuir adsorption isotherm.

One may also consider another set of assumptions, similar to those of the Langmuir model, for the fairly commf the adsorption of a diatomic gas, in which the gas molecule dissociates in the adsorption process to yield twodsorbed atoms, one per adsorption site, and in which the two adsorbed atoms must recombine in order to desoase, the following equation is based on the assumption that in order for the molecule to adsorb dissociatively, djacent unoccupied sites are necessary:

he desorption rate for this case will be

eading to

ubstitutingθ = neq/n0 and solving forθ yields







his equation, which is sometimes referred to as thedissociative Langmuir isotherm , is shown in Fig. 10.5.

n physical adsorption, in which strong chemical binding forces are not involved, the potential well associated dsorption process arises from the relatively weak van der Waals interactions between the adsorbate and the atohe solid surface. This potential well can be approximated by summing the pairwise interactions between the adnd the atoms in the surface as shown in Fig. 10.6, summing over as many atoms as necessary to include all ato

make a significant contribution to the system potential energy. These individual pairwise interactions

Fig. 10.5The dissociative Langmuir isotherm.



Fig. 10.6Summation of pairwise interatomic interactions to

determine the energy of adsorption for physicaladsorption.





an generally be represented by an expression of the form

wheren and m are integers. For the case in which the attractive forces involved are the induced dipole forces (vWaals or dispersion forces), the appropriate values of these parameters aren = 6, m = 12,

the so-called LennardJones potential. Hereε is the maximum negative value of tair potential andre is the internuclear separation associated with this energy minimum. In the event that the surhat of a crystalline solid, with regular atomic spacing, the system energy,u( xyz ), will depend on the x, y, z coordinaf the adsorbing species relative to some reference point on the crystal surface. We may represent the z dependence his energy by plottingu( z ) versus z , as shown schematically in Fig. 10.7. Here the zero of potential energy is takhe gas-phase species at infinite distance from the surface. As z decreases, the energy of the system becomes negamplying attractive forces between the gas-phase species and the surface), reaches a maximum negative value alue ze, and then rises and becomes positive (repulsive) at very small values of z . The variation ofu( x, y, z ) as aunction of x or y is most conveniently expressed in terms of the variation of the minimum of theu( z ) curve,u0, withr y. A schematic plot ofu0 versus x is shown in Fig. 10.8. The regular variation ofu0 with x reflects the regularnteratomic spacing on the crystal surface. A plot ofu0 versus y would be similar in appearance. This plot indicatehere are favored values of x (and y) at whichu0 has a maximum negative value. These sites, characterized byu00 ohe figure, represent the equilibrium binding sites for the species adsorbed on

Fig. 10.7One-dimensional potential energy curve showing potential energy

as a function of distance to the surface for the Lennard-Jones612 interatomic potential.





Fig. 10.8Variation of adsorption potential well depth with lateral position along a crystalline solid surface.

Fig. 10.9A two-dimensional potential energy surface showing

the variation of potential well depth with impact parameter for an atom approaching a solid surface.

Dotted contours indicate areas of strongestattractive interaction; solid contours indicate

regions of weakest interaction.



he surface. The intervening minima in the absolute value ofu0, designated byv0, represent less stable configuratiohat the absorbed species must pass through in order to migrate from one favored site to another. This variationdsorption energy as a function of position on the surface may also be shown by plotting contours of equalu0 as aunction of x and y, as shown in Fig. 10.9. If the value ofkT is small compared tov0, negligible migration will occund the adsorbed species can be considered as bound at the equilibrium sites, a situation known asimmobile adsorption the alternative case,kT comparable to or greater thanv0, migration will be possible, andmobile adsorption result





n many cases of physical adsorption, it has been observed that the adsorption process continues well beyond thmonolayer coverage limit imposed by the Langmuir model. Several treatments have been developed to describ

otherm equation for this case. The most commonly used is the so-called BrunauerEmmettTeller [3], or BET, mhese workers concluded that many of the experimentally observed adsorption isotherms reported in the literathysical adsorption showed evidence of multimolecular layer adsorption. These isotherms could be characterizelonging to one of five types, shown in Fig. 10.10. The isotherms of type I are, of course, Langmuir isothermsharacteristic of adsorption of only a single molecular layer. The other four types are generally considered to re

multilayer adsorption.

he derivation of the simple form of the BET equation is based on the same assumptions as those involved in terivation of the Langmuir equation, with the added hypothesis that the formation of successive layers can occdsorption of molecules on top of an already formed previous layer. The model assumes that when adsorptivequilibrium has been attained, the total surface area can be broken down into patches, each of which is coveredero, one, two, or more monolayers of adsorbed material, as shown in Fig. 10.11. Over a period of time, the frahe surface having a given coverage will remain constant. That is, ifθi is that fraction of the surface covered byi

monolayers, then at equilibrium we obtaind θi/dt = 0 for alli, and the total amount of material adsorbed is

Fig. 10.10The five isotherm types observed in physical adsorption, according to Brunauer et al. [3].





Fig. 10.11Model used to develop the BET adsorption equation.

Patches on the surface are classified in terms ofthe number of monolayers in that patch.

r

onsidering the dynamic nature of the adsorptive equilibrium, it is evident that this implies that the net rate of ontributing to an increase of a givenθi must be the same as the net rate of those processes contributing to a decrhat sameθi. Processes contributing to the increase in a givenθi are (a) the impingement of molecules on patches ) to convert them to patches ofθi and (b) desorption of molecules from patches ofθ(i + 1). Processes contributingecrease inθi include the adsorption of molecules on patches of coverageθi, to convert them to patches ofθ(i + 1), esorption of molecules from patches ofθi to convert them to patches ofθ(i 1). Thus, for eachθi one may write anxpression stating that







ubtracting the expression for the change inθ0 from that for the change inθ1 leaves

y a similar process for the otherθi, subtracting the expression for changes inθ(i 1) from the expression for changi leaves a set of simultaneous equations of the form

When this set of equations is solved, subject to the assumption thatτa2 = τa3 = τai one obtains an expression forna he form

ubstituting I = p/(2πmkT )1/2 in the expression for x and making the further substitution thatβ = 1/(2πmkT )1/2, onebtains

Note that x is dimensionless, becauseβτa2/n0 has units of (pressure)1. It is thus convenient to define another par having units of pressure, as

he final expression for adlayer coverage is thus







quation (10.41) has the property that as p → q, the denominator in the expression approaches zero. Thus, as p → q,.

is observed in many systems in which physical adsorption occurs that as p approaches p0 (the equilibrium vaporressure of the bulk condensed phase of the adsorbed species at the temperature of the experiment), the amoun

dsorbed rises sharply and appears headed for infinity. It has thus been customary to associateq with p0 and,onsequently, to associateτa2 with∆ Hv, the enthalpy of vaporization of the condensed adsorbate. No fundamentgnificance is to be attached to this choiceit is merely a convenient choice based on empirical observation. The

he final expression for the adsorption isotherm in the BET model leads to the adsorption isotherm shapes show0.12. In this figure, the curve forq = p0 corresponds to the type III isotherm, while the curves forq < p0 and q > p0orrespond to types V and I respectively.

he isotherm equation may be rearranged into a form convenient for determining the values of the parametersn0 any presenting the experimental results as

where the substitutionq = p0 has been made, and the adlayer coverage has been expressed in terms of the volumt STP adsorbed at equilibrium,V , and the volume of adsorbed gas associated with monolayer coverage,Vm. This isquivalent to stating

hus, for an adsorption isotherm which obeys this relation, a plot of the expression pV 1 ( p0 p)1 versus p/p 0 should ystraight line for which the intercept is 1/(VmkB) and the slope is (kB 1)/(VmkB).

Fig. 10.12The BET adsorption equation for various values of the relation ofq to p0.







f the adsorption is limited ton layers, Eq. (10.42) must be replaced by the relation

where x = p/p 0.

should be noted that this equation has two limiting cases: Whenn = infinity, it reduces to Eq. (10.42) (since x musess than 1), whereas ifn = 1 (that is, if only one layer can be adsorbed) it assumes the form

hat is, the Langmuir equation with Langmuir's constantχ having the valuekB/p0 and θ = V/Vm.

f it is assumed that the adsorption process is influenced by the presence of capillaries and that bulk liquid condhe capillaries as the pressure of the adsorbate gas approaches saturation, a rather more complex equation can berived. This was done by Brunauer et al. [4]. Their extended equation, although not commonly used, is of inteecause it represented the first equation to be derived which could describe isotherms of all of the five types shig. 10.10. The subject of capillary condensation is treated in more detail later in this chapter.

he BET equation has found widespread use for the determination of surface areas. It has been found that thedsorption isotherms for nitrogen and the rare gases argon and krypton at low temperatures (commonly liquid nemperature, 77.4 K, is used) on a large variety of adsorbents fit the BET equation over a considerable range. Aumber of investigations have yielded reasonable values forVm on various adsorbents when these isotherms areetermined and plotted according to the BET equation. The measurement of ''BET surface areas" is a standard n many laboratories. The determination of a surface-area value involves the measurement of adsorption over aressures up to p/p 0 about 0.3. These data are then plotted in accord with Eq. (10.42) as p/V ( p0 p) versus p/p 0. The

ope and intercept of the resulting linear plot then give the values ofVm and kB. In the model used to derive thequation,Vm is the volume adsorbed in the first monolayer;kB is a constant which is proportional to exp (∆ H 1∆ HvT , where∆ H 1 is the average heat of adsorption in the first layer and∆ Hv is the heat of liquefaction of the bulkdsorbate.

A second class of models of the physical adsorption process treats the adsorbed layer as a two-dimensional gaseatment will be justified in those cases where the barrier to motion between sites is small compared tokT , and thedsorbed species can be considered to be free to move over the surface. The equation of state for the gas is staterms of a two-dimensional pressure,Π, and an area per molecule,σ, analogously to the three-dimensional pressurnd volume,V . Models of this type are useful, in that they permit one to take into account the interactions amondsorbed species.

One may treat this behavior in the simplest case by assuming that adatoms interact only with the edges of the twimensional surface and make no allowance for the fact that each adatom occupies a finite amount of surface a, assuming that the





whole surface is available to each adatom). Furthermore, one may assume that adatoms collide elastically on thwith no energetic interaction, and that this two-dimensional gas can be described by the two-dimensional analohree-dimensional ideal gas law.

onsider the application of these assumptions to a clean surface bounded by some kind of barrierfor example, turface of a liquid in a vessel. There will be a force,γ , exerted on the barrier because of the surface tension of the

When adsorption takes place on this surface,γ will be reduced. The tension on the barrier is consequently reduce reduced. One can equally well look on this reduction in tension as a pressure exerted on the barrier by the twimensional gas.

One can develop this relation mathematically by beginning with the Gibbs absorption isotherm,

where µi is the chemical potential per molecule for speciesi. For the case of adsorption from a one-component gahase onto a surface, using

ne can determine that

f, now, a two-dimensional pressure,Π, is defined as

his leads to

ntegration of this expression yields

wherena may be a function of p.onsider the case of Henry's law adsorption, as discussed previously. In this case

t any given temperature. Thus







r

ubstituting these results into Eq. (10.51) yields

whereσ = 1/na is the surface area per adatom. This expression has the same form as the three-dimensional idea

where N Av is Avogadro's number. The behavior of the ideal two-dimensional gas is thus seen to be exactly anao that of the ideal three-dimensional gas.

Alternatively, one may make more realistic assumptions concerning the behavior of the two-dimensional gas. Ossume that each molecule occupies some finite area on the surface,b2, and that there is an interaction energy betwny two adsorbed molecules, leading to a lateral interaction force,a2. These are essentially the same assumptions re made in developing the van der Waals equation of state for a three-dimensional gas and lead in this case to imensional equation of state:

Making the additional assumption thatb2 is 1/n0 and using

q. (10.59) may be rearranged to yield







Using this relation and the previously stated relation betweenΠ and p [Eq. (10.51)], one can determine that

where K is a constant related to the adsorption energy,∆ Ea . This relation, known as the HillDeBoer equation , is thedsorption isotherm equation for a two-dimensional gas with lateral interactions on a homogeneous surface. Thf the lateral interaction energy appears in the last term in the brackets on the right-hand side of Eq. (10.62).

he form of the HillDeBoer equation is shown in Fig. 10.13. At high temperature and low coverage, where thef excluded area and lateral interactions will be minimal, the exponential term approaches unity, (1θ) approaches und the isotherm equation reduces to

which is the Henry's law isotherm. At lower temperatures, or for larger values ofa2, and at higher coverages, increeviations from Henry's law are observed. Below a certain temperature,Tc2 (the two-dimensional critical temperahe curve described by Eq. (10.62) becomes double-valued, and a first-order phase change is observed, just as iase of a three-dimensional van der Waals gas. Within the region bounded by the dashed curve, two phases exiquilibrium: a two-dimensional gas and a two-dimensional solid or liquid. At higher pressure, only the condens

will be present.

Fig. 10.13Adsorption isotherms according to the HillDeBoerequation showing two-dimensional condensation.





An additional complication in the characterization of physical adsorption behavior is that of surface heterogenehis point, it has been tacitly assumed that the heat of adsorption, or desorption energy, is the same for all potendsorption sites on the surface. In practice, this is seldom the case. The surfaces of real crystalline materials conumber of surface defects. Even on single-crystal surfaces, defects such as surface steps, vacant surface sites, atoms, and sites of dislocation emergence from the bulk are present. The configurations associated with a numbhese defects are shown schematically in Fig. 10.14. The surfaces of polycrystalline materials are even more coecause surfaces made up of different crystal planes will have different atomic arrangements and consequentlydsorption energies.

he net effect of these surface defects is a quasicontinuous range of adsorption site energies. This distribution mself in adsorption isotherms on nearly perfect surfaces as an increase in the amount adsorbed at low adsorbateressures relative to that expected for the perfect surface, because the adsorption energies associated with the dtes are in most cases larger than those associated with perfectly ordered surface regions. At any given temper

urface lifetimes on these high-energy sites will be longer than for the perfect surface sites, resulting in a highequilibrium coverage. There have been no direct correlations between heterogeneous adsorption behavior and sypes of surface defects, but empirical models based on assumed distributions of adsorption site energies, such

Gaussian distribution, have had considerable success in fitting adsorption isotherms on heterogeneous surfacespproach has been treated in detail by Ross and Olivier [5].

or completeness, it is necessary to mention two empirical adsorption isotherms that have been used extensivelast to describe adsorption data, especially physical adsorption data. These are the Freundlich isotherm,

nd the Temkin isotherm,

Fig. 10.14Typical surface sites and defects on a simple cubic (100) surface.





oth of these isotherms have the property that the adlayer coverage increases more slowly than linearly withemperature, as is commonly observed. In the case of the Freundlich isotherm, the parametern is temperature-ependent, andn tends to be large at low temperature. The parameter K is also temperature-dependent, and it decr

with increasingT . Comparing the forms of these isotherm equations with the other isotherm equations developehe parameter K in both cases must contain the surface lifetime, explaining its decrease with increasing temperaarametern in the Freundlich isotherm corresponds in part to the exponent of p in the Langmuir and dissociativeangmiur isotherms. The fact that it is temperature-dependent probably is related to surface heterogeneity, becaotherm has been most frequently used to characterize adsorption on nonuniform surfaces. Similarly, the logarependence of coverage on pressure in the Temkin isotherm would arise from a combination of site blocking aurface heterogeneity effects, both of which would lead to a less rapid than linear rise of coverage with pressur

0.1.3Heat of Adsorption

n many cases, measurement of the heat liberated in the course of the adsorption process may be used to characariation of the adsorption energy with coverage due either to surface heterogeneity or to adsorbateadsorbatenteractions. For systems in which the adsorption process is reversible at the temperature of measurement, one etermine the adsorption energy as a function of coverage using a form of the ClausiusClapeyron equation relat

hange in equilibrium pressure required to attain a given adlayer coverage to the temperature of adsorption, nam

whereqst is the so-called isosteric heat of adsorption and will be numerically equal to the adsorption energy at overage of interest. If isotherms are available at two or more slightly different temperatures,qst may be calculated

where p2 and p1 are the equilibrium pressures at the temperaturesT 2 and T 1, respectively, for a constant coverageMeasurements ofqst for a range of coverages will show the effects of surface heterogeneity as a decrease inqst withncreasing coverage. Adsorbateadsorbate interactions can lead to either an increase or a decrease ofqst with coveragepending on whether the interaction is attractive or repulsive. In most cases of physical adsorption, the interace attractive (e.g., van der Waals). In the case of chemisorption, the nearest-neighbor adsorbateadsorbate intera

may be repulsive due to polarization of the adsorbed species in its interaction with the surface.





0.1.4Observed Behavior

Over a period of many years, adsorption isotherms have been obtained for a wide variety of systems over a widf temperatures. Representative examples, chosen to show the correspondence between the theoretical equationeveloped above and experimental measurements, are given below.

onsider first physical adsorption isotherms. At low pressures, on energetically uniform surfaces, the simple Haw behavior may be observed, as in the case of the adsorption of CO2 on wood charcoal shown in Fig. 10.15 [hat even at the relatively low coverages involved here, the isotherm data show deviations from Henry's law at emperatures measured. More typical physical adsorption isotherms are shown in Fig. 10.16, taken from the wo

Ross and Olivier [7]. These figures show isotherms for argon on two different samples of carbon black, having egrees of surface heterogeneity. P33 is a carbon black graphitized by heating to the temperature shown in parehe isotherms show effects due to both adsorbateadsorbate interactions and surface heterogeneity. Isosteric headsorption curves derived from these isotherms are shown in Fig. 10.17. The initial decrease in the heat of adso

with increasing coverage is due to surface heterogeneity (the 2700°C sample being much more homogeneous),he increase in heat at higher coverages reflects adsorbateadsorbate interactions. Similar effects are seen in Fig.or argon adsorption on Linde molecular sieve 13X, a material commonly used in sorption roughing pumps [8]

hysical adsorption isotherms taken at low enough temperatures on very energetically uniform surfaces often srst order phase changes in the adsorbed layer predicted by the two-dimensional gas treatment described previ

ypical example showing this behavior is shown in Fig. 10.19, for the case of CFCl3 adsorbed

Fig. 10.15Isotherms for the sorption at low pressures of

carbon dioxide by wood charcoal [6].





Fig. 10.16Comparison of experimental adsorption isotherms (individual points) with the

theoretical description of a mobile adsorbed film (solid line). (a) Argonadsorbed by P33 (2700°C) at 77.5 K; (b) argon adsorbed by P33 (1000°C)

at 77.5 K [7].

n a very energetically uniform graphite surface [9]. Note that the extent of the discontinuous rise in coverage wressure decreases in extent with increasing temperature and would disappear atTc2, the two-dimensional criticalemperature.



urrently, the bulk of the physical adsorption isotherm measurements being made are in connection with theetermination of surface area using the BET technique discussed above.

he literature on chemisorption isotherms is much more sparse than that for physical adsorption. The reason fohat in order to attain equilibrium between adsorbed and gas phases, the molecular impingement rate must be in

with the





Fig. 10.17Isosteric heat curves as a function of coverage for argon

adsorbed by two thermally conditioned carbon blacks [7].

Fig. 10.18Comparison of experimental adsorption isotherm (individual points) withthe theoretical description of a mobile adsorbed film (solid line) for argon

on Linde molecular sieve 13X at 77.5 K [8].



esorption rate, as set by the surface lifetime and equilibrium adlayer coverage. In most chemisorption systemsurface lifetime, except at very high temperatures, is so long that the equilibrium pressure in the submonolayer

would be below the capability of ultrahigh-vacuum systems. As a result, most of the available data on chemisoystems are in the form of uptake curves, showing the amount adsorbed as a function of gas exposure, or in theesorption kinetic measurements. Both of these types of measurement will be discussed in Section 10.1.5, "Adinetics."

n a few cases, however, in systems showing relatively weak chemisorption, isotherm data have been obtained.uch example is the adsorption of oxygen on





Fig. 10.19Comparison of experimental adsorption isotherms (individual points)

with the theoretical description of a mobile adsorbed layer(solid lines) for CFCI3 adsorbed on P33 (2700°C) [9].

lver. This system has been studied by Buttner et al. [10], using the Gibbs adsorption isotherm,

whereγ is the surface tension andk is Boltzmann's constant. Results of this measurement are shown in Fig. 10.20

hemisorption isotherms have also been measured by conventional techniques in a few systems, primarily for ases on refractory metal filaments. Data obtained by Hickmott [11] for H2 on tungsten are shown in Fig. 10.2overing the temperature range from 77 K to 373 K. These results were shown to fit the Temkin isotherm, chary a coverage-dependent heat of adsorption. This apparent temperature dependence may be related to the fact t

measurements were made on a surface showing a range of crystalline planes, each of which may have had a difnteraction energy with hydrogen. Measurements of N2 adsorption on tungsten, in the temperature range from 1540 K by Kisliuk [12], are shown in Fig. 10.22. These data are well fit by the dissociative Langmuir isotherm

ecause of the difficulty in measuring adsorption isotherms for systems in which strong chemisorption occurs, he available equilibrium data on chemisorption systems is in the form of qualitative measurements of which gaombinations lead to the formation of chemisorbed monolayers and which don't. Because the chemisorption preads to the formation of strong chemical bonds, the process is quite specific, permitting classification of systems those shown in





Fig. 10.20Variation of the surface tension of silver with

oxygen partial pressure.Reprinted with permission from J. Phys. Chem . 56, 657

(1952) [Ref. 10]. Copyright 1952 AmericanChemical Society.

able 10.2 [13]. This table presents a classification of a large number of metals in terms of their tendency to chgroup of common gases. Note that the transition metals, as a group, tend to be very active in chemisorption, woble metals are somewhat less so, with the non-transition metals and the semiconductors being much less actielectivity in chemisorptive properties has been used to selectively purify less active gases of more active impu

0.1.5Adsorption Kinetics

or the case of physical adsorption, the energy associated with the minimum in the potential well will be comphe heat of condensation of the adsorbate, typically between 1.5 and 2.0 times∆ Hv. For this case, the desorption

equency will be given by

ecause there is no barrier to adsorption, the accommodation coefficient into the physically adsorbed state is gnity, except for light adsorbates or very low surface temperatures.



he overall from of the expressions for Ra and Rd for this case will depend on the effect that the presence of onedsorbed molecule has on the adsorption or desorption of another molecule and on the energetic uniformity of urface. A number of models have been developed to describe the consequences of various assumptions concerhese parameters. The simplest assumption that one can make is that molecules adsorb and desorb independentnother, on an energetically





Fig. 10.21Hydrogen isotherms on tungsten over a range

of temperatures [11].



Fig. 10.22 Nitrogen isotherms on tungsten. Here P ′ is the pressure multiplied

by (Ts/Tg )1/2, whereTs is the temperature of the solid andTg is thetemperature of the gas. The lines are drawn with a slope of 0.5 [12].





Table 10.2. Classification of Metals and Semimetals Based on Adsorption Propertiesa

GasesbGroup Metals O2 C2H2 C2H4 CO H2 CO2 N2

A Ca, Sr, Ba, Ti Zr, Hf, V, Nb Ta, Cr, Mo, W Fec, Red A A A A A A AB1 Ni, Cod A A A A A A NAB2 Rh, Pd, Pt, Ir d A A A A A NA NAC Al, Mn, Cu, Aue A A A A NA NA NAD K A A NA NA NA NA NAE Mg, Agc, Zn, Cd In, Si, Ge, Sn

Pb, As, Sb, BiA NA NA NA NA NA NA

F Se, Te NA NA NA NA NA NA NA

a From Bond [13].b A, adsorption; NA, no adsorption.c The adsorption of N2 on Fe is activated, as is the adsorption of O2 on Ag films sintered at 0°C.d These metals probably belong to the group in which they are included, but the behavior of films is notknown.e Au does not adsorb O2.

niform surface, with no limit on the amount adsorbed. These assumptions lead to the Henry's law model for thdsorption process described above. This model is an idealization; but it should, in principle, be approached by

hysically adsorbed systems at low pressure and high temperature (i.e., asna → 0).he net rate of adsorption or desorption in this case is given by

ntegration of this relation leads to

or the case ofna < neq, and to

or the case ofna > neq. Equation (10.71) would describe the behavior expected when a clean surface is exposedsorbate, as would be the case in a sorption or getter pump. Equation (10.72) describes the expected behaviorystem is pumped





om high pressure to a lower pressure. If the partial pressures of adsorbable gases in the system are rapidly redow values, as is often the case in pumping a vacuum system, then the adlayer population will decrease expone

with time, with the rate being proportional tovd .

he behavior of real systems is more complicated than the Henry's law model suggests. In general, even in phydsorption systems, the adsorption rate will depend on whether the incoming molecule strikes the bare surface

whether it strikes an area already covered by adsorbate. The desorption rate will be sensitive to any factor that Hd , such as energetic interactions between adsorbed species, the position of the incoming atom relative to the .e., first layer, second layer, etc.), and the presence of sites of different∆ Hd on the surface. Complications of thisre difficult to treat analytically.

0.1.6hemisorption Kinetics

he kinetics of the chemisorption process, in which strong chemical bonds are formed between the adsorbate aubstrate and which may involve dissociation of the adsorbed molecules, are considerably more complicated thhysical adsorption process considered above. In such cases, the shape of the potential well will be much moreomplicated than that shown in Fig. 10.2, leading to more complicated expressions for the desorption frequencxpressions in general show a dependence onna and involve multiple adsorbed states, some of which may represissociation of the adsorbed species. This process may again be considered in terms of potential energy diagramdsorbate substrate system.

he form of the potential energy curves in this case will depend on whether the incoming molecule is adsorbedwithout the breaking of any intramolecular bonds, or whether the molecule must dissociate in order for its comtoms to reach the chemisorbed state. The simpler case of nondissociative adsorption is shown in Fig. 10.23. Farticular case of a homonuclear diatomic molecule, the case of

Fig. 10.23One-dimensional potential energy curve for the

nondissociative chemisorption of a diatomicmolecule showing both a weakly physisorbed stateand a more strongly adsorbed chemisorbed state.







issociative adsorption is shown in Fig. 10.24. In the first of these cases, the observed energy of desorption wilpproximately equal to the well depth relative to the zero of potential energy,∆ Ea in the diagram. In the case ofissociative adsorption, one must consider both the possibility of desorption as individual atoms, for which theesorption energy is approximately (∆ E )a per atom, and the possibility of recombination to reform the diatomic

molecule and subsequent desorption of this species, for which the desorption energy is approximately 2(∆ E )m per

molecule. These two desorption energies are related by

where∆ ED is the dissociation energy of the diatomic molecule. (Recall that, as they have been defined, adsorptnergies are inherently negative; dissociation energies are inherently positive.)

he case of heteronuclear diatomic molecules that adsorb dissociatively is even more complex. Figure 10.25 isiagram appropriate to CO adsorption on a metal surface, in the case where the adsorption is nonactivated. Thigain shows a potential well for the molecularly adsorbed species; but here one must show a single potential wombination (Ca + Oa), because the potential wells for the adsorbed carbon and oxygen atoms will not necessaroincide. Moreover, one must use as a reference for the desorption of (C + O) atoms the dissociation energy of Additional possible outcomes for the desorption process also arise in this case, because it is possible that O2 orO2 species as well as CO could desorb from a layer containing adsorbed carbon and oxygen atoms. This case

akes one over the boundary between simple adsorption processes and surface chemical reactions, which will bater in this chapter.

A final complication that may arise in the case of dissociative chemisorption is one in which the crossover betwurves for the physisorbed and chemisorbed states

Fig. 10.24One-dimensional potential energy curves for the

dissociative adsorption of a homonuclear diatomicmolecule, showing both a weakly physisorbedstate and a dissociatively chemisorbed state.








dissociative chemisorption of a heteronuclear diatomicmolecule, showing both a weakly physisorbedstate and a dissociatively chemisorbed state.


dissociative adsorption of a homonuclear diatomicmolecule for the case of a finite activation

energy barrier to chemisorption.



ccurs at an energy greater than that of the zero of energy, as shown in Fig. 10.26. In this case, the chemisorptirocess will be activated, with a finite activation energy being required to surmount the energy barrier leading hemisorbed state. The kinetics of the adsorption process may show a complicated temperature dependence in nd the adsorption rate may depend on the kinetic energy of the incident gas molecules. The rate equations for rocess will be considered in the section on activated adsorption (Section 10.2.3).

hese more complicated adsorption energetics lead to more complicated adsorptiondesorption kinetic behaviorhe simplest case to consider is that of the





ondissociative adsorption of a molecule into a strongly bonded configuration followed by the desorption of thmolecule. Typical systems showing this behavior include CO on nickel or platinum. The potential energy diagrhis case was shown in Fig. 10.23. The shallow potential well for physical adsorption of the molecule discussedill present; but in this case, there is an additional well, with a much larger∆ Ea (typically in the 25-kcal/mol rangeconsiderably shorterre . In the simplest case, there is no significant barrier to the capture of the adsorbing speci

he shallow potential well, so that a constant fraction,α , will be accommodated into this state at a rate governed bmpingement rate, I . In the deeper potential well state, however, since strong chemical bonds are formed betweedsorbate and one or more surface atoms, molecules can only be accommodated onto vacant sites.

he fact that we have two possible adsorbed states in this case, the physically adsorbed state and the chemisorbeads to a potential complication in the adsorption and desorption rates. Referring to Fig. 10.23, if the energy detween the bottom of the physical adsorption well and the crossover point between the two states is≥ kT , then it isossible that the incoming molecule may be trapped in the physical adsorption state. Once in this state it may eesorb, with a rate constantkp, or pass into the chemisorbed state with a rate constantka . Once in the chemisorbed may return to the physical state with a rate constantkd . The overall adsorption and desorption rates in this case

e obtained by considering the system in terms of a generalized chemical reaction scheme

ormulation of the overall rate equations for the adsorption and desorption process using this scheme is compleenerally requires that some assumptions be made in order to obtain a specific result. For example, in the preseone assumes that chemisorption occurs on a fixed number of sites, that there are no lateral interactions amon

dsorbed species, that there is a maximum of one chemisorbed species per site, that the weakly adsorbed molecprecursor" species behaves the same over both filled and empty chemisorption sites, and that the surface lifeti

molecular state is short (so that the coverage in this state is always small and the population in this state will alwt its steady-state value), then one can write for the overall rate of the desorption reaction that

whereθ is the fractional coverage in the chemisorbed state. The rate of adsorption can be written





wheren0 is the number of chemisorption sites per unit area as before andα is the accommodation coefficient forapping in the weakly bound precursor state. When adsorptive equilibrium has been reached, Ra and Rd will be equo that

his may be solved to yield the equilibrium coverage in the chemisorbed state as

which is simply the Langmuir isotherm developed earlier.he net rates of uptake or emission in this case will depend on the relative values of the rate constants,ki. These in t

will depend on the various activation energy terms, if we assume that the form of theki is

or the case where is small compared tokT , the presence of the weakly bound precursor state will not affedsorption and desorption processes, and we will have

or the case of desorption into a vacuum and

or the case of adsorption into a state from which the desorption rate is negligible. In this case, will beumerically equal to∆ Ea . In either of these cases, the rate of change of surface coverage with time will be expo

he case of the dissociative chemisorption of a homonuclear diatomic molecule may be treated similarly, usinghemical reaction sequence

sing the same notation as in the previous case of nondissociative adsorption. In this case, making the same asss before, the expressions for Rd and Ra become







n this case, equating Ra and Rd to find the equilibrium coverage yields

which was previously shown to be the "dissociative Langmuir isotherm."

he rates of adsorption and desorption are considerably more complicated in this case than in previous cases. Hor cases in which is small compared tokT the rate expressions reduce to

or the case in which the adsorption rate is negligible and

or the case in which desorption may be neglected.

Alternatively, the effects of the precursor state may be considered explicitly for both the adsorption and desorprocesses. This is of interest for a number of reasons. First, for many chemisorption systems, the binding energhemisorbed state is so high thatθeq = 1 at ambient temperature, even for very low gas-phase pressures. Conseqmeasurement of the equilibrium coverage does not provide any information on the details of the adsorption prohis case, kinetic measurements of the rate of approach to equilibrium offer the only means of determining the aeaction sequence and reaction order and, in turn, the values of the various rate constants and their associated eerms. As a practical matter, the major importance of chemisorption is in relation to the rate of surface processerystal growth, corrosion, catalysis, and the operation of getter pumps such as the titanium sublimation pump oetters. The rate of chemisorption is in many cases the rate-controlling step for the overall process.

onsider as an example the adsorption rate for the case of the dissociative adsorption of a homonuclear diatommolecule, as discussed above. In order to describe the rate of adsorption in such a process, one generally talks if the sticking coefficient for chemisorption, defined as

hat is, the unit collision adsorption probability. Clearly, the upper limit onS is unity. In practice,S is often much lehan unity and in general will change as adlayer coverage changes. For the case of the dissociative adsorption oiatomic molecule,





has already been shown that

One may consider the form of this equation in terms of the relative values ofka and kp. If as shown in F0.24, the surface lifetime in the molecular state will be long compared to the time required for the dissociationeading to

nd the sticking coefficient will be independent of coverage right up to the point whereθ→ 1.

is also useful to look at the effect of various ratios of the rate constants on the overall rate of the desorption p

onsider the case in which For this case

nd the desorption process will follow second-order kinetics. Alternatively, if we obtain

which would show a significant departure from second-order kinetics, especially at large values ofθ. Further exampf this type will be found later in this chapter when surface reaction kinetics are considered in detail.

onsider finally the kinetic behavior observed in systems in which the crossover between the molecularly physnd dissociatively chemisorbed states occurs at an energy greater than zero, as shown in Fig. 10.26. In such casnite barrier is present for both the adsorption and desorption processes. This not only influences the temperatuependence of the adsorption rate but also gives rise to two new phenomena, namely, the desorption of molecuaving excess kinetic energy and a dependence of the adsorption rate on the kinetic energy of the incident mole

onsider first the dependence of the adsorption rate on substrate temperature. In terms of the precursor mechan

iscussed previously, since the ratio of the rate constantkp to ka, which is

will decrease with increasing temperature, leading to an increasing chemisorption probability. The alternative c

leads to a decreasing chemisorption probability with increasing temperature.







n the case of activated adsorption, it is also possible to have direct desorption from the chemisorbed state, withnite residence time for the desorbing molecule in the precursor state. This leads to the desorption of moleculen excess energy equivalent to the barrier height shown in Fig. 10.26. This energy may be carried off either asanslational kinetic energy or as excess energy in the internal modes of the molecule. Excess translational kinenergy can be observed either by a time of flight measurement of the desorbing molecules or as a departure froxpected cosine spatial distribution of the desorbed species.

Direct adsorption from the gas phase is also possible in the case under discussion, and measurement of the adsorobability as a function of the kinetic energy of the incident molecules provides a means of measuring the heiarrier to chemisorption. If one considers the behavior of an impinging molecule in terms of the concept of a curning point, defined by the distance from the surface at which the kinetic energy of the impinging molecule ialanced by the repulsive part of the adsorptive potential well, one sees that an impinging molecule having an inetic energy greater than the barrier height will have a classical turning point beyond the location of the barrian reach the chemisorbed state directly, in a single collision, without trapping in the precursor state. This behaeen observed in a number of systems by using seeded free jet expansions to produce fluxes of adsorbate molenown, high kinetic energies and measuring the chemisorption probability as a function of this energy.

0.1.7

Kinetic Measurementshe kinetics of adsorption and desorption processes have been studied in detail for many systems, using a widef techniques. The parameterτa has been measured directly in a number of systems using molecular beam scatteechniques, using a system similar to that shown schematically in Fig. 10.27 [14]. In these measurements, the aurface, usually a single crystal, is mounted on the axis of the system, and exposed to pulses of the adsorbing spenerated by the modulated molecular beam source. A mass spectrometer, mounted in line of sight to the sampurface, measures the flux of gas desorbed from the surface. The surface lifetime may be determined either fromf desorbed flux versus time, using Eq. (10.72), or by measuring the phase and amplitude of the desorbed flux o the modulation wave form the incident molecular beam [15]. This technique was first reported by Scheer and16] and has been used extensively by Hudson et al. [14, 1721], Wharton et al. [22], and Campbell et al. [23], athers. Data obtained in a range of systems are summarized in Table 10.3, reported asτ0 and∆ Ed for the systemsudied. Additional values ofτa , determined from capillary transit time measurements, are summarized later in thhapter in the section on capillarity effects (Section 10.1.8).

he sticking coefficient for chemisorption has been measured in many systems at temperatures low enough thaesorption rate in negligiblethat is, under conditions in which the adsorption rate should be described by equatis Eq. (10.89) or Eq. (10.90). A summary of sticking coefficient measurements for nitrogen chemisorption on vungsten surfaces is shown in Fig. 10.28, taken from the work of King [24]. It can be seen that both the initial vhe sticking coefficient and the variation of the sticking coefficient with coverage differ greatly from one





Fig. 10.27Schematic top view of an ultrahigh-vacuum molecular beam scattering

system used for direct measurement of the surface lifetime,τa . Reprintedfrom D. A. Hoffman and J. B. Hudson, "The Adsorption and Decompositionof N2O on Nickel (100),"Surf. Sci . 180, [Ref. 14] with kind permission of

Elsevier Science NL, Sara Burgerhartstraat 25, 1055 KV,Amsterdam, the Netherlands.

able 10.3. Experimental Measurements of Surface Lifetime by Mass Spectrometric Molecular Beam TechniquesAdsorbate Substrate τ0 (s) ∆ Ed

(kcal/mol)Temperatures (K) References

d W(110)9 × 1011 41.1 7501000 17

Ag W(110)3 × 1013 66 9501300 18

2H4 C on Ni(110)4 × 1010 11.9 300380 19

N2O Ni(110)1012 6.2 120160 14, 20

N2O O on Ni(110)1011 4.7 120160 14

O C+O on Fe(110)3 × 1010 13.7 > 700 21

O Pt(111)4 × 1014 31.1 419505 22

O2 Pt(111)42a 51 686780 23

Second-order recombinative desorption. Units ofτ0 are s/cm2.



ystal face to another. Note that all faces have sticking coefficient values less than unity even at zero coverage, indicating eitherαss than unity or that there is a finite probability of desorption from a precursor state rather than passage into the chemisorbed stthe faces show a range of nearly constant sticking coefficient, suggesting the importance of precursor states in the adsorption p





Fig. 10.28Sticking coefficient for the chemisorption of nitrogen on various

tungsten single crystal planes. Reprinted fromCRC Crit. Rev. Solid

State Mater. Sci . 7, 167 (1977) [Ref. 24]. Copyright 1977CRC Press, Boca Raton, Florida.

More detailed measurements, over a range of temperatures, would be necessary in order to fully characterize thdsorption process in this system.

An example of desorption over a barrier, to produce desorbed species having excess kinetic energy, is shown in0.29 for the case of D2 desorption from Fe (110) [25]. The experimental results show an approximate cos2θ istribution, indicative of excess kinetic energy normal to the surface. Desorption of molecules in thermal equil

with the surface would be expected to show a cosθ dependence. Results of adsorption measurements in a systemhowing activated adsorption are presented in Fig. 10.30, for the case of O2 chemisorption on W (110) [26]. Inudy, the sticking probability,S 0, increased rapidly as the translational kinetic energy of the impinging O2 mole

was increased. The rate of increase implies a barrier height on the order of 0.20.3 eV (47 kcal/mol). The fact thicking coefficient scales as the normal component of the incident kinetic energy implies that the barrier is essne-dimensional.

0.1.8apillarity Effects

Up to this point, it has been implicitly assumed that the surfaces on which adsorption was taking place were flaearly flat. The structures of many practical adsorbent materials contain networks of small-diameter pores. In sases, such as the so-called "activated carbons," this porosity arises from the method of manufacture. In others,he synthetic zeolites, the porosity is an inherent feature of the crystal structure of the material. In either case, thresence of small-diameter pores can have







Fig. 10.29Desorption flux as a function of detector angle relative to the

surface normal for angle resolved thermal desorption ofdeuterium from Fe(110). Reprinted from E. A. Kurz and J. B.Hudson, "The Adsorption of H2 and D2 on Fe(110) II,"Surf.

Sci. 195, [Ref. 25] 34 (1988), with kind permission of ElsevierScience NL, Sara Burgerhartstraat 25, 1055 KV, Amsterdam,

the Netherlands.

ppreciable effects on both the equilibrium adsorption behavior and the rate of uptake into the adsorbed phase.

onsider first the effect of pores on adsorptive equilibrium. This can be explained by a purely thermodynamic ased on the effect of surface curvature on the equilibrium vapor pressure of the adsorbing species. The physictuation in this case is shown in Fig. 10.31, which shows a pore of circular cross section containing a liquid wh

he surface of the pore. The relation between the equilibrium vapor pressure and the geometry of the system forke this is given by the Kelvin equation,



where pβ is the vapor pressure over the liquid in the pore, p0 is the vapor pressure over the flat surface of the liquhe surface tension of the liquid, andV α is the molar volume of the liquid. As an example of the magnitude of thffect, consider the case of water adsorbed into a 10-nm-diameter pore at 300 K. A calculation based on Eq. (1eads to a value of pβ/ p0 of 0.313, implying that the pores would be filled by





Fig. 10.30Sticking coefficient for chemisorption of oxygen ontungsten, as a function of incident oxygen molecule

kinetic energy [26].

Fig. 10.31Schematic representation of the condensation of

an adsorbed gas in a small-diameter pore.

ondensed water if they were exposed to the atmosphere at a relative humidity exceeding 32%. This illustrates ource of the large amounts of water that are released during pumpdown of systems containing porous materialollowing exposure to the atmosphere.



he kinetics of the adsorption process will also be significantly changed from the values determined previouslydsorbate must penetrate into a porous material to achieve adsorbed equilibrium. This kinetic effect can be experms of the diagram shown in Fig. 10.32, which shows the path of a gas molecule through a tube under condithat the mean free path in the gas,λ, is large compared to the tube diameter,d . This process can be one of the signiactors controlling the net





Fig. 10.32Schematic representation of the path of a gas molecule

through a capillary having a diameter that is short comparedto the mean free path in the gas phase.

ate of flow of gases through small-diameter tubes at pressures low enough that few gasgas collisions occur. Thelevant both to the time required to saturate a sorption roughing pump and to the time required to pump down hamber through a capillary tube.

onsider the average time required for a molecule to traverse a capillary of lengthl and diameterd as shown in F

0.32. For the case ofλ > d, will be the product of the number of collisions with the wall required to traverse apillary, multiplied by the sum of the average time of flight per jump and the mean surface lifetime per collisie shown from kinetic theory considerations that

where the term outside the parentheses is the number of collisions required to traverse the capillary, the first terarentheses is the average time of flight, and the second term in the parentheses is the surface lifetime. This ex

may be rearranged to separate the effects of the two processes, yielding

Note that the first term depends onT 1/2, due to the presence of , and that the second is exponentially dependeue to the temperature dependence ofτa , as shown in Eq. (10.7). If the molecule moves over the surface due to suiffusion while it is adsorbed, this will contribute a third term to Eq. (10.96). For the present we will ignore thi

he values of calculated for various gases for various-sized tubes are summarized in Table 10.4, taken from27]. Each entry in this table shows separately the effects of the two terms in Eq. (10.96). The cases shown repralues for the surface lifetime that would be representative of H2 (1012), N2 (1010), and an organic molecule (dsorbed at ambient temperature.

he general trend shown here is that for heavier, and consequently more strongly adsorbed, molecules and for alues of 1/d , the adsorption term becomes more important. For the organic molecule it is the dominant term fohe cases shown. Note in passing that this is how a gas chromatograph works: The more strongly adsorbed spec

mixture take longer to pass through the tube of the chromatograph, resulting in a separation of the components mixture. Note too that in







acuum systems, where pumping speed and the conductance of tubes are the factors of importance, the effects shown in Table 1ansient. At steady state the surface concentration will become larger at the high-pressure end of the tube relative to the low-preith the net effect of canceling out the adsorption-dependent term in the flow rate.

his technique has been used in practice to determine surface lifetimes in a number of systems. A summary of available data, taedhead et al. [28], is shown in Table 10.5 [2931].

he implications of these results for the operation of sorption roughing pumps are obvious. Saturation of the external surfaces odsorbents such as the zeolites typically used in sorption roughing pumps will occur rapidly at liquid nitrogen temperature. Thee time required to reach adsorptive equilibrium will be the time required for adsorbing gas to penetrate the pore structure of thased on the figures shown in Table 10.4, the required time for a typical adsorbent particle will be on the order of 5000 s.

able 10.4. Delay Times for transmission of pressure pulses through a capillary of length / and diameterd . Mean stayme for adsorption isτa and mean molecular velocity is

τa = 1012 s

= 15 × 104 cm·s1

τa = 1010 s

= 5 × 104 cm·s1

τa = 104 s

= 104 cm·s1

= 10 cm= 101 cm 3 × 103 + 5 × 109 102 + 5 × 107 5 × 102 + 5 × 101

= 10 cm= 104 cm 3 × 104 + 5 × 107 103 + 5 × 105 5 × 103 + 50

= 102 cm= 106 cm 3 × 104 + 5 × 105 103 + 5 × 103 5 × 103 + 5000

= 103 cm= 107 cm 3 × 105 + 2 × 105 104 + 5 × 103 5 × 104 + 5000

Adapted from DeBoer [27].

Table 10.5. Mean Stay Time for Adsorption of Molecules on Surfaces Measured by Time Delay Methoda

Gas Surface Range of Measurement τa (s) ReferencesAr Glass 7890 K

τa = 1.7 × 1014 exp(3800/RT)29

He Glass 13.820.4 K τa1 = 109 exp(299/RT)τa2 = 109 exp(530/RT)(two states)

30

NH3 Analcite 278308 K τa = 3.1 × 1011 exp(4300/RT)

31

O2 Analcite 278308 K τa = 6.6 × 1011 exp(3010/RT)

31

Adapted from Redhead et al. [28].





0.2bsorption

onsider next the complications that arise when a species is not only present in the gas phase and as an adsorbeut is also dissolved in the bulk of a material in the system or in the system walls. In this case, one must considnly the equilibrium and fluxes of gas molecules between gas and surface, but also equilibrium and fluxes asso

with flow in an out of the bulk of the solid. In most cases, the gases that will dissolve readily in the materials foacuum systems are simple gas molecules, and in most cases they dissolve as single atoms. Thus the typical pr

we deal with here, say for the flow of a gas into and out of a solid, can be represented as

where A(sol) represents A atoms dissolved in the bulk of a solid and we will haven = 1 for gases that dissolveondissociatively andn = 2 for dissociative dissolution. The potential energy diagram for this process is shown i0.33. The new features that we see here are, first, that the energy does not rise indefinitely as the molecule apphe surface, but goes through a maximum, then decreases to a minimum representing a stable site for the dissolpecies, and, second, that there will be a succession of such sites extending into the bulk, separated by maximaotential energy. Note that the energy associated with the minimum in the potential well representing the absorpecies may be higher or lower than the minimum associated with the adsorbed species and may be higher or lhe energy of the species in the gas phase. The energy difference between the minimum in the absorbed speciesotential well and the gas-phase species is the heat of solution,∆ Hs . In the event that the minimum for the absorbepecies is lower than the energy for the gas-phase species, solution will be an exothermic process, and the solubecrease with increasing temperature. In the alternative case of a positive heat of solution, as shown in Fig. 10.olubility will increase with increasing temperature.

Fig. 10.33One-dimensional potential energy diagram for the transport ofgas through a solid by adsorption followed by dissolution and

bulk diffusion.





0.2.1quilibrium Solubility

onsider first the case in which the solid and gas phases are in equilibrium. Based on purely thermodynamiconsiderations, one can represent the process shown in Eq. (10.97) as a generalized chemical reaction and writquilibrium constant

where aA(sol) is the activity of A in solution andaA(gas) is the activity in the gas phase. If one makes the substitu

he equilibrium concentration in the solidthat is, the solubilitymay be written as

whereC 0 is a constant for any particular gassolid combination and∆ Hs is the heat of solution defined by the potennergy diagram of Fig. 10.33 above (that is, the heat released in the sorption process, per gram mole of gas abs the so-called solubility constant. Solubilities may be expressed in terms of the concentration in the solid, as maction of solute, as grams per unit volume, or as the volume of gas (at STP) taken up by a given mass of solid

may be expressed in terms of the mass of gas taken up by a given mass of solid.

A similar result may be obtained by a kinetic argument that takes specific account of the role of an adsorbed laorption process. This argument will be presented later, in a discussion of the combined effects of permeation aesorption on the rate of outgassing.

0.2.2Diffusion Rates

he rate of transport in the bulk can be characterized by a jump frequency, the rate at which absorbed atoms mne equilibrium site to another. Using absolute reaction rate theory, this jump frequency can be represented as

he one-dimensional flux arising from this jumping process is given, assuming that the jump direction is rando





which is known as Fick's first law [32]. In this equation, D is the diffusivity and is related to the jump frequency b

ick's first law is adequate to define the diffusive flux in the case of steady-state transport, as would occur in thate permeation of gas through a solid slab, such as the wall of a vacuum system, with constant gas pressures b

maintained on both sides of the slab. In order to describe the transport process in the more common case of thef a gas into or out of a solid, in which the concentration of the gas is changing with time at any point in the so

must use a form of Fick's law which takes account of the change with time in the amount of material in any smolume of the solid. For one-dimensional diffusion, the form of this equation is

which is known as Fick's second law . Solution of this equation requires specification of the boundary conditionsppropriate to any specific situation.

0.2.3Kinetics of Absorption and Permeation

Absorption involves successive passage from the gas phase to the adsorbed phase and then into a near-surface bollowed by penetration into the bulk by a series of diffusive jumps. Desorption involves the reverse sequence.verall process of removal of gas from the bulk of a solid can thus be treated as a process of bulk diffusion, folesorption. The desorption steps can be treated as described earlier in this chapter and, in many cases, will be rompared to the bulk diffusion process, especially when material must be removed from deep within the bulk. mplicity, the absorptiondiffusion and the adsorptiondesorption processes will first be treated separately.

onsider first the kinetics of the uptake of gas into the solid by absorption followed by diffusion processes, forwhere the details of the adsorptiondesorption sequence do not affect the overall transport rate. For this case, the

e an equilibrium between the gas phase and the near-surface bulk phase set by

where J is the net diffusion flux from the bulk at the surface, andS is the sticking coefficient for adsorption. At

quilibrium, this flux will be proportional to the concentration at the surface of the solid,Cx=0. The impingement ret by the gas-phase pressure, and the value ofS will depend on the nature of the adsorption process. For the caseondissociative adsorption, at adsorptive equilibrium,S will be a constant; for dissociative adsorption,S will beroportional to p1/2.





0.2.4teady-State Permeation

f it is assumed that the adsorption and desorption processes are fast relative to absorption and permeation, thenf gas uptake or release from a solid will be controlled by the rate of diffusion of the gas through the solid. Conrst the case in which a region at high pressure is separated from a region of low pressure by a solid material thermits passage of the gas from the high-pressure region to the low-pressure region by bulk diffusion. In this cn initial transient, the rate of permeation will be constant. The resulting concentration gradient through the solnear, as shown in Fig. 10.34, and the permeation process can be described by Fick's first law. The steady-stateermeation rate will be given by

whered is the thickness of the solid and the concentrations on the high- and low-pressure sides will be given (ahat the adsorption and dissolution processes involved are rapid relative to the diffusion process) by the equilibolubilities at the two pressures. For the case of gases that dissolve without dissociation, this leads to

r, taking account of the temperature dependence of the diffusivity,

he temperature dependence of the permeation process will thus depend on the algebraic sum of the activationor diffusion and the heat of solution.

Fig. 10.34Schematic representation of steady-

state permeation througha solid of thicknessd .







or the case of diatomic gases that dissociate on solution, the corresponding expression will be

he steady-state permeation of gases through solids has been the subject of numerous studies. Those cases releontemporary vacuum technology include the permeation of gases from the atmosphere through materials usedacuum walls or as gasketing materials, as well as the use of materials that have a high permeability for specifielative to all other gases, and may thus be used as a method of admitting pure gases to vacuum systems. In theategory, the only case of current interest is that of the permeation of helium, and possibly other atmospheric ghrough glass, especially quartz glass. This process has been extensively studied over a long period of time. In he measurements made, Eq. (10.108) has been rewritten as

where K is the permeability, K 0 and Ep are given by

nd it is assumed that

Results have commonly been reported as the volume of gas at STP per second per square centimeter of surfacemillimeter of thickness, or asQµl = micron-liters at 0°C per square centimeter of surface per millimeter thicknesnit pressure. The permeation rate can thus be characterized by an equation of the form

he most comprehensive studies of the permeation of gases through various glass compositions are those of No33], who has reported permeation measurements in which not only the amount of gas but also its composition udied with the aid of a mass spectrometer. His observations on the heliumsilica system covered the range 78°, and they agree fairly well with those of previous investigators.





n addition, he studied helium permeation through a number of glasses, as well as the transport of several otherhrough silica. The results of his helium permeability measurements are shown in Fig. 10.35, and the data repother gases are given in Tables 10.6 and 10.7. Data for the permeation of helium, neon, hydrogen, and nitrogen

Vycor glass have been given by Lieby and Chen [34]. It should be noted that Alpert [35] has shown that permetmospheric helium is one of the limiting factors in the attainment of ultrahigh vacua.

Urry reported that Pyrex is permeable to hydrogen; and this result was confirmed by Taylor and Rast [36], whopermeability of 1.86 × 1013 g/cm2/s/mm/atm. They also emphasized the importance of the history of the glas

n affecting the permeability observed. In this connection, it has been found, for example, that the permeation rltered if the glass is under stress.

he other situation in which steady-state permeation is encountered is the use of selectably permeable membrahe purification of gases, or for the admission of pure gases into a vacuum system. This technique has been used

Young and Whetten [37] for the purification of helium using a quartz tube assembly for the admission of the gaacuum system. With this device, they found that the only impurity remaining above one part per million was himilar techniques have

Fig. 10.35Permeability of various glasses to helium [33]. K is the permeation velocity of heliumthrough glass in units of cm3 gas (N.T.P.) per second per cm2 area per mm thickness

per cm Hg gas pressure difference.







Table 10.6. Permeability Constant K through SilicaaGas 700°C 600°CHelium 2.1 × 108

Hydrogen 2.1 × 109 1.25 × 109Deuterium 1.7 × 109Neon 4.2 × 1010 2.8 × 1010Argon Under 1015Oxygen Under 1015Nitrogen Under 1015a From Norton [33].

Table 10.7. Hydrogen Permeation Constant, Ka

Glass 665°CNo. 1720 (Corning) 4.5 × 1012Mullite 1.8 × 1011a From Norton [33].

een used for the admission of hydrogen into a vacuum system using a palladium or palladium alloy tube, as whe admission of oxygen using a silver tube. In these two cases, the appropriate expression for the permeation r

10.109), because in both of these cases the absorption process involves the dissociation of the diatomic molecu0.2.5ransient Permeation

here are many situations in which one must deal with transient permeation. One such case is that in which theeparating two regions of different pressure is initially clean and is abruptly exposed to a change in conditions, n increase in pressure on one side or an increase in temperature that allows gas uptake and diffusion to begin. his transient case one must use Fick's second law, as stated in Eq. (10.104). For the case described above, whichown diagrammatically in Fig. 10.36, we have the boundary conditions

C = 0

for 0 ≤ x ≤ d at t = 0,

C = Chifor x = d at t > 0,

C = 0for x = 0 at t > 0.

This last condition is satisfied if we assume that plo is maintained essentially at zero.) The solution to Fick's secoaw for these boundary conditions is







Fig. 10.36Transient permeation curves showing

the approach of the concentration profilein the solid to the steady-state

value of a constantdC/dx .

his yields an instantaneous outgassing rate on the low pressure side of

At very small values of Dt , dQ/dt is approximately zero. That is, it takes a finite time for the first gas to diffuseompletely across the slab. At large values of Dt , dQ/dt → DC hi/d , the value determined previously for the steadyase. At intermediate times,dQ/dt will lie between these two extremes.

Alternatively, one may be concerned with the process of gas initially present in a solid diffusing out into the vapace over a period of time, or the opposite case, the diffusion of a species present in the gas phase into the bul

material exposed to that gas phase. The first case is representative of outgassing from the walls of a vacuum chom objects within the chamber. The second case represents the process of pumping by a bulk getter.

As a practical matter, the first of these processes is the principal source of gas in well-prepared ultrahigh-vacuuystems, and it can be a significant fraction of the total gas load in a vacuum system in many other cases. Two n which these processes can take place may be considered, both of which involve desorption of gas from the whe vacuum system, or from objects completely within the system, into the gas phase.

he first case, which involves desorption from the vacuum wall, or desorption from a thick piece of material wacuum system, can be treated as a process of diffusion from a semi-infinite slab. The second case, which invoiffusion from a thin source, such as a heated filament, may be treated as diffusion from a finite slab.

onsider first the case of the semi-infinite slab, shown schematically in Fig. 10.37. For this case, one must agaiick's second law, but this time the appropriate







Fig. 10.37Concentration profiles for the diffusion of a dissolved gas

out of a semi-infinite slab.

oundary conditions are

C = C 0for x ≥ at t = 0,

C = 0for x = 0 at t > 0,

ssuming again that the pressure in the vacuum space is essentially zero. The solution in this case is

he right-hand side of Eq. (10.118), except for the termC 0, is what is known as theerror function . Values of thisunction have been tabulated for a wide range of values of the argument y. The instantaneous rate of outgassing forase may be obtained from Eq. (10.118) as







he total amount of gas removed per unit area in timet will thus be

Note thatdQ/dt increases with increasing values of D , which implies an exponential increase ofQ with temperatureecreases ast increases. Consequently, if one wishes to thoroughly outgas the system walls it is advisable to heaystem to the highest possible temperature to maximize D . After such a process, when the system is brought back oom temperature,C 0, and consequentlydQ/dt , will be much lower than they were initially.

he case of the finite slabfor example, a thin piece of material within a vacuum system or a hot filament initiallontaining a dissolved impuritymay be treated similarly. Here again, one must solve Fick's second law, this timoundary conditions

C = C 0for 0 ≤ x ≤ d at t = 0,

C = 0for x = 0, x = d at t > 0.

his case is shown schematically in Fig. 10.38. The solution in this case is

his leads to an instantaneous outgassing rate of

he complication in this case relative to the semi-infinite slab is thatC 0 is not constant with time at some distance= 0. However, at short timesthat is, times for



Fig. 10.38Concentration profiles for the diffusion of a dissolved gas

out of a finite slab.





which ( Dt )1/2 < d Eq. (10.124) reduces to the same form as that for the semi-infinite slab, because under theseonditions the concentration deep within the slab is stillC 0. Consequently, at short times we obtain

At longer times,dQ/dt will decrease more rapidly than this equation predicts.

One may also consider the case of uptake of gas from the vacuum system into an infinite or semi-infinite slab, ae the case in the operation of a bulk getter pump. In this case, the appropriate boundary conditions are

C = C 0for x = 0, t ≥ 0,

C = 0for x > 0, t = 0.

his case is shown in Fig. 10.39. Solution of Fick's second law in this case leads to

where the second term in the parantheses is again the error function defined in Eq. (10.118).

he rate of uptake of material per unit area per unit time is, in this case,



Fig. 10.39Concentration profiles for the uptake of a gas into an initiallyclean semi-infinite slab. Note that the depth of penetration for

a given concentration ratio, such asC ', increases as





eading to a total uptake in timet of

his behavior is commonly observed in the oxidation rate of metal surfaces and is described as parabolic kinetiimilar equations may be derived for other geometries, and additional examples are treated in Chapter 5, Part Ind Getter Pumps."

0.2.6ffect of Desorption Kinetics on Permeation

o this point, it has been assumed that the kinetics of the adsorption and desorption processes that must take plurfaces of materials undergoing permeation processes are rapid relative to the permeation rates involved, and tot influence the overall permeation rate. In many cases, this assumption is not valid. For example, if the surfac

material is covered with an adsorbed layer that inhibits the adsorption process that must take place prior to absohen the near-surface concentration of the permeating species may not be the equilibrium solubility that was tacssumed in the development of the permeation rate equations developed above. This is an especially importantn cases in which a gas must adsorb dissociatively prior to solution and permeation. The inherent kinetics of thedsorption process may also effect permeation rates even on an atomically clean surface. This case has been tre

Arbab and Hudson [38] for the case of hydrogen permeation through pure iron. These authors measured steadyermeation rates for hydrogen through a thin iron membrane under conditions in which surface cleanliness counsured, and they found that the permeation rate showed an anomalous decrease at low temperatures. This decrxplained in terms of the potential energy diagram shown in Fig. 10.40, which is based on the observed energeydrogeniron system. In this figure, the potential energy of a hydrogen atom is shown as a function of distancehe permeation wall. The zero of energy is taken as a hydrogen molecule in the gas phase. The potential wells aurface represent the sites for stable chemisorption of hydrogen as hydrogen atoms. The series of minima betwhemisorption wells represent stable sites in the bulk. The intervening maxima represent the barriers surmounteiffusion.

As has already been shown, under steady-state conditions, Fick's first law for steady-state one-dimensional tranhrough the bulk of a solid is normally stated as [39]

where J is the steady-state flux, D is the diffusion coefficient,C hi andC lo are the volume concentrations of theiffusing species at the planes just below the entrance and exit interfaces of the permeation wall, respectively, a L he wall thickness.

Assuming that the concentration in the near-surface side of the membrane is in equilibrium with the gas phase, write the following equation using Eq. (10.100):






whered is the interplanar spacing. The factor of ½ is necessary to account for the fact that permeation data are xpressed on a per H2 molecule basis.





Mass balance expressions for the hydrogen atom fluxes onto and away from planes 2 and 3 (as defined in Fig. eady state (i.e.,dn2/dt = dn3/dt = 0), may be written as

wheren1 = 2Sp1/2, n0 is the number of surface sites per unit area available for hydrogen adsorption,kij is therobability for the transition of a hydrogen atom from a site on planei to a site on plane j, and kd is the desorptionrobability. The parameter (1n3/n0) in the above equations expresses the assumption that a site on plane 3 alreaccupied by an adsorbed hydrogen atom is unavailable to other hydrogen atoms attempting to arrive on that pla

milar term for plane 2 can be neglected if we assume

imultaneous solution of Eqs. (10.133) and (10.134) yields

he steady-state permeation flux, J , can be expressed in terms ofn3 as

with n3 obtained from the solution of Eq. (10.135). These equations contain five temperature-dependent terms, D , k 23, k 32, andkd , whose activation energies are shown in Fig. 10.40.

he application of this treatment to the authors' data for hydrogen in iron is shown in Fig. 10.41. In evaluating heoretical equation, literature values were used for the crystallographic parameters for iron, the equilibrium so40], and the absorptiondesorption behavior of hydrogen on iron [41]. The activation energy for permeation obheir study and the value for the activation energy for desorption were adjusted to obtain a best fit to the data. Tolution of Eqs. (10.135) and (10.137), using∆ Hd = 25 kcal/mol up to a saturation coverage of one monolayer, wound to agree well with the experimental results, as shown by the solid curve in Fig. 10.41. This value is in gogreement with the results of previous studies. Application of the analysis developed above to the data reported

Nelson and Stein [42],





Fig. 10.41Arrhenius plot of hydrogen flux as a function of temperature

for hydrogen permeation through iron. The straight lineshows the result of a linear regression analysis of data for

T > 200°C. The solid line is based on the model developedin the text. Reprinted from M. Arbab and J. B. Hudson,

"The influence of Desorption Kinetics on HydrogenPermeation in lron." Appl. Surf. Sci. 29, 6 (1987) [Ref. 38],

with kind permission of Elsevier Science NL, SaraBurgerhartstraat 25, 1055 KV, Amsterdam, the Netherlands.

sing the heat of adsorption assumed above, showed that the apparent activation energy for permeation at high

emperatures increased only by 0.1% over that experimentally measured. Therefore, unless much stronger surfaeactions are shown to be operative, the scatter in previous results at high temperatures may be attributed to bulrocesses or to experimental errors.

An interesting feature of the results shown in Fig. 10.41 is that the deviation from Arrhenius behaviour occurs qbruptly. Therefore, the value of the true activation energy for permeation may be reliably found by linear regrenalysis of the high-temperature data. At temperatures even slightly below the point of deviation, the hydrogenontrolled almost entirely by the desorption kinetics; an evaluation of the activation energy for permeation at loemperatures shows it to be equivalent to that for hydrogen desorption. Hence, if Eq. (10.131) is applied to lowemperature permeation data, anomalously high values of the apparent activation energy for diffusion, equivaleHd ∆ Hs , will be obtained. This deviation from Arrhenius behavior would occur at higher temperatures for plan

which absorb the hydrogen atom more strongly.







Fig. 10.42Effect of membrane thickness on the ratio of calculated apparent

diffusion, Dapp, to that extrapolated from the high-temperature data, Dtrue.Reprinted from M. Arbab and J. B. Hudson, "The Influence of Desorption

Kinetics on Hydrogen Permeation in Iron." Appl. Surf. Sci . 29, 15(1987) [Ref. 38], with kind permission of Elsevier Science NL, Sara

Burgerhartstraat 25, 1055 KV, Amsterdam, the Netherlands.

igure 10.42 shows the effect of the permeation wall thickness on the value of the apparent diffusivity, as predihe analysis of Arbab and Hudson. The calculated value of diffusivity approaches the value expected from extrf the high-temperature measurements as the wall thickness increases, causing the bulk transport process to becominant in the determination of the overall rate of permeation.

he trend in apparent diffusivity with wall thickness is similar to that reported by Wach and Miodownik [43] inlectrochemical permeation study at 25°C. Similarly, Palczewska and Ratajczyk [44] considered the effect of whickness on gas permeation between 30°C and 40°C. They reported that diffusivity was independent of membhickness above 0.78 mm, while for thicknesses below 0.42 mm, decreased values of apparent diffusivity are o

Nelson and Stein [42] also studied the influence of wall thickness on permeation for temperatures of 240°C andy geometrical arguments they concluded that, based on that part of their study, permeation was not influenced

urface processes. However, since the data used in their analysis describe the permeation behavior above the deemperature observed in their experiments (100°C), they are outside the range in which the permeation rate is ay surface processes and thus do not provide a critical test of the effect of these surface processes on permeatio

urface contaminants may also lead to the observation of incorrect values of the apparent diffusivity if their preesults in the retardation or enhancement of the desorption process. For example, preadsorbed submonolayers oxygen, and





arbon were observed to decrease both the energy and the frequency factor for desorption of hydrogen from Feurfaces, while preadsorbed potassium seemed to increase the value of the former [45]. Direct evidence for this

was observed for the permeation of hydrogen in palladium in an electrochemical permeation study [46]. In thatnvestigation it was noticed that sulfur deposition on the membrane surface resulted in a reduced permeation fluonsequently low values for the apparent diffusivity.

he treatment developed above may also be applied to other hydrogenmetal systems. Among the transition menteraction of iron, nickel, and palladium with hydrogen has received considerably more attention than others.herefore, a comparison of the results for iron may be most appropriate with those for the latter two metals. Thiffusivity values obtained by various permeation methods for these metals do not indicate the anomalies obseron, even at room temperature or below [47].

Hydrogen permeation in nickel was examined using the model developed above. Because of the consistency inalues of diffusivity reported by various authors [47], it is sufficient to consider the experimental results of onlyudyfor example, the work of Ebisuzaki et al. [48] for the permeation parameters. The required parameters rele

he desorption of hydrogen from various nickel surfaces were taken from the work by Christmann et al. [49]. Tnalysis showed excellent agreement with the experimental data of Ebisuzaki et al. [48]. A deviation from Arrhehavior was predicted only for temperatures lower than 20°C.

imilar to nickel, there is good consistency among various experimental values of hydrogen diffusivity in palla47]. There is, however, substantial evidence that hydrogen adsorption on this metal is more complex than that y the potential energy diagram of Fig. 10.40. Adsorbed hydrogen atoms were observed to readily occupy substes on Pd(111) surfaces [50, 51], while desorption from Pd(100) surfaces was observed to follow "quasi-first-inetics beyond very low coverages [52], in contrast with iron [41, 53]. Therefore, the model described here can adequate description of the effect of the desorption kinetics on hydrogen permeation in palladium. In spite obove evidence, Engel and Kuipers [54] found that a potential energy diagram similar to that shown herewitharameters chosen to yield a best fit to the experimental dataadequately described their results on the interactioetween hydrogen and deuterium on a Pd(111) surface for temperatures above 75°C. Their study indicated thatansport between the surface and the bulk is an important factor for hydrogen adsorption on the Pd(111) surfac

he kinetic model developed above was applied to the case of hydrogen in palladium by curve fitting, using thf k 32 andkd as the fitting parameters. The values of all other parameters involved in Eq. (10.135) were taken fterature [55, 56]. The equation developed in this fitting process predicts an anomalous decrease in the value oiffusivity, similar to that found in iron, for temperatures below 75°C for vicinal surfaces. However, no experimudies report such a deviation. Only contaminated surfaces have shown values of the apparent diffusivity beloxpected from the extrapolation of the high temperature data, as mentioned above [42]. The reason for this lackgreement is not obvious, but may be related to the existence of a strongly bound subsurface hydrogen site.





0.3urface Chemical Reactions

Many of the surfaces present in vacuum systems can, especially at high temperatures, serve as catalysts for surhemical reactions. Those of importance in vacuum technology fall into three classes:

. Reactions in which a gas is decomposed to form reactive radical speciesfor example, H2 on tungsten filamen

. Reactions in which a gas reacts to deposit material in a layer on the surfacefor example, C2H4→ C + 4H2.

. Reactions in which a gas reacts with an adsorbed species, or with the surface itself, to form new volatile specxample, O2 + C→ CO + CO2, H2O + C→ CO + CH4, O2 + Mo→ MoO3.

All classes of surface reactions can be thought of in terms of a sequence of steps. In its most general form, the snvolves adsorption from the gas phase into a molecular precursor state, chemisorption, surface migration to thete, the actual reaction step, surface diffusion away from the reaction site, return to a physically adsorbed statenally desorption into the gas phase. Figure 10.43 diagrams this process. It is seldom that all of these steps wil

nvolved in any given reaction, and in many cases only one of these steps will control the overall reaction rate. rinciple, however, all of these steps must be considered in formulating the detailed reaction mechanism.

A number of these processes have already been discussed in detail previously in this chapter, such as accomodan adsorbed state, physisorption and chemisorption, and surface migration. The only new step in the sequence ctual reaction step itself. In discussing this step, it is useful to introduce some new terms that describe this steparious cases.

Reactions are often referred to as being either structure-sensitive or structure-insensitive, depending on the waywhich the reaction rate changes as a function of

Fig. 10.43Schematic view of the possible steps involved in a surface

chemical reaction between two homonuclear diatomic molecules.





ither (a) surface perfection or (b) the particle size of the catalytic material. Reactions whose rate depends onlymount of surface present, and not on its structure, are said to be structure-insensitive. Those that show a rate dn surface defect structure are said to be structure-sensitive.

Depending on the importance of chemisorption before reaction, reactions are classified as following either aangmuirHinshelwood or an EleyRideal mechanism. A bimolecular reaction that proceeds by chemisorption o

eactants prior to the reaction step is said to follow a LangmuirHinshelwood mechanism. A bimolecular reactioetween one chemisorbed species and a second species that impinges directly from the gas phase is said to follleyRideal mechanism.

n the catalysis literature there is also frequent mention of active sites for reaction. This is a term that developedarly days of the study of catalytic reactions, as an explanation of the observed structure sensitivity of many rea

Much current research in the field is aimed at elucidating the nature of surface configurations that provide espeavorable sites for the surface reaction step. To date, positive correlations have been found between surface reand the presence of ledge or kink sites on a crystal surface, but a detailed understanding of their effect on reactiacking.

A wide variety of reactions can take place between the residual gases in a vacuum system and heated surfaces w

ystem. The most obvious place for such reactions to take place is at the surfaces of heated filaments used as elmitters. Possible reactions of this type have been discussed by Redhead [57] and by Alpert [58]. Possible reache case of hydrogen include

H2(g) → 2H(a),

H(a) + O(a) → H2O(g),

H(a) + C(a) → CxHy(g).

he dissociation reaction was observed on tungsten as long ago as 1915 by Langmuir [59]. Hickmott [60] obseormation of atomic hydrogen at a tungsten surface at an appreciable rate for surface temperatures above 1000

measured an activation energy for the production of atomic hydrogen of 67 kcal/mole. The rate of formation asunction of filament temperature and residual hydrogen pressure is shown in Fig. 10.44, taken from the paper b

Hickmott.

Atomic hydrogen produced at hot filaments can also react with other adsorbed species both at the heated filamacuum chamber walls. This reaction has been used as a practical source of atomic hydrogen in many studies. nclude qualitative studies of adsorption of hydrogen on semiconductors, which show a vanishingly small stickoefficient for H2(g). It has also been used by Mesters et al. [61] in a study of the removal of adsorbed oxygen u(111) surface. Results of this study indicated that the rate of removal by gas phase H2 was limited by inhibitissociative adsorption of hydrogen by the adsorbed oxygen, whereas the adsorption of atomic hydrogen andubsequent removal of the absorbed oxygen suffered no such limitation. The use of atomic hydrogen producedeated filament as a reactant has also been applied quantitatively, as in studies of hydrogen adsorption on silico

mentkowski et al. [62].





Fig. 10.44Dependence of the rate of formation of atomic hydrogen

(VA) on tungsten filament temperature and hydrogen pressures ( p2). Gas temperature = 298 K [60].

An example of the second type of reaction listed above is the decomposition of ethylene, C2H4, on the Ni(110his reaction has been studied by Zuhr and Hudson [63]. Results indicated the rapid, complete dehydrogenatiodsorbed ethylene, with desorption of the hydrogen liberated as H2, at temperatures above 150°C. At temperatuelow 350°C, the decomposition process led to an adsorbed carbon phase at monolayer coverage. Decompositiigher temperatures led to the formation of a graphitic monolayer, which was stable up to 550°C, and dissolvedulk of the nickel crystal at higher temperatures. The resulting surface carbon concentration as a function of suemperature during the reaction, as measured by Auger electron spectroscopy (AES), is shown in Fig. 10.45.omparison with other studies of ethylene adsorption of nickel surfaces, using surface spectroscopic technique5], indicate dissociative adsorption at temperatures as low as 25°C in this system. This is consistent with thebservations of Zuhr and Hudson [63], because hydrogen evolution would have been too slow to detect by the pectrometric techniques used in their study.

An example of the third type of reaction listed abovethat is, one in which a gas-phase species reacts with an adpecies to form a new gas-phase productis the reaction of adsorbed carbon with gaseous O2. In studies of this ry Sau and Hudson [66, 67], adsorbed carbon layers were formed by the decomposition of ethylene on a Ni(11urface as described above, then removed by reaction with







Fig. 10.45Steady-state surface carbon coverage on Ni(110), arisingfrom decomposition of ethylene, as determined by AES atvarious substrate temperatures. Reprinted from R. A. Zuhrand J. B. Hudson, "The Adsorption and Decomposition of

Ethylene on Ni(110),"Surf. Sci . 66, 414 (1977) [Ref. 63], withkind permission of Elsevier Science NL, Sara Burgerhartstraat

25, 1055 KV, Amsterdam, the Netherlands.

O2 to form CO. This is an example of a so-called cleanoff reaction and is similar to volatilization reactions. Theaction was studied using molecular beam relaxation spectroscopy, with an O2 molecular beam used as reactahe gas-phase O2 and CO fluxes from the surface being measured mass spectrometrically. In addition, the surfaarbon and oxygen coverages were measured by AES. These measurements were made for both (a) the monolaarbon structure formed by ethylene adsorption at low temperatures and (b) the graphitic monolayer formed at emperatures.

he results of measurements on the graphitic monolayer, for a surface temperature of 873 K, are summarized in0.46, which contains much kinetic information. If one looks first at the rate at which carbon disappears from turface, on the basis of the carbon AES signal, one sees that the rate is at first slow, accelerates to a maximum, rops back to zero as the carbon adlayer is depleted. This same behavior is mirrored in the curve of CO producbtained mass spectrometrically. The phase lag of this CO signal initially increases with increasing extent of rehen saturates. The surface oxygen coverage remains low until very late in the reaction sequence.







Fig. 10.46Summary of kinetic measurements of the oxidation of a graphitic carbon layer on Ni(110).Reprinted from R. Sau and J. B. Hudson, ''The Oxidation of Graphitic Monolayers on

Ni(110),"Surf. Sci . 95, 468 (1980) [Ref. 66], with kind permission of Elsevier Science NL,Sara Burgerhartstraat 25, 1055 KV, Amsterdam, the Netherlands.

he reaction sequence deduced from these data is shown in Fig. 10.47. It involves initiation of the reaction at dtes in the carbon layer, followed by the growth of "holes" in the adlayer, at which oxygen chemisorption occu

eadily. The adsorbed oxygen, which is mobile on the surface, diffuses to the edge of the hole and reacts to formwhich is readily desorbed. This reaction takes place quite efficiently initially, until the hole size grows to the powhere there is competition for adsorbed oxygen between the surface reaction and dissolution of oxygen into thhe crystal. It is at this point that the phase lag of the product signal saturates. A theoretical rate equation has beeveloped embodying this reaction sequence. The fit of the theoretical curves to the experimentally measured coverage curve is shown in Fig. 10.48.

Results of the reaction of oxygen with the low-temperature carbon layer were more complex. The significant fiar as vacuum technology is concerned was that after heating to 525 K, the adsorbed layer was reactive with gat temperatures as low as 333 K, but was unreactive with previously chemisorbed oxygen or oxygen present ashis suggests the involvement of a weakly chemisorbed oxygen species on the carbon-covered surface, and poossibility of CO production from adsorbed carbon on the walls of metal vacuum chambers, even in cases whe

walls are covered by an oxide layer.





Fig. 10.47Schematic view of the proposed reaction mechanism for the oxidation of a graphitic

carbon monolayer on Ni (100).



Fig. 10.48Comparison of rate of removal of surface carbon from Ni(110) by

O2 gas with theoretical equations based on the mechanism shown inFig. 10.47. Reprinted from R. Sau and J. B. Hudson, "The

Oxidation of Graphitic Monolayers on Ni(110),"Surf. Sci . 95,471 (1980) [Ref. 66], with kind permission of Elsevier Science NL,Sara Burgerhartstraat 25, 1055 KV, Amsterdam, the Netherlands.





A second reaction in which an adsorbed species is removed by reaction with a gas-phase species is the oxidatiodsorbed CO by the overall reaction

his reaction has been extensively studied by many investigators using a variety of techniques on a wide rangeurfaces [68]. The major questions that these studies have tried to answer are whether the reaction proceeds by angmuirHinshelwood or an EleyRideal mechanism; the effects of varying either the gas-phase pressure or thedlayer populations of the two reactants; and the effect of surface structure on the reaction rate and mechanismverall reaction scheme deduced is

he overall mechanism is thus the LangmuirHinshelwood mechanism, with both reactants being chemisorbed (O2 molecule dissociated) prior to CO2 formation. Because of the differences in the heats of adsorption of CO ahe reaction rate as a function of temperature and the relative partial pressures of the two reactants is complex. lso depends on whether CO is adsorbed and the surface then exposed to O2 or vice versa. All of the results obowever, are consistent with the reaction scheme presented in Eq. (10.139).

Measurements have also been made in a few cases of reactions between adsorbed species and gas reaching the y permeation through the bulk. Arbab and Hudson [69] have studied the reaction between permeating hydrogxygen chemisorbed of the surface of a thin, polycrystalline iron membrane to form water. The hydrogen was so the surface as atomic hydrogen by maintaining an atmosphere of hydrogen on the back side of the iron samphe front side was maintained at ultrahigh vacuum in a conventional surface science research system. Reaction

were measured both by mass spectrometric detection of the desorbed product water and by AES measurement eduction in the surface oxygen concentration as the reaction proceeded. Results indicated a rapid removal of owater, as long as the surface oxygen coverage exceeded one monolayer. Submonolayer coverages were inert to

A typical mass spectrometer plot of water evolution rate versus time is given in Fig. 10.49, showing an initial rs hydrogen is admitted to the back side of the sample, followed by a slower decrease as the surface oxygen layonsumed. Measurements of water formation during oxygen exposure to the surface concurrent with steady-staydrogen permeation showed the reaction to be half-order in O2 pressure. Kinetic analysis of the results indicahe reaction proceeded by the formation of surface hydroxyl groups, followed by their disproportionation to fornd adsorbed oxygen. The overall activation energy for the process was 16 kcal/mol, of which 8.5 kcal/mol is a

with the temperature dependence of the hydrogen permeation.

Another reaction sequence of importance in vacuum technology is the so-called water cycle in tungsten filamenhis cycle involves two sets of reactions. At the heated surface of a tungsten filament, water vapor in the system

eact





Fig. 10.49Evolution of water during the titration of adsorbed oxygen by hydrogen

permeating through a thin iron membrane, as measured massspectrometrically. Hydrogen permeation was initiated att = 305.

Reprinted from M. Arbab and J. B. Hudson, "The Titration of OxygenAdsorbed on a Polycrystal-line Iron Surface by Hydrogen Permeation,"Surf. Sci . 209, 191 (1989) [Ref. 69], with kind permission of ElsevierScience NL, Sara Burgerhartstraat 25, 1055 KV,

Amsterdam, the Netherlands.

ccording to

H2O( g ) → H2( g ) + O(a),

O(a) + W( s) → WO3( s) → WO3( g ).

At cold surfaces adjacent to the filament, the reverse reaction will be favored, leading to



WO3(a) + H2( g ) → WO3(a) + 2H(a),

WO3(a) + 2H(a) → WO x( s) + H2O(a) → H2O( g ).

his reaction sequence is responsible for the blackening observed on the walls of ionization gauge tubes operatigh partial pressures of water vapor.





n electric illumination technology, the development of halogen lamps was a reaction to this problem and the reroblem of an excessively high tungsten evaporation rate at high filament temperatures. In these lamps, a low pf a halogen gas such as iodine is used to effect the return of tungsten to the heated filament by the series of rea

W( s) + I2( g ) → W( s) + 2I(a)

W( s) + 3I(a) → WI3( g )

t the relatively cold bulb surface, and

WI3→ W( s) + I2( g )

t the filament surface, thus reversing the reaction that led to tungsten loss initially. This cycle permits operatioungsten filament at higher temperature, and it consequently provides a brighter more efficient light source.

0.4utgassing Behavior

xcept during the early stages of a pumpdown cycle, when the air or other gas in a system is being removed, thhe gas load to the pumping system consists of gas evolved from surfaces in the system, including both the systnd any objects within the vacuum system. This gas load arises from a combination of desorption from adsorbend permeation of gases dissolved in the system walls or other surfaces. Since the system ultimate pressure is delated to the magnitude of this gas load, measures taken to reduce outgassing are critical to the production of hltrahigh vacuum. Measures include both treatments applied to the materials of system construction, prior to orourse of system fabrication, and treatment of the system as a whole in the course of system operation. The firsategory includes both (a) heat treatments to reduce the amount of dissolved gases in the materials of constructb) surface treatments intended either to reduce the total surface area or to develop a surface layer that will bempermeable to gases or unreactive to chemisorption or surface reactions. The second category includes varioubakeout" techniques intended to desorb adsorbed layers present prior to pumpdown and to deplete the near suegion of materials of dissolved gases.

he question of outgassing will be considered below, in terms of both (a) the development of pressure versus tiurves based on various assumptions concerning the adsorption, desorption, and diffusion behavior of the gasenvolved and (b) measures that may be used to decrease the contribution of adsorption, desorption and diffusionrocesses to system residual pressure.

0.4.1Desorption of Adsorbed Gases

arlier in this chapter, equations were developed for the rate of desorption of adsorbed gases based on a range ssumptions concerning desorption energetics and mechanism. In the simplest cases, the desorption rate decreaxponentially with time as the adlayer population was depleted by desorption. The time constant for this





xponential decrease is the mean stay time for adsorption, which in turn depends on the activation energy for thesorption process. Because of this, the effects of various adsorbed species on system pumpdown rate and ultimressure fall into three classes. Adsorbates with a very short surface lifetime, such as weakly physisorbed gasesncluding the rare gases, oxygen, and nitrogen, will be desorbed and removed by the pumping system rapidly aot appreciably affect the overall pumpdown rate. At the other extreme, gases that are very strongly adsorbed assentially infinite surface lifetimes at ambient temperature, such as chemisorbed oxygen, nitrogen, or halogenave a vanishingly small desorption rate and will likewise not significantly affect pumpdown rates. It is the gasaving surface lifetimes in the intermediate range of seconds to hours that provide the principal impediment to ystem pumpdown. Included in this category are most organic species, water, and weakly chemisorbed speciesO and CO2. This effect is shown graphically in Fig. 10.50 [71], which shows the pressure versus time for a 1-

ystem pumped by a 1-liter/s pump and having a surface area of 100 cm2, initially covered with a monolayer oaving the desorption energy shown in the figure. Note that for desorption energies less than 15 kcal/mol, the d rapid; also note that for desorption energies of 25 kcal/mol and higher, the outgassing rate contributes a partiressure below 1011 Torr. Also shown in Fig. 10.50 is the rate of decrease in system pressure in the course of at 300°C for adsorbates having desorption energies in the troublesome 15- to 25-kcal/mol range. At these temphe contribution to system pressure from these gases effectively disappears in a matter of seconds. Note that thialculation includes only gases adsorbed at the surface of the system and does not account for replenishment ofdsorbed layer by permeation from the bulk, which is a much more serious problem in the bakeout of practical

Fig. 10.50Pressure vs. time curves for the pumpdown of vacuum systems having adsorbed layers of

gas with the adsorption energies shown. System parameters areV =1 liter, S =1 liter/s, A=100 cm2. Initial adlayer coverage is one monolayer att =0 [71].





0.4.2Dissolved Gases

he release of species by permeation through the bulk of materials exposed to the vacuum is usually the final fmiting system ultimate pressure. Here the major contributors are usually hydrogen released by permeation of ydrogen atoms followed by recombination and desorption as H2 molecules, and CO or CO2 formed by permearbon atoms and surface reaction with water followed by desorption. In glass systems, CO and CO2 remaininlasses made by calcining carbonates can also permeate as molecules and be desorbed into the vacuum.

0.4.3Overall Pumpdown Curves

he pressure vs. time behavior of a typical vacuum system will depend on both the inherent adsorption-desorptiffusion behavior of the gases present in the system when pumpdown begins, and on the past history of the sy

will also depend on system configuration, in particular the extent of the surface area of the system relative to thumping speed or the area of any orifice that limits that pumping speed. In typical systems, the surface area wiarge compared to the size of the orifice through which gas must be pumped. As a result, a gas molecule desorbhe surface will be much more likely to readsorb on another site on the surface than to be removed by the pump

ystem. Consequently, treatments of the pumpdown process must take account of both the desorption and readsrocesses. Moreover, in cases in which there is a finite rate of replenishment of the adsorbed layer by diffusionom the bulk of the system walls or objects within the system, the effect of this process and the extent to whichissolved gases are replenished when the system is exposed to the atmosphere must also be considered.

here have been numerous treatments of the rate of gas removal and its effect on system pressure. These genernto one of two categories: (1) treatments of the adsorption desorption process, which are most applicable to thages of pumpdown and have been primarily concerned with the removal of adsorbed water, and (2) treatmentiffusion and desorption of dissolved gases, important primarily in later stages of the pumping process and whisually assume that desorption is not rate-limiting and that no readsorptionabsorption processes are important.

onsider first treatments of the effect of adsorptiondesorption processes on pumpdown behavior. This case haseated in detail by Redhead [72, 73] for both monolayer and multilayer adsorption. The basic conservation of quation relating system pressure and pumping time in this case is given by Redhead as

where K is a constant to convert from pV units to molecules (3.27 × 1019 molecules/Torr-liter or 2.45 × 1019 mmbar-liter at 295 K),S is the pumping speed and N is the total number of adsorbed molecules. This equation has bolved by several authors, subject to various assumptions concerning the form of the desorption rate equation aeadsorption probability. Hobson [74] and Bills [75] have solved this equation subject to the assumption of ads

with a constant sticking





oefficient and a first-order desorption rate with desorption energy independent of coverage. This leads to an eqf the form

he problem with this approach is that it assumes that both the adsorption probability and the desorption energoverage-independent. A more realistic approach is to assume a quasistatic system, in which the adlayer is inquilibrium with the gas phase. Use of this assumption is based on the fact that readsorption of a desorbed mol

much more probable than removal by the pumping system, as mentioned above. This assumption, along with thssumptions of perfectly reversible adsorption and a form for the adsorption isotherm, permits solution of Eq. (ubstitution of a generalized adsorption isotherm equation of the form

wheren is the number of adsorbed molecules per unit area and the subscriptm refers to monolayer coverage (assumo be the maximum coverage), into Eq. (10.140) yields

which may be integrated to yield

where p0 is the pressure att = 0. The solution is completed by using the expression ford θ /dp found by differentiatinhe isotherm equation chosen.

his approach has been taken by Venema [76], using the Langmuir isotherm, by Mizuno and Horikoshi [77, 78he Freundlich isotherm, by Weiss [79], using the DubininRadushkevich isotherm, and by Redhead [72], using quation based on the Temkin isotherm.

Redhead [73] has extended the treatment based on the Temkin isotherm to cover multilayer adsorption, using ampirical multilayer adsorption isotherm of the form

n whichΨ = p/ps and ps is the saturated vapor pressure of water at the temperature of interest. Application of thotherm equation to Eq. (10.140) showed that the system pressure decreases exponentially with a time constanV/S

he adlayer coverage





rops through the multilayer region. This is the same behavior as one would expect in the absence of adsorptio

reatments that consider the effect of gas diffusing out of the bulk of the system walls are based on the diffusioquations presented in Section 10.2. In the simplest case, in which the gas being removed is present in the systet the time of construction and is not replenished by exposure of the system to the atmosphere, the mass balancquation is again

where in this casedN/dt = dQ/dt for the appropriate solution to Fick's second law. For example, for the case of dom a semi-infinite slab, we have, from Eq. (10.121),

ntegration of this equation is complicated by the fact thatC 0 is not an explicit function of p. However, as a practicamatter, the system pressure will be dominated by permeationdesorption processes only after the gas initially in ystem volume and the bulk of the adsorbed gases have been removed. The pressure in the system can thus beepresented by the quasi-steady-state expression

or the case of the semi-infinite slab.

he more complicated case of a dissolved or adsorbed gas source that may be replenished by exposure to thetmosphere has been considered by Dayton [80]. The analysis is complicated in this case by the fact that the bebserved in any situation depends on the extent to which the dissolved or adsorbed gas has been replenished, aonsequently on the time that the system has been exposed to the dissolving gas since the previous pumpdown he extent to which the dissolved gas was desorbed during previous pumpdown cycles. Dylla et al. [81] have obmpirically that the initial pumpdown of such a system follows an outgassing equation of the form

wheren is a constant of order unity, whose exact value depends on the details of the system involved.





0.4.4Mitigation of Outgassing

inally, consider techniques that may be used to reduce the rate of outgassing of surfaces in vacuum. These genall into three categories; (1) surface treatments carried out prior to or during system fabrication aimed at develurfaces that are relatively inert to chemisorption or provide low diffusivity barriers to the release of absorbed gurface treatments carried outin situ following system construction, and (3) bakeout procedures aimed at reducinmount of adsorbed or absorbed gases present in the system subsequent to pumpdown.

0.4.5urface Treatments during Construction

irst consider treatments carried out during the construction of the system. For the case of stainless steel systemse of vacuum-melted alloys, or the vacuum degassing of construction materials prior to or during system consas been used to reduce the amount of dissolved gases (primarily hydrogen) and to refine the structure and comf the surface oxide. This technique has been found to significantly reduce hydrogen outgassing in baked UHV82], but has yielded only slight improvements in water outgassing rates in unbaked systems [81, 83].

A number of techniques have been developed aimed at reducing the ratio of real surface area to the geometricahe surface (the surface roughness factor) and at producing a thin, dense surface oxide layer that will be relativeo chemisorption. For the case of stainless steel systems, these have been primarily electropolishing techniquesrocess, the surface to be treated is made the anode in an electrochemical cell. As the cell operates, protrusionsurface are dissolved preferentially, and the surface is progressively flattened as the process proceeds. Yoshimu84] found that an electropolished system, after a 150°C, 20-hour bakeout, yielded an outgassing rate of 1.1 × 1

mbar-liter/s-cm2. Okamura et al. [85] found that electropolishing or electrolytic abrasive polishing produced suhat had an outgassing rate below 1012 mbar-liter/s-cm2 following a 250°C, 80-hour bakeout. In contrast to theesults, two studies of water outgassing in unbaked electropolished stainless steel systems [81, 86] found that thlectropolishing process had little effect on water outgassing. For the case of aluminum systems, Ohi and Konnound that electropolishing produced a highly hydrated oxide and had little effect in reducing water outgassingnbaked system.

urface machining processes such as diamond machining [87], or mirror polishing by mechanical polishing tec8891], have been found to reduce water outgassing in aluminum systems by as much as a factor of 10 relativentreated surfaces. Suemitsu et al. [88] also found that the outgassing rate was proportional to the surface roughactor, with the surface roughness of the mirror polished surface being roughly a factor of three smaller than throduced by other machining or electropolishing procedures.

xtensive use has also been made of "alcohol lathing" techniques in the construction of aluminum systems [92his process, a thin layer of material, roughly 500 µm, is machined from the surface of the material, using an alhe cutting fluid. This process produces a smooth surface, covered with a thin, dense oxide layer. A study by Sut al. [92] indicated that isopropanol gave the best results of





series of alcohols and reported an outgassing rate of 7 × 1012 mbar-liter/s-cm2 after a 100°C, 24-hour bakeou

he oxide layers on stainless steel may also be modified by various passivating techniques involving exposure xygen or fluorine at high temperatures [95, 96]. Treatments of this sort leave the surface covered with a thin, dxide or fluoride coating, which is inert to chemisorption of most gases and has a very low specific surface are

water adsorption.

0.4.6n Situ Surface Treatments

n situ treatments in the course of system commissioning, primarily glow discharge or plasma processes, have bo reduce the amount of adsorbed water and also to remove surface carbon-containing compounds by oxidationrocess involves either (a) applying a high voltage to some element in the system in order to initiate a plasma dr (b) attaching a separate plasma source to the piece being cleaned. The desorption rate of adsorbed gases is ey bombardment of the interior surfaces of the system by energetic ions, electrons, or excited neutral species, wause desorption by a number of energetic particleadsorbate interactions, and, in the case of oxygen plasmas, reurface carbon-containing compounds to produce volatile species such as CO. This process is, of course, limiteystems in which production of the required plasma is possible, and it is not deleterious to fixtures within the ch

Dylla et al. [81] found small but significant improvements in water outgassing in both aluminum and stainless ystems when using helium glow discharge cleaning. Similarly, Chou [83] found that oxygen glow discharge cf an unbaked aluminum system reduced outgassing due to photodesorption in an ultraviolet synchrotron beamt al. [97], using an oxygen plasma source attached to a high-purity aluminum synchrotron housing, found thatxygen plasma could reduce outgassing due to photon bombardment by a factor of 10 when the housing was pervice. Auger electron spectrometric analysis of surfaces treated by this process showed virtually complete remarbon from the surface oxide layer.

0.4.7akeout Processes

he fact that both desorption and permeation rates depend exponentially on temperature is used extensively in eduction of outgassing through various bakeout procedures. Typically, the system is pumped into the range whesidual pressure is dominated by desorption or permeation processes. The temperature is then raised, either byeaters or by a high-intensity light source within the vacuum chamber. After a period of hours, the system is reoom temperature.

Adsorbed materials will be removed from the system rapidly by this process. The analyses of system pumpdowmentioned earlier [72, 73, 7679] also apply to conditions during the bakeout process, with the difference that thesorption rate and equilibrium adlayer coverage are those appropriate to the bakeout temperature. This will re

much higher system pressure at the beginning of the bakeout process, and consequently to a much more rapid removal for a given system pumping speed. As an example, consider the case of water adsorbed on





ainless steel. If a heat of adsorption of 15 kcal/mol and a bakeout temperature of 150°C are assumed, the rate emoval will be increased by a factor of roughly 5000 relative to the value at room temperature. This will resultssentially complete removal of the adsorbed water in a matter of seconds.

Removal of adsorbed gases by permeation through the bulk followed by desorption is a more lengthy process. may consider the case of a thick-walled system, so that the diffusion step can be treated as diffusion out of a senfinite slab. For this case, the equation developed previously for the rate of outgassing for diffusion out of a senfinite slab, namely

may be used to calculate the rate of outgassing both before and after the bakeout process. Prior to bakeout, theutgassing rate will be given by

where Dlo is the diffusivity of the gas involved at room temperature andt lo is the time that the system has been put room temperature. Following bakeout for a time,t hi, the outgassing rate will be given by

Using the literature values for the diffusion of hydrogen in iron [98] (namely,QD = 1600 cal/mol and D0 = 1 × 103m2/s), and assuming a 10-hour bakeout at 150°C shows that the rate of outgassing after the bakeout is a factor

maller than that prior to bakeout. This relatively modest reduction is due to the very low activation energy asswith the permeation of hydrogen through iron. A large increase in permeation rate can be attained only at a muemperature, as was used in the vacuum degassing process described earlier [82, 83]. Species with higher activnergies for permeation will be more efficiently removed by bakeout at temperatures in the 150°C range, and hakeout temperatures would result in an even greater reduction in outgassing. As a practical matter, the limit onemperature is usually set by the presence of temperature-sensitive components in the system, or by the desire txidation of the external surfaces of the system. Pyrex ultrahigh-vacuum systems were typically baked out at 4ighest temperature that could be used without exceeding the softening point of the glass. Stainless steel systemypically baked out at 150°C to avoid surface oxidation.

High-intensity ultraviolet light sources located within the vacuum chamber are also finding increasing use in barocesses. In this case, the mechanism of removal of adsorbed gases involves both heating of surfaces in the vand, possibly, direct photon-excited desorption of adsorbed species. This approach has the advantage of concenhe heating on the surfaces where the adsorbate resides, rather than heating the whole system to the required baemperature.





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1Ultrahigh and Extreme High Vacuum

aul A. Redhead

Ultrahigh vacuum (UHV) is defined by the American Vacuum Society (AVS) [1] as the range of pressure betwnd 1010 Pa (7.5 × 1010 to 7.5 × 1013 Torr), and extreme high vacuum (XHV) is defined as the range of presselow 1010 Pa (7.5 × 1013 Torr). British [2] and German [3] standard definitions differ from those of the AVS;hese standards define ultrahigh vacuum as the range of pressure below 106 Pa (108 Torr).

he development of vacuum techniques adequate to reach ultrahigh vacuum started with the investigations of Lnd his associates in 19121913. At that time a considerable number of physicists believed that electron emission incandescent metal surface at low pressures was due to the presence of residual gas and that consequently thhermionic emission would disappear in a good vacuum. In order to demonstrate the existence of pure thermionmission, as well as the validity of the space-charge relation, Langmuir [4] used a bulb containing two hairpin

ither of which could serve as an electron emitter and the other as anode. During exhaust (by a Gaede rotary mump) the glass bulb was heated for 1 hour at 360°C, which was the highest practical temperature without defof the bulb by atmospheric pressure. A liquid-air trap was placed between bulb and pump. The filaments were 7002800°C in order to degas them, and the bulb was sealed off. In order to improve the vacuum, the filamentsged at 2400°C for about 24 hours, which served to clean up the residual gases oxygen and






itrogen. ''To still further improve the vacuum in some cases," Langmuir states that "the entire bulb was immerquid air and the filaments heated to a high temperature for a short time." As shown subsequently by Dushman

measurements with the molecular-drag gauge indicated that the lowest pressure obtained in Langmuir's experimwell below 5 × 105 Pa.

angmuir's techniques became general practice in the 1920s and 1930s to obtain very low pressures (with the dump replacing the older types of pump and pressure measured by a hot-cathode ionization gauge). Even with gorous processing techniques discussed above, the lowest pressure indicated by the contemporary ionization g, a hot-cathode gauge with a cyclindrical ion-collector of large area) was about 106 Pa. However, there was

onsiderable evidence from measurements of the rate of change of surface properties (work function, thermionmission, etc.) in the 1930s and 1940s that much lower pressures were being obtained than were indicated by tonization gauges. In the late 1930s Anderson [6] and Nottingham [7] showed, from measurements of the rate of work function, that the pressure of adsorbable gases in their systems was much less than that indicated by thonization gauge. It can be estimated from Anderson measurements of the rate of change of the work function oungsten surface that the pressure of adsorbable gases in his system was below 109 Pa. For a review of these eattempts to approach UHV in the period before 1950, see Redhead [8].

n 1947 Nottingham [9] suggested that the limit to the lowest measurable pressure was caused not by the pump

n x-ray effect in the hot-cathode ionization gauge. Nottingham proposed that soft x-rays, produced when electmpinged on the anode with energies of about 150 volts, released photoelectrons from the ion collector; thishotocurrent was indistinguishable in the measuring circuit from the current due to positive ions arriving at theollector. This hypothesis was soon confirmed, and in 1950 the BayardAlpert ionization gauge [10] was annou

which reduced the lowest measurable pressure by a factor of about 100 (i.e. to about 108 Pa) by reducing the sion collector, from a large cylinder surrounding the other electrodes in the conventional gauge, to a fine wire onf the grid. The ion collector in the form of a fine wire intercepted only about 1% of the soft x-rays that would ylindrical ion collector of a conventional gauge. This simple and elegant gauge is still the most widely used foot-cathode ionization gauge. Since the invention of the BayardAlpert gauge (BAG), several other types of totaressure gauges, both hot- and cold-cathode, suitable for use in UHV and XHV have been developed and masspectrometers have been modified to measure partial pressures in UHV and XHV.

quipment to measure and produce UHV is now commercially available in great variety, and UHV technologywidely used in industry and the laboratory whenever it is essential to keep surfaces free from contamination, galasmas undefiled, and charged particles unscattered. UHV is widely used in industry in the development andmanufacture of semiconductor devices to keep surfaces uncontaminated during processing and testing. In spaceesearch, UHV and XHV technologies are needed to simulate space conditions for testing components and for

measurement of gas density in space (e.g., UHV gauges have been used to measure the atmospheric pressure ourface of the moon). Particle accelerators and storage rings require UHV conditions to minimize the loss of charticles from the beam by collisions





able 11.1. Gas-Phase Parameters at UHV/XHVressurePa)

MolecularDensitya

Molecular Fluxb(molecules· cm2·s1)

Molecular MeanFree Pathb

Time for 1/10 Monolayer c

042.5 × 1010 cm3 2.9 × 1014 34 m

1.9 s

072.5 × 107 cm3 2.9 × 1011 34 km

32 min

0102.5 × 104 cm3 2.9 × 108 3.4 × 104 km

22 days

01325 cm3 2.9 × 105 3.4 × 107 km

60 years

0170.25 m3 29 0.03 light years

600 millenia

At 298 K.For N2 at 295 K.Assuming a constant sticking probability of 0.1 and a density of adsorption sites of 1015 cm2.

th gas molecules. Magnetic confinement devices for research in thermonuclear fusion require UHV conditions to ensure the purity ofnfined plasma and to minimize plasma loss. UHV technology is essential to experimental surface science in order to maintain surfacecontaminated for the duration of experimental procedures. It was the development of UHV technology in the 1950s that permitted theodern surface science where the initial state of the surface could be rigorously controlled. The commercial availability of UHV hardw60s led to the almost exponential expansion in surface science to the point where it is now one of the most active sectors of research ysics and chemistry.

HV technology is still in the development stage; it is in use in some accelerators and storage rings and has potential application in theadvanced semiconductor devices.

ble 11.1 indicates in a general way the properties of the UHV and XHV environment which make it essential for studies requiring clerfaces, pure gases, or unscattered particles. UHV technology has been discussed in detail in several texts [11, 12].

he problems in achieving UHV or XHV can be seen in a general way by examining the conservation of mass equation for a vacuum slumeV and surface area A, pumped by a pump of speedS with a leak rate of L and an outgassing rate per unit area ofQ; then if L, Q , and S

e constant and a single gas is predominant, we obtain

hen the ultimate pressure p∞ is reached, thendp/dt = 0 and assuming that L → 0 (which is essential for UHV/XHV) we obtain





hus a value of p∞ in the UHV or XHV range may be achieved by decreasingQ or increasingS . Since the maximualue ofS is limited both by available space and by budgets, it is usually necessary to take vigorous action to reutgassing rateQ from the walls and internal parts of the system, and in particular from vacuum gauges, residuanalyzers, and other components with heated cathodes.

he pumping speed of a surface at which all impinging molecules are removed from the gas phase is

whereT is the temperature of the gas and M is its molecular weight. For hydrogen (the most prevalent gas at UHVXHV) at 300 K we obtain

hus the maximum pumping speed of any type of pump for H2 is 44 liter·s1 for each square centimeter of effecumping area. The above equations are a considerable simplification since they are only strictly correct if the gensity is uniform throughout the vacuum chamber. At very low pressures in the presence of adsorbing surfaceocalized pumps (e.g., gauges acting as pumps with limiting conductance to the chamber), this is not necessarilyractice, most extended UHV/XHV systems tend to exhibit nonuniform pressure distributions, particularly of themically active gases which are readily adsorbed on surfaces in a system at room temperature (hydrogen is an this respect). The problems of pressure and temperature nonuniformity at low pressures has been consideredxtent by Da [13], Grigorev [14] and Haefer [14a].

n general, the maximum pumping speed that can be applied to a vacuum system of arbitrary size is approximaroportional to the surface area; this is true for all types of pump from cryopumps to diffusion pumps. Thus weq. (11.2) that when the maximum pumping speed is applied to a system, the ultimate pressure is proportional utgassing rateQ and is independent of the system volume or surface area.

n the following sections the limitations to the measurement and attainment of UHV/XHV are discussed.

1.1imits to the Measurement of UHV/XHV

Only the various types of ionization gauge or residual gas analyzer (RGA) are capable of making pressuremeasurements in the UHV/XHV region. Several physical and chemical processes limit the measurement of ver

ressures by both hot-cathode and cold-cathode ionization gauges and by RGAs; these processes are examinedollowing sections. Detailed description of total pressure gauges may be found in Chapter 6, and partial pressur

measurements by residual gas analyzers are described in Chapter 7.





1.1.1Residual Currents

he residual current in an ionization gauge is defined as the current to the ion collector if the pressure were sudeduced to zero; in other words, it is that part of the collector current which is independent of gas pressure. Theurrent consisted of two components: (1) the x-ray photocurrent described above and (2) the positive ion currenollector caused by electron stimulated desorption (ESD) of gas adsorbed on the anode (grid). Both of these effroportional to the electron current in a hot-cathode gauge.

he electron current to the anode of a cold-cathode gauge is proportional to pressure, so that the x-ray and ESDo not cause a limit to the lowest measurable pressure in these gauges.

he x-ray effect as described above causes a limit to the lowest pressure measurable by all types of hot-cathodehe design of hot-cathode gauges may be modified to reduce the x-ray effect by:

. Reducing the surface area of the ion collector to minimize the fraction of x-rays intercepted . This was first intrody Bayard and Alpert [10] and leads to an x-ray limit (pressure at which the ion current equals the x-ray photocf about 5 × 109 Pa in modern BA gauges. Watanabe [15, 16] has taken this approach to the limit by placing thollector within a spherical grid and reducing its length to 0.05 mm; an x-ray limit of 2.7 × 1011 Pa was achiev. Placing the collector outside the grid and shadowing it from the source of x-rays . This method, though very effe limited by the reflection of soft x-rays from metal surfaces with a reflection coefficient of some tens of percextractor gauge [17] and the bent-beam gauge [18] (also known as the Helmer gauge) are examples of this arrahe former having an x-ray limit of 2 × 1010 Pa (8 × 1012 Pa in a modified form [19]) and the latter having an mit of about 1012 Pa when modified [20].

. Suppressing the x-ray photocurrent by placing a negatively biased grid in front of the ion collector to reflecthotoelectrons back to the collector . This method is limited by photoelectrons being generated at the grid and thttracted to the positive collector. This method was first used by Metson [21] in an early rival to the BA gauge nd later in the bent-beam gauge and other designs.

. Compensating for the residual current either by subtracting it electronically from the collector current or byalancing the photocurrent from the collector with the photocurrent to the collector from a close spaced metal envelope22] or other electrode at about the same potential as the collector . By careful choice of the potential and/or spacihe other electrode, it is possible to reduce the net photocurrent at the collector to near zero. The principle ofompensation of a "forward" photocurrent by balancing it with a "reverse" photocurrent from another electrodeescribed [23] for a BA gauge in 1963 and has since been used to reduce the x-ray limit in BA gauges. Theounterbalancing of two photocurrents in opposite directions has an advantage over the electronic subtraction mnce it is not affected (to first order) by changes in electron current. There are no published data on the long-teability of this arrangement; exposure to chemically active gases may cause a shift in contact potential betweenollector and the other electrode involved and thus change the balance conditions. Unless a method of frequenthecking the residual current is





vailable, such as the modulation method (see page 635), the compensation method of reducing the x-ray limitnreliable when chemically active gases are present.

ositive ions may be desorbed by the impact of electrons on adsorbed layers on the anode (grid) surface of ioniauges or the electron collector of the ion source of mass spectrometers; this process is known aselectron stimulatedesorption (ESD). The current of ESD ions constitutes part of the residual current because it is not proportionalressure. The ESD effect is most troublesome after exposure of the gauge or RGA to chemically active gases (

O2, H2O, CO, CO2, C xH y, and halogens or halides), and the ESD current can be reduced by heating the grid or lectron bombardment (thus operating the gauge or ion source at a high electron current tends to minimize the urrent). The ESD effect is the limitation to UHV/XHV measurements which is most difficult to eliminate.

everal methods have been developed to reduce the limit due to the ESD effect; they all depend on distinguishSD ions from gas-phase ions by the difference in their kinetic energy. This differences arises from the followiffects:

. The mean, initial energy of most ESD ions is several electron-volts (e.g., O+ from O2, 6 eV; O+ from CO, 2 whereas the initial energy of gas-phase ions is usually below 1 eV.

. The electron space charge in an initially field-free space (such as the grid of an extractor or bent-beam gaugeonizing region of the ion source of a mass spectrometer) can cause a depression of potential of several tens of lectron currents of a few milliamps. Thus the ions from the grid surface have a considerably higher energy thahase ions after extraction from the ionizing region.

hree types of hot-cathode gauge are insensitive to the ESD effect. The first is themodulated BayardAlpert gauge MBAG), where the ESD ions are separated from the gas-phase ions by the modulation process; this has been cxperimentally and reasonably accurate measurements of oxygen pressure can be made with an MBAG [2426]eason for the lack of modulation of the ESD ions is the low collection efficiency in a BAG for ions with signifnitial kinetic energy (see Redhead [24] and Comsa [27] for a more detailed explanation). The H+ ions produceSD at the grid of an MBAG are modulated like gas-phase ions [28] because of the low kinetic energy of the H

he second type of gauge which is insensitive to ESD effects is theextractor gauge , in which the ion collector isurrounded by a hemispherical reflector electrode at grid potential [29, 30]. This gauge is insensitive to ESD efecause ions released from the grid surface by electron bombardment have sufficient energy to reach the reflecwhich is at grid potential) while the collection efficiency of these ions on the fine collector wire is small. Gas-ons cannot reach the reflector because of the depression of potential within the grid caused by electron space chus to improve the separation of ESD and gas-phase ions the gauge should be operated at high electron curren

he third group of hot-cathode gauges that can separate ESD from gas-phase ions have electrostatic energy anahis group includes (a) several types of bent-beam





Fig. 11.1Ion collector current versus deflector voltage

for the 180° bent-beam gauge (ionspectroscopy gauge) for various electron

currents [33], after exposure of the Mo gridto O2 at about 107 Pa.

auge [18, 20, 31, 32] with a 90° analyzer and (b) Watanabe's bent-beam gauge [33] with a 180° hemisphericalalso known as the ion spectroscopy gauge). The gauges with 90° analyzers do not provide complete separationwo types of ions. The gauge with the 180° analyzer has sufficient resolution to achieve complete separation; theen in Fig. 11.1, which shows the collector current as a function of deflection voltage for various values of eleurrent after the gauge has been exposed to about 107 Pa of oxygen. It can be seen that complete separation of

as-phase ions is achieved while the position of the peak of the gas-phase ions shifts with electron current becahe space charge effect. The Bessel box gauge uses a "Bessel box" energy analyzer to separate ESD from gas-p34a]; this gauge is shown schematically in Fig. 11.2. This type of analyzer is capable of complete separation oypes of ions, as shown in Fig. 11.3.

Methods for reducing the errors caused by ESD in the measurement of total pressure in the UHV/XHV range aeviewed in Watanabe [35].

n an RGA there is no x-ray limit since any x-ray induced photocurrent only adds to the mass independent backurrent. However, ESD ions are produced by electron bombardment of material adsorbed on the electron collecon source; the ESD ions most frequently seen are mass 1 (H+), 10 and 11 (B+ when LaB6 cathodes are used), 9 (F+), 23 (Na+), 28 (CO+), 35 and 37 (Cl+), and 39 (K+).







Fig. 11.2Schematic diagram of Bessel box gauge showing dimensions (mm) and applied

potentials [34a].



Fig. 11.3Ion energy spectrum of the Bessel box gauge [34a] at a pressure of

2.3 × 1010 Pa (H2 eq.). The background signal, 63 counts s1,is the x-ray background equivalent to 3.5 × 1011 Pa.





Fig. 11.4Mass spectrum with a 90° magnetic sector instrument [37] in an

aluminosilicate glass and stainless steel system. The peaks at mass

2 (H2), 4 (He), and 28 (CO) are true gas-phase peaks; the peaks atmass 1 (H+), result from ESD ionsfrom the surfaces in the ion source.

With a double-focusing mass spectrometer (i.e., one that focuses ions with both spatial and energy dispersion), ycloidal EXB mass spectrometer, it is impossible to differentiate between ESD and gas-phase ions. With a sinocusing instrument (i.e., one that focuses the ions for spatial dispersion only), such as magnetic sector instrumuadrupoles, the two types of ions can be readily separated on the basis of their initial energy. With a single foc0° magnetic sector instrument the ESD ion peaks are displaced upward on the mass scale [36]; the shift in thef the ESD peaks is larger when low accelerating voltages are used. Figure 11.4 shows a mass spectrum taken w0° magnetic sector mass spectrometer [37] in an aluminosilicate glass and stainless steel system. The peaks atH2), 4 (He), and 28 (CO) are true gas-phase peaks; and the peaks at mass 1 (H+), 16 1/3 (O+), and 19 1/4 (F+

om ESD ions released from the grid of the ion source.igure 11.5 shows a mass spectrum with a quadrupole mass spectrometer [38] at a total pressure of 3 × 1010 Paeaks at mass 16 (O+), 19 (F+), and 35 (Cl+) are ESD ions. The mass-filter action of a quadrupole MS is very o the kinetic energy with which the ions are injected into the quadrupole structure. A complete separation of thypes of ions is possible either by modulating the ion accelerating voltage (typically at 125 Hz) and adjusting thalue of the ion accelerating voltage while detecting the ion current with a lock-in amplifier [39] or by placing lectrostatic energy analyzer (e.g., a Bessel box analyser as used in the Bessel box gauge [34]) between the ionnd the quadrupole structure [40].





Fig. 11.5Mass spectrum with a quadrupole mass spectrometer [38] at a total pressure of

3 × 1010 Pa. The peaks at mass 16 (O+), 19 (F+), and 35 (Cl+) are ESD ions fromsurfaces in the ion source.

o measure very low pressures with a hot-cathode gauge, when the residual current is a non-negligible fractionotal collector current, it is necessary to measure the residual current; this may be done in four general ways [41

. By reducing the pressure in the gauge to near zero . This is not often possible but has been achieved for severalf gauge [41] (BA, suppressor, bent-beam, and extractor).

. By plotting the collector current as a function of the electron accelerating voltage (the Alpert method [10]). In thimethod it is assumed that the collector current versus electron voltage characteristic is the superposition of a "gonization" curve and a "residual current" curve. It is also assumed that the residual current results from x-rays hat the x-ray photocurrent is given by

whereVe is the electron accelerating voltage (the grid-filament voltage in a BA gauge) andm is 1.2 to 1.8. At

ufficiently low pressure, when the gas ionization part of the characteristic plotted on a loglog scale can be subnear extrapolation through the operating voltage is taken to be the residual current. This method has severalifficulties: (1) It is a lengthy procedure and the grid is bombarded with electrons up to 1000 volts, which may utgassing or a change in surface conditions; (2) only the x-ray effect is measured, and the presence of an ESD

makes the measurement more unreliable; and (3) the photocurrent versus electron energy characteristic on a log not usually a straight line but exhibits changes of slope [41]. Figure 11.6 demonstrates the separation of gas-p





Fig. 11.6Determination of residual current (ir ) by the Alpert method

for a modulated extractor gauge [42]. The measuredcollector current isic, and the estimated gas phase ion

current gas isi+.

urrent from the x-ray photocurrent [42], which is the basis of the Alpert method of determiningir .

. By measuring the collector current as a function of the pressure measured with a reference gauge having a muchwer residual current limit .

. By modulation of the ion current . The modulation method was first applied to the BA gauge [43] and has sincpplied to most types of hot-cathode gauge. In general, it consists of modulating the potential of a suitable elechat the current from gas-phase ions is modulated while the modulation of the residual current is insignificant. Wotential of the modulating electrode atVm1, the ion collector current is

where i+ is the current of gas-phase ions andir is the residual current. When the potential of the modulating electt Vm2, the collector current becomes







f the modulation of the residual current is negligible (ε = 0), theni+ and ir can be readily determined:

where∆i = ic1 ic2. The modulation factork may be determined by making modulation measurements at pressureufficiently high that or by making modulation measurements at two different pressures (a and b) when

is not always negligible when making pressure measurements well below the residual current limit. Hobson [measurements on a modulated BA gauge in a cryopumped system capable of reaching a pressure of 9 × 1013 Pstimating the quantityεir by modulation measurements at three different pressures, measurements could be mao 4 × 1012 Pa even though the residual current was equivalent to a pressure of about 7 × 109 Pa. The value ofεir w

o small that Eqs. (11.7) were applicable to measurements above 109 Pa. There have been many investigationsifferent modes of modulating a BA gauge, as well as methods of modulating other types of hot-cathode gaugere summarized in Redhead [45]. Figure 11.6 shows the result of determiningi+ and ir by the modulation method aunction of grid-filament voltage in a modulated extractor gauge [42].

he modulation method of measuringir is very convenient since it gives a rapid method of observing changes inurrent due to ESD ions during the operation of a system; this gives a clear indication of whether the gauge hasontaminated by a chemically active gas. Modulation also allows accurate pressure measurements of gases whiSD such as oxygen. Singleton [25] has shown that the pressure indicated by a modulated BA gauge was in gogreement with the oxygen pressure indicated by a mass spectrometer while the unmodulated BA gauge readinonsiderably too high.

1.1.2ffects at Hot Cathodes

he hot cathode in an ionization gauge or RGA can cause problems in UHV/XHV measurements, which may bivided into four categories:

. Increased outgassing resulting from the heating of electrodes and the envelope by radiation from the hot cath

. Evaporation of neutrals and positive ions from the cathode.

. Chemical reactions of gas molecules at the hot surface resulting in changes in gas composition.

. Light from an incandescent filament (e.g., a pure tungsten filament) causing photoelectron emission, which croblem if an electron multiplier is used.hese effects all increase rapidly with temperature, so that the most effective remedy is to use a cathode with a

work function which can provide the required emission





Pag

able 11.2. Comparison of Cathodes Used in UHV/XHV

athode φ(V)

Te(K)

R(g·cm2·s1)

η(A·W1)

References

W4.5 2180 6.4 × 1012 1.3 × 104 46

aB6/C2.7 1370 ~1015 ~103 47

aB6/Rh2.7 1370 1010 ~103 48

hO2/W, Ta, Mo2.6 1400 ~2 × 1016 ~103 49, 50

mpregnated1.51.6 ~1000 <1015 51

Y2O3/W2.0 Less than

ThO250

Y2O3/Re, Nb2.9

BaSr]O/Ni 1.01.2 750 ~1017 ~102 52average work function.

e temperature for emission density of 102 A·cm2.rate of evaporation atT = Te .

emission efficiency atT = Te , amps of emission per watt of heating power.

a low temperature. The most widely used low work function cathode materials are thoriated tungsten, thin coatings of thorium oxides on tungsten, rhenium, or iridium, and lanthanum hexaboride on a carbon substrate (LaB6 coated on a refractory metal suchsults in the boron diffusing into the metal and producing an unacceptably high rate of evaporation of lanthanum; a carbon layer pffusion of boron). Barium/strontium oxide cathodes are not normally used in UHV/XHV instruments (although they have the low

nction of any cathode material) because their emission is easily poisoned by chemically active gases and they emit negative ionsbstantial amounts (Cl, O, and H mainly). Table 11.2 [4652] compares the properties of thermionic cathodes used in UHV/XHV.ommercially available impregnated cathodes have been used in an ionization gauge [53] at pressure down to 7 × 1011 Pa; electroabout 7 mA could be obtained at a cathode temperature of 1080 K.

eld emission arrays of the Spindt type [54] have been tested as electron sources in a quadrupole RGA [55] and in a 256.4° bent-b6], in the latter case, stable emission of 1 mA was obtained and the outgassing was sufficiently low to achieve a pressure 1011 Pcathode operating at room temperature is potentially very useful in UHV/XHV, provided that problems with outgassing and stabposure to chemically active gases can be minimized in routine use.

he temperature increase caused by radiation from the hot cathode can be reduced by using a metal of high conductivity and low e7] for the envelope of the gauge or ion source; an example is aluminum, which has an emissivity of only one-tenth that of stainlen source using a thoria-coated rhenium filament and an aluminum alloy envelope could be turned on and off at a pressure of 3 × ithout any observable change in the measured total pressure [57].

he evaporation of material from a hot cathode can cause a significant contribution to the residual current at sufficiently high cathmperatures. Alpert and Buritz first measured this effect in a BA gauge with a pure tungsten filament [58] and showed





hat the apparent pressure ( pev, Pa) was related to the rate of evaporation of tungsten ( R, molecules·m2·s1) by thexpression

where A is the surface area of the cathode (m2). The measured limit due to tungsten evaporation is about 1010 A gauge and about 7 × 1011 Pa in the bent-beam gauge at electron currents of 10 mA. The pure tungsten filament-beam gauge has been replaced by a thoria-coated filament resulting in a reduction of a factor of 10 in the mit due to evaporation [20]. Measurements of the modulation of the ion current due to evaporated material fro

ungsten filaments show that it is modulated in the same way as gas-phase ions [59]; thus the modulation methoncapable of separating this component of the residual current.

he emission of positive ions of impurities from a hot tungsten filament (mainly sodium) can cause false pressueadings; to prevent this effect the filament should be completely immersed in a positive electric field. The evaf neutrals or positive ions by various types of cathodes is reviewed in Redhead et al. [12, pp. 299303].

A hot cathode can behave like a chemical factory causing substantial changes in gas composition in the UHV/Xegion; some of the common reactions of molecules with heated tungsten are outlined below:. H2 + W→ H + H

. O2 + W + C→ O, CO, W xO y

. H2O + W→ 2H + W xO y

. H2O + W + C→ O, CO, W xO y, H, H2

. CH4 + W→ WC( s), H, H2

he atomic species produced in the above reactions are very active, and the following interactions with other uurfaces in the system are possible (where M is a metal):

. H + H + M→ H2

. H + C + M→ C xH y

. H + C + M xO y→ CO

. H + M xO y→ H2O

0. O + M→ M xO y

he atomic hydrogen formed at a hot cathode (reaction 1 above) is adsorbed on the other surfaces of the systemesulting in an anomalously high pumping speed for hydrogen when the cathode temperature exceeds 1000 K.ontaminant speciesin particular, CO (reaction 8 above)are produced by the interaction of atomic hydrogen wihamber walls and electrodes. The complex interactions of hydrogen in ion sources with hot filaments at pressu09 Pa have been studied in detail [60]. A fuller account of the interaction of gases with hot electrodes may be

Redhead et al. [12, pp. 275280].





1.1.3Gauges with Long Electron Paths

Magnetic ionization gauges suitable for UHV/XHV employ electron trapping to obtain very long electron pathsmall volume and hence increase the sensitivity of the gauge; these include the magnetic cold-cathode gauges bTownsend discharge (magnetron and inverted-magnetron gauges) and thehot-cathode magnetron . The space char

n the magnetic gauges is electronic at low pressures and behaves like a pure electron plasma which can have mifferent modes of oscillatory behavior and anomalous electron transport mechanisms [61]. Although not fullynderstood, these effects may lead to anomalous behavior of the discharge such as mode jumping, resulting in hanges of sensitivity with pressure, low-frequency fluctuations, and nonlinear relations between ion current anressure.

o minimize instabilities and nonlinearities in magnetic cold-cathode gauges, it has been suggested that (a) thend electric fields should be orthogonal and cylindrically symmetric, (b) all electrodes surrounding the plasma f high conductivity material, and (c) the cathode end-plates should be electrically separated so that only the ioo the cylindrical portion of the cathode is measured, thereby permitting the application of a small axial electricelp stabilize the plasma. Since high voltages (up to 6 kV) are used in these gauges, it is necessary to have goonsulation of the high-voltage electrode to ensure that leakage currents do not affect low-pressure measurement

roblems are offset by the advantages of cold-cathode gauges in the UHV/XHV region, which include:. Absence of a hot filament, thus avoiding the effects outlined in Section 11.1.2 above.

. Absence of an x-ray limit; the low pressure limit is usually set by the noise level of the discharge. Pressures 011 Pa have been measured.

. Low outgassing (cold-cathode gauges usually are significant pumps).

. Rugged construction.

At very low pressures the time to establish the discharge may be quite long; this delay is composed of two partatistical lag (which is the time before a chance event, such as the arrival of a cosmic ray, initiates the discharg

he formative lag (which is the time for the discharge to build to its stable condition). The statistical lag can be o a very short time at all pressures by the addition of a weakly radioactive source to the ionizing volume. Ni63mitter) was first used in the 1960s to trigger cold-cathode gauges and sputter-ion pumps. In 1996 Welch et al. 62] that the use of a 1-µCi Am241 source (a 5.6-MeV alpha emitter used in smoke detectors) reduced the startt 5 × 109 Pa for inverted-magnetron gauges to about 10 minutes; gauges without the Am241 source required as 12 hours for ignition to occur at this pressure. Kendall and Drubetsky [63] used the same type of Am241 sououble inverted magnetron gauge (i.e., a single set of electrodes immersed in two opposed magnetic fields giviffect of two inverted magnetrons in parallel) and showed that the product of starting time and pressure waspproximately constant; at 7 × 109 Pa the starting time was 22 ± 10% seconds; it was also found that a 0.5-µCiource was much





ess effective than the Am241 source in reducing the starting time. The use of a pulse of photons has also been e effective in starting cold-cathode gauges at low pressures, either from an external photographic flash unit fonvelope gauge or an internal source for metal-envelope gauges.

Most experimenters have found that both the magnetron gauges (MGs) and inverted-magnetron gauges (IMGsonlinear response to pressure in the UHV/XHV range. The ion current is given byi+ = kpn, wheren is in the range.6; the value ofn is dependent on the anode voltage (Va ), the magnetic field ( B), and the dimensions of the gaugebrupt change in the value ofn as the pressure is changed has been observed by many experimenters for both the

magnetron and inverted-magnetron gauge; the cause of this change of slope is not fully understood.

With the IMG, Feakes and Torney [64] found for p < 105 Pa thatn = 1.2 whenVa = 6 kV and B = 0.22T. Nichiporo65] has measured an IMG with the anode formed by a tungsten wire spiral which could be heated either to trigauge or to outgas it by electron bombardmentin this case,n = 1 from 4 × 1010 to 104 Pa atVa = 6 kV and B = 0.2 T

Mennega and Schaedler [66] found thatn = 1.65 for p < 107 Pa withVa = 3.3 kV and B ≈ 0.1 T, a 7-µCi source of was used to trigger the gauge at low pressures. Peacock and Peacock [67] measured the response of an IMG wiVaV: below 107 Pa,n = 1.35 ± 0.03 for B = 0.16 to 0.22 T; for B < 0.1 T, n increased to 1.8 at 0.062 T.

eakes and Torney [64] have calibrated the MG to 5 × 1011 Pa withVa = 4.8 kV and B = 0.105 T: below 107 Pa,n =.35. Nichiporovich and Khanina [68] have calibrated the MG down to 1010 Pa forVa from 3 to 8.5 kV and for B =.118 and 0.099 T; atVa = 34 kV and B = 0.099 T,n = 1.04 below 107 Pa. This MG had a spiral wire cathode thaould be heated both to trigger the gauge and to degas it by electron bombardment. Grishin and Grishina [69] hmmersed an MG in a liquid He bath whose temperature was varied by pumping on the liquid He; hydrogen wantroduced into the gauge and the H2 pressure calculated from the known variation of H2 vapor pressure withemperature; it is claimed that pressures down to 1013 Pa were obtained. WithVa = 2.5 kV and B = 0.12 T, n = 1 fro

1013 to 104 Pa; the reported sensitivity of 4 × 103 A Pa1 for H2 is about 10 times higher than that observed ther experimenter. In general, the sensitivity of the MG is found to be about 2.5 × 102 A·Torr1, about 10 timehe IMG. More details on cold-cathode gauges can be found in Redhead et al. [12, pp. 329 et seq.].

he hot-cathode magnetron gauge (also known as the Lafferty gauge [70]) is operated at a very low electron emvoid the instabilities and nonlinearities observed in cold-cathode magnetic gauges which operate at the maximlectronic space charge. The sensitivity of the Lafferty gauge with an operating anode current of 2.5 × 109 A (1mission at zero magnetic field) is 6 × 104 A Pa1, which is comparable to a typical BA gauge sensitivity. How-ray limit of the hot-cathode magnetron gauge is only 3 × 1012 Pa. Modifications to the original Lafferty gaugncluding the addition of an electron multiplier, have been made by several experimenters; the addition of a suplectrode [71] to reduce the current of photoelectrons leaving the ion-collector is predicted to reduce the x-ray less than 1014 Pa. The hot-cathode magnetron gauge is potentially capable of measuring lower pressures in theange than any other design.





Pag

.1.4omparison of UHV/XHV Gauges

should be pointed out that many of the hot-cathode gauge designs capable of making total pressure measurements in the XHV ramplex and expensive; in most cases a quadrupole RGA is more suitable since it provides information on the gas species present dicated above, with suitable care to reduce ion source outgassing, can measure to about 1014 Pa.

ables 11.3A and 11.3B [7277] compare the lower limit of pressure and the sensitivity of some selected hot-cathode total pressureitable for the UHV/XHV range. It can be seen that the immersed collector gauges (i.e., gauges which have the ion collector imme ionizing volume such as the BA gauge)

able 11.3A. Comparison of Some Hot-Cathode Gauges for UHV/XHV: Immersed Collector GaugesGauge

ypeCollector Diameter

(µm)Grid-Filament Voltage

(V) px

(Pa)aSensitivity (A·Pa1)b References

AG175 105 4 × 109c 7.5 × 104 44

AG150 170 5 × 109 4 × 104 72

AG50 100 2.4 × 1010 1.3 × 103 73

AG4 75 9 × 1011 4 × 104 74

oint30 110 3 × 1011 1.5 × 103 15, 16

ollector (50 long)px is the pressure at which the ion current equals the residual current (the x-ray limit). The minimum measurable pressure isiven approximately by pm = 10 px when px is not measured and by pm = px/10 when px is measured.Sensitivity to nitrogen at electron current of 4 mA.

For modulated BA gauge pm = 4 × 1011 Pa whenε is measured.

able 11.3B. Comparison of Some Hot-Cathode Gauges for UHV/XHV: External Collector GaugesGauge Electron

Emission(A)

px(Pa)a

Sensitivity(A·Pa1)

References

xtractorLeybold IE511)

1.3 × 1032 × 1010 1 × 104 (N2)

75

ent-beam 90°Helmer gauge)

3 × 103< 2 × 1012 1 × 103 (N2)

20

ent-beam 180°on spectroscopy gauge)

5 × 103< 3 × 1013 4 × 104 (N2)

76

ent-beam 256.4° 1 × 104< 6 × 1012b 1.8 × 106 (H2)

77

essel box 3 × 1054 × 1011c 2.5 × 107 (Ar)

34

px is the pressure at which the ion current equals the residual current (the x-ray limit).The lowest measurable pressure is about 4 × 1013 Pa for 1 min measurement.The lowest measurable pressure is estimated to be 3 × 1012 Pa or lower.





re capable of measurements in the XHV range; for example, the point collector gauge with modulation is capameasuring to about 3 × 1012 Pa. All the external collector gauges, except the extractor gauge, have electrostatinalyzers which permit the separation of ESD ions from gas-phase ions on the basis of their initial energy; the nalyzer gives only partial separation. Of this group of gauges, the simplest in construction are the extractor gawhich is commercially available) and the Bessel box gauge.

here are only three gauge types using magnetic fields that have found use for UHV/XHV measurements. Whequipped with an electron multipler [78], the hot-cathode magnetron gauge has an estimated lower limit of 4 ×n an ion counting mode; when provided with a suppressor electrode in front of the collector [31] but no multipstimated lower limit is 1014 Pa with a sensitivity of about 7.5 × 104 A Pa1. The cold-cathode magnetron and

magnetron gauges appear to have a lower limit of measurable pressure of about 1011 Pa which is not set by anySD effect but rather by the decrease in sensitivity with pressure and the noise level. Both gauges tend to be no

n their response in the UHV/XHV region, following a power law relationi+ = kpn, wheren = 1.0 to 1.5 dependinghe gauge design and the operating conditions.

1.2imits to Pumps at UHV/XHV

We next examine the limits to the lowest pressure attainable with those types of vacuum pumps which are suitaUHV and XHV. These may be considered in two categories:kinetic pumps , which impart momentum to the gasmolecules and remove them from the vacuum system; andcapture pumps , which trap gas molecules by ionicntrapment, condensation, adsorption, or chemical reaction at a surface within the vacuum system. A more comiscussion of vacuum pumps can be found in Chapters 4 and 5.

1.2.1Kinetic Pumps

wo types of kinetic pump are suitable for UHV/XHV: They are thediffusion pump and the turbomolecular pump (ourbopump). The advantage of kinetic pumps is that they can maintain a low pressure indefinitely and remove luantities of gas permanently from the system, whereas most capture pumps require some form of regenerationhey have pumped a specific quantity of gas and do not remove the gas from the system.

Many of the early experiments to achieve UHV in the 1950s used oil [79] or mercury [80] diffusion pumps wititrogen or other types of trap to prevent the backstreaming of pump fluid into the UHV chamber. Diffusion puetain their pumping speed indefinitely as pressure is reduced, and they are available with H2 pumping speeds o over 3.5 m3·s1, but the forepressure must be maintained as low as possible because hydrogen in the fore-vacackdiffuse to some extent through the vapor jets, thus reducing the effective hydrogen pumping speed. In modiffusion pumps, about half the molecules crossing the input plane are pumped away, while the other half retur

UHV chamber. Uncontaminated pressure in the UHV/XHV range cannot be reached with a diffusion pump wit





xtremely careful trapping to prevent any backstreaming of the diffusion pump fluid or the rotary pump oil. Alhe first to demonstrate [79] that an oil diffusion pump with a copper foil trap at room temperature maintained iumping speed to below 109 Pa. It has been claimed that with properly trapped oil diffusion pumps it is possibchieve 1012 Pa [81]. Diffusion pumps are not now widely used for UHV or XHV, partly as a result of these din ensuring dependable, long-term trapping.

urbomolecular pumps (TMPs) have considerable advantages for UHV/XHV since they can provide a completee system, and, unlike diffusion pumps, most designs can be operated in any position. This is possible becausMP can be designed to operate against a high backing pressure which can be provided by an oil-free diaphragnd the rotor can be magnetically suspended to avoid lubricated bearings. The predominant gas at UHV/XHV iydrogen; thus special steps must be taken to increase the low compression ratio for hydrogen (about 104) in thnd the conventional TMP is only capable of achieving about 108 Pa. In 1990 a tandem TMP structure (with muspension) consisting of two TMPs on the same shaft was developed [82]; the upper section was designed for ompression ratio and the lower portion for high throughput. This pump had a H2 compression ratio of 5 × 108

maximum backing pressure of 0.5 Torr, and it achieved a pressure of 109 Pa. It was shown [83] in 1995 that thurrent losses in the magnetic suspension can cause a temperature increase in the rotor of 60°C, resulting in outy coating the lower half of rotor and stator with a high emissivity layer (SiO2 with emissivity of 0.9) the rotor

emperature was reduced to 25°C, allowing a pressure of < 1010 Pa to be obtained. Cho et al. [84] used a TMP

magnetic suspension backed by a small molecular drag pump followed by a dry diaphragm pump. The stainlesystem was first baked at 450°C and then opened to dry nitrogen and pumped again with a 200°C bake for 140he final pressure was 1010 Pa. Thus it has been clearly demonstrated that pressures in the XHV range can be a

with a turbopump alone, provided that steps are taken to achieve a high compression ratio for H2.

1.2.2apture Pumps

apture pumps suitable for the UHV/XHV range include ion, getter, and cryopumps (and combinations thereofhey have been reviewed in some detail by Welch [85]. No traps are required and no fluids are introduced into ystem. The main disadvantage of these pumps is that the pumped gas is stored within the vacuum system and otentially available for later release into the vacuum.

on pumps may be divided into two categories: (a) sputter-ion pumps (SIP), which pump chemically active gases bputtering fresh adsorbing surfaces and pump rare gases by ionic entrapment, and (b) getter-ion pumps (GIP), whichontain an evaporable getter (usually titanium). Ion pumps have the advantage at UHV/XHV that the ion curreough measure of pressure. The main problem with an SIP at UHV/XHV is that the pumping speed tends to de

with pressure [86] as the discharge intensity (current per unit pressure) decreases. Re-emission of previously puare gases is also a problem with SIPs. The main purpose of an ion pump in





Fig. 11.7Discharge intensity (A·Pa1) versus pressure for sputter-ion pumps[89] at three different magnetic fields. Anode voltage 5 kV, anode

diameters 19 and 25 mm. Curves 1,2,3: 19 cells of 33-mm diam.; B=0.1,0.15, 0.2 T, respectively. Curves 4,5,6: 25 cells of 19-mm

diameter; B=0.1, 0.15, 0.2 T, respectively.

he UHV/XHV range is to provide some pumping speed for the gases which are not pumped by getter pumps (nd the rare gases).

was shown in the early 1960s that some speed was retained by an SIP at very low pressures: In 1961 Klopfer chieved a pressure of 8 × 1010 Pa with a small SIP, and in 1962 Davis [88] achieved pressures in the 1011 Pa

with a commercial 5 liter·s1 SIP; in both cases the pressures were measured with mass spectrometers. The rate ecrease of the pumping speed of an SIP at pressures in the UHV/XHV range is critically dependent on magnenode voltage, and dimensions of the pumping cell. Pumping speed is proportional to discharge intensity (i+/ p); Fig1.7 showsi+/ p as a function of pressure in a diode sputter-ion pump for various magnetic fields and anode diam89]. It can be seen thati+/ p increases with the larger anode diameter and that increasing the magnetic field tendaise i+/ p at low pressures. The long time delays in starting a SIP discharge at very low pressures have been redhe addition of a radioactive source (e.g., Ni63, which is a beta emitter) to trigger the discharge [90].

Getter-ion pumps have the advantage that re-emission of previously pumped gas can be prevented by evaporatiayer of getter material (usually titanium) over the surfaces where gas has been pumped. Getter-ion pumps haveen widely used in the UHV/XHV range in spite of their advantage in preventing re-emission. Kornelsen [91]escribed a small cold-cathode magnetron pump containing a titanium evaporator which maintains some speed08 Pa range and is capable of pumping 67 Pa·liter of helium and 13 Pa·liter of argon without re-emission. An

magnetron SIP containing a titanium evaporator has been described by Komiya [92, 93] which maintains somepeed to 1011 Pa; both of the





bove-mentioned pumps are in effect combined sputter-ion and getter-ion pumps. Hot-cathode GIPs, such as thrbitron pump which has achieved pressures in the 1010 Pa range [94], have not been widely used at UHV/XHpite of their potential advantage thati+/ p does not decrease at low pressures.

Getter pumps, both evaporable and nonevaporable, are widely used in UHV/XHV; however, they do not pumpases and their speeds for hydrocarbons are negligible. Evaporated titanium films at room or liquid nitrogenemperatures have been used, in combination with other pumps needed, to remove the rare gases and methane ressures of 1011 Pa and below. For chemically active gases (e.g., H2, H2O, CO, CO2, O2, and N2) a stickingrobability of about 0.5 is achieved on freshly evaporated metal films; thus pumping speeds of about 5 liter·s1·e achieved. Renewal of the film is necessary after about a monolayer of gas has been adsorbed. For a titaniumapacity of about one pumped molecule to one evaporated titanium atom is possible. Freshly evaporated titaniuend to outgas methane unless very pure titanium is used or the film is baked at 100°C for a few hours. Nonevaetters (NEGs) are very effective in the UHV/XHV range because of their high pumping speed to hydrogen. Narticularly useful in accelerators and storage rings since they can be placed very close to beam lines. For examenvenuti [94a] has achieved pressures as low as 5 × 1012 Pa in a 3 m long section of an accelerator ring usinge NEG strip (43.5 m long), a sputter-ion pump (400 liter·s1), and a titanium sublimation pump cooled with liqitrogen.

ryopumps used in the UHV/XHV range fall into two categories: (a)cryo-condensation pumps , which physisorb mhan 23 monolayers of gas on a smooth surface of relatively small area, and (b)cryo-sorption pumps , which have aorous surface of very large effective area with less than 23 monolayer of physisorbed gas.

or the cryo-condensation pump the limiting pressure is the vapor pressure of the adsorbed gas at the temperatuurface, and the capacity of the cryo-condensation pump is essentially infinite, at least until the thickness of theresents problems. Condensation coefficients of about 0.5 are typical, and hence maximum pumping speeds ofter·s1·cm2 are possible; however, maximum speeds cannot be obtained in most situations because the cryosur

must be protected from room temperature radiation by suitable baffles at an intermediate temperature; the excepre when the complete wall of the vacuum system is a cryosurface (e.g., in the cold bore of an accelerator or stng with superconducting magnets). The low-pressure limit can in principle be made infinitely low since re-eman be reduced to near zero by lowering the temperature. Table 11.4 shows the temperatures at which the vaporf some common gases is equal to 1.3 × 108 and 1.3 × 1011 Pa, respectively [95]; it can be seen that only hydreon, and helium may limit the pressure in a cryo-condensation pump at 10 K to more than 1011 Pa.or the cryo-sorption pump the limiting pressure is established by an appropriate isotherm relating the equilibriressure to the surface coverage; for the UHV/XHV region the DubininRadushkevich isotherm has been foundppropriate for most gases [96]. Theory indicates that at very low pressures and surface coverage the equilibriuressure should be proportional to the coverage (Henry's law); so far this has never been observed. A cryo-surfess than a monolayer coverage at 4.2 K will pump all gases to extremely low pressures; for example, a system-liter volume pumped to UHV, sealed off, and then totally immersed in liquid helium, will drop to an estimateressure of about 1028 Pa based on an extrapolation of the





Table 11.4. Temperatures (K) for Two Selected Vapor Pressures of Common Gases95]

Gas Vapor Pressure1.3 × 108 Pa(1010 Torr)

Vapor Pressure1.3 × 1011

Pa (1013 Torr)H2

3.21 2.67

He0.303 0.250

CH428.2 24.0

H2O130.0 113.0

Ne6.47 5.5

CO23.7 20.5

N221.1 18.1

O225.2 21.8

Ar 23.7 20.3

CO268.4 59.5

Kr 32.7 27.9

Xe45.1 38.5

Data mainly from R. E. Honing and H. O. Hook, RCA Rev. 21, 360 (1960).

DubininRadushkevich isotherm [97]. After pumping to UHV, Thompson and Hanrachan [98] immersed a compurface analysis system containing a mass spectrometer in liquid helium at 4.2 K; the pressure dropped to 1012

K as the system cooled and then became immeasurable.

n the preparation of highly porous surfaces for cryo-sorption pumps at UHV/XHV it is necessary to obtain goohermal contact between the porous material and the underlying cooled surface to achieve rapid thermal equilib

Metal or metal oxide sponges have good thermal contact to the substrate. Hobson [96] has used porous silver bmetal substrate and achieved an effective area about 1000 times that of a flat surface. Figure 11.8 shows adsorotherms for hydrogen on several different surfaces [99] at 4.3 K; the sudden drops at pressures in the 1013 Tore probably due to the x-ray limit of the extractor gauge used to measure pressure. It can be seen that the poroluminum oxide surface (anodized aluminum with an oxide layer having small pores and a thickness of about 4as a hydrogen adsorption capacity more than 103 times as great as a smooth stainless steel surface.

1.2.3omparisons of Pumps for UHV/XHV



he choice of pump(s) for UHV/XHV depends on the application and the resources available. For relatively smystems requiring the absence of hydrocarbon contamination a good choice is the magnetically suspendedurbomolecular pump backed with a diaphragm pump. This arrangement is completely oil-free, does not requireriodic regeneration, and can obtain pressures below 1010 Pa. When pumps requiring starting pressures lowerhose of turbopumps are used (e.g., ion pumps), then to obtain hydrocarbon free conditions it is necessary eitheil-free backing pumps or sorption backing pumps or to trap the oil vapor from the backing pump





Fig. 11.8Hydrogen adsorption isotherms at 4.3 K on various surfaces [99].

with great care. For extremely low pressures (< 1010 Pa) the use of liquid helium cryopumps, including the posf complete immersion, is a practical solution.

or large systems the choice of pumps is dominated by costs and frequently by the difficulty of access to the vahamber (as in accelerators and storage rings). Nonevaporable getters combined with sputter-ion or cryopumpsequent choice. Where superconducting magnets are used, it is possible to use the cold bore of the beam line aump; this has been done in some storage rings and accelerators.

1.3eak Detection at UHV/XHV

As was pointed out in connection with Eq. (11.1) above, it is necessary to reduce the leak rate into an UHV or ystem to as close to zero as possible; this raises the problem of the measurement of very small leak rates. The roblems of leak detection have been described in Chapter 8, and we only discuss here the measurement of extmall leak rates. The sensitivity of a conventional helium leak detector is about 1012 Pa·m3·s1 (1011 atm·cm3·igher sensitivity is desirable to test UHV and especially XHV systems. To achieve this increased sensitivity it ecessary to accumulate the helium that enters the system through the leak, either in the gas phase or in the adshase.

he sensitivity of a helium leak detector can be increased by reducing the helium pumping speed to zero in a cystem and allowing the helium to accumulate in the gas phase; the pumping speed to active gases can be kept he use of nonevaporable getters or a cryopump operating at about 18 K, neither of which will





ump helium. The leak rate is determined, after calibration, by the rate of rise of the helium ion current in the mpectrometer (usually a quadrupole). Bergquist and Sasaki [100] have described a helium leak detector system onevaporable getters and the rate of rise method; they claim that this system can routinely detect leaks as smaa·m3·s1 (1015 atm·cm3·s1).

Another leak detection method has been developed [101] in which the inleaking helium is adsorbed on a smootlate maintained at 9 K or lower in a closed system; the active gases are adsorbed on surfaces at about 20 K whave porous carbon or nonevaporable getter material on them. The temperature of the helium adsorbing plate i020 K by an internal heater, and the pressure of the desorbed helium is monitored with an RGA. This cycle is

with the plate cooled to 9 K or lower for 1 min and then heated to 1020 K for 1 min. With a 1-min accumulatio9 K, a sensitivity of 1016 Pa·m3·s1 (1015 atm·cm3·s1) is claimed; with longer accumulation times, a sensitiv

019 Pa·m3·s1 (1018 atm·cm3·s1) is claimed.

1.4utgassing

o achieve pressures in the UHV, and more particularly the XHV, range it is essential to minimize the outgassinhe walls of the vacuum chamber and the internal parts, as is evident from Eqs. (11.1) and (11.2). In the early d

UHV, most systems were of borosilicate glass which could be baked at 450°C to minimize outgassing of wateremaining outgassing resulted from the permeation of atmospheric helium through the glass walls; this could bminimized by the use of aluminosilicate glass, which has a much lower He permeation rate at room temperatur

ressures as low as 1012 Pa were obtained by Hobson [44] in 1964 with an aluminosilicate glass system and aryosorption pump. Modern systems are almost entirely constructed of metal, most commonly stainless steel orluminum alloy, where after processing and bakeout the principal component of the outgassing is usually hydrohis section is concerned with methods to minimize hydrogen outgassing from stainless steel and aluminum al

with the measured values of outgassing rates that result from the best practices to reduce outgassing.

Reduction of outgassing from the internal parts of an UHV/XHV system is normally achieved by degreasing, cleaning, and vacuum firing of the parts before assembly followed by electron bombardment, I2R heating, or requency (rf) heating in the vacuum system. Thein situ degassing process is particularly important for any parts tperate at elevated temperaturesfor example, electrodes of hot-cathode devices.

he SI unit for outgassing rate per unit area is Pa·m·s1 (i.e., Pa·m3·s1·m2); another widely used unit isorr·liter·s1·cm2, which equals 1.33 × 103 Pa·m·s1.

1.4.1Reduction of Outgassing Rates

Reduction of the outgassing rates of the metals used in the construction of vacuum chambers is essential if preshe UHV/XHV range are to be achieved efficiently. Outgassing rates from metals can be reduced by:





. High-temperature vacuum firing to reduce the amount of dissolved hydrogen (as high as 1000°C for stainles

. Baking of the vacuum system to remove water (150450°C). It is important to achieve as uniform a temperatuistribution as possible while baking.

. Degreasing and chemical cleaning.

. Surface treatment to reduce surface roughness and remove porous oxides. This includes electropolishing, surmachining under special conditions, and glow-discharge cleaning.

. Surface treatments to create oxide or other films on the surface that act as a barrier to diffusion of hydrogen fulk.

. Deposition of films of low hydrogen permeability on a metal substrate (e.g., titanium nitride or boron nitride

. Choice of metal with a low solubility for hydrogen.

xamples of the effects of these treatments are given below.

Outgassing rates in the first few hours of pumpdown of an unbaked system are dominated by water. Barton and102] have compared the outgassing rate of an unbaked stainless steel specimen (a) after vapor degreasing and apor degreasing, vacuum baking, and exposure to atmosphere. The short-term outgassing rates achieved by th

methods were within a few percent of one another. Mathewson [103] has compared three methods of cleaningluminum alloy vacuum chambers: vapor degreasing only, weak alkaline etch, and strong alkaline etch. The strlkaline etch was found to be best. Suemitsu [104] has prepared mirror-polished surfaces of aluminum alloys blectrochemical buffing techniques and has shown that measured outgassing rates at 10 h are proportional to thoughness factor. Dylla [105] has compared the effects of several different surface treatments on the measuredutgassing rates of unbaked stainless steel (type 304) and aluminum alloys (type 6061/63) at relatively short pume. The outgassing rates at 100 min did not differ by more than a factor of 9, lying between 8 × 107 and 7 × a·m·s1. The short-term outgassing rate was not much affected by surface roughness. Li and Dylla [106] have m

he outgassing rate of an electropolished stainless steel surface after it was exposed to a glow discharge followienting for 1 h to the atmosphere. The most effective treatment was a helium discharge for 2 h at a dose of mor.2 C·cm2·h which reduced the outgassing rate by a factor 13.

he ability to reach UHV without having to bake has considerable advantage for many applications. Kato [107chieved 1010 Pa without baking in a stainless steel system after electrochemical buffing. Pressures of 3 × 107 eached in 4 days, and the turbopumps and the titanium sublimation pump (TSP) only were then baked at 12032 h; the pressure then dropped on day 15 to 8 × 1010 Pa with the TSP cooled in liquid nitrogen. A pressure ofa could be maintained without cooling or operating the TSP.

ystems capable of very fast pumpdown to the UHV range without bakeout have great potential for semicondurocessing. Miki [108] has developed an aluminum system machined in a controlled atmosphere of oxygen andhe EX process), which was first pumped to 109 Pa after a bakeout and then vented to dry nitrogen. The system

hen repumped by a turbopump and a cryopump reaching 106 Pa in





.5 min and 108 Pa in 170 min. The system had been vented to dry nitrogen with only a few ppb of water or otontaminant gases; the nitrogen was introduced over a moisture trap and a NEG trap.

aking the vacuum system rapidly removes the adsorbed water leaving hydrogen as the main constituent of theutgassing in metal systems, which then limits the lowest pressure attainable in the UHV/XHV range. Thus whystem bakeout is possible, the main effort should then be directed to the reduction of the hydrogen outgassing oom temperature.

n a classic paper, Calder and Lewin [109] studied both theoretically and experimentally the reduction of outgaom stainless steel. After baking for about 25 h at 300°C the measured outgassing rates were about 4 × 109 Pa

H2). After vacuum furnacing for 3 h at 1000°C followed by baking in the vacuum system for 25 h at 360°C, thutgassing rate had dropped to well below 1011 Pa·m·s1 (H2), which was the lower limit of measurement. Stra110] has compared the outgassing rates of stainless steel after (a) vapor degreasing only and (b) vapor degreasihemical cleaning, and glass-bead blasting. Minimum outgassing rates for H2 of about 5 × 109 Pa·m·s1 were o

with process (b) above being the better of the two by less than a factor of 5.

he effects of oxidation of a stainless steel surface (200°C for 3 h in atmospheric air) on outgassing rates has budied [111]; the reduction in outgassing rate of the oxidized surface compared to the well-outgassed unoxidiz

urface was a factor of 4. Ohmi [112] has developed a method to produce a continuous film of chromium oxiden stainless steel which passivates the surface and prevents corrosion by HCl gas; this process may prove effeceducing outgassing in UHV/XHV chambers.

A high-current Penning discharge in oxygen has been used to clean the surface of aluminum (99.99%) vacuumhambers used in a storage ring [113, 114]. Hydrocarbon contaminants were removed by sputtering, and thehotodesorption yield was reduced by a factor of 10.

oating the interior surface of a vacuum chamber with a thin film of material having a low permeation rate forydrogen is a promising way to reduce outgassing rates. Titanium nitride has been found to be a suitable mater

when deposited on stainless steel by ion plating in a film 12 µm thick; the outgassing rates with and without thewere 1.7 × 1011 and 2.2 × 109 Pa·m·s1 (H2), respectively, a reduction of about two orders of magnitude.

shimaru [116] has described an aluminum alloy system where the chamber was machined in an atmosphere ofxygen and argon (the EX process). After bakeout at 150°C for 24 h the outgassing rate was about 1010 Pa·m·sltimate pressure of 4 × 1011 Pa was claimed.

opper has been used in the manufacture of vacuum tubes since the 1930s but has not been widely used for UHystems. Watanabe [117] has measured outgassing by the throughput method from an electropolished, oxygen-onductivity copper chamber; the lowest outgassing rate observed after bakeout at 300°C was 5 × 1012 Pa·m·s1

itanium coated with titanium nitride, deposited by the hollow cathode discharge ion plating method, has also xamined [118] as a low outgassing material; preliminary results indicate that this combination has an outgassiery similar to well degassed stainless steel.





able 11.5. Some of the Lowest Measured Outgassing Rates (H2)Material Measurement Methoda Surface Treatment Hydrogen Outgassing Rate

(Pa·m·s1)Gauges in

Test Chamber bReferences

t. St.c (321Ti) GA 12 × 1010

None 119

t. St. (316L) T 21.3 × 1010

RGA + IG 120

t. St. (316LN) GA 32 × 1010d

RGA + IG 121

t. St. (316L) GA 42.3 × 1011

SRG 122

Al (99.99%) T 5~1011

IG 116

Al alloy (A6063-T6) T 5~1010

IG 116

u (OFHC) T 12 × 1013

None 119

u (OFHC) T 65.4 × 1012

IG 117

iN on St. St.e St. St.e T 7 1.7 × 1011 None 115

GA, gas accumulation method; T, throughput method.Type of pressure sensor(s) used in test chamber: IG, ionization gauge; RGA, residual gas analyzer; SRG, spinning rotor gaugeSt. St., stainless steel.

Outgassing rates for other gases;≤ 1 × 1015 (CH4),≤ 3 × 1014 (H2O),≤ 4 × 1013 (CO),≤ 2 × 1014 (CO2).

TiN film 12 µm thick.ote : All surface treatments included an initial chemical cleaning, alkali detergent wash, and/or vapor degrease.. Glass bead blast + 250°C bake for 3 days + 400°C in UHV furnace for 3 days + 250°C bake for 1 day.. 950°C in vacuum furnace for 2 h + 200°C bake for 2 days.. 150°C bake for 10 days.. Vacuum fired + 250°C bake for 3 days.. Machined in O2 + Ar atmosphere (EX process), or machined under ethanol (EL process) + 150°C bake for 24 h.. 300°C bake for 3 days.. Electropolish + TiN ion-plated + 150°C bake for 2 days.

able 11.5 [119122] lists some examples of the lowest measured outgassing rates for hydrogen from stainless steel, aluminum anloys, and copper surfaces. Two methods of measurement have been used: (1) the gas accumulation method (also called the presethod) where the test chamber is sealed off after pumping to the ultimate pressure and the pressure rise with time is measured aroughput method where the test chamber is pumped through an orifice of known conductance and the pressure drop across the easured. The presence of a hot-cathode RGA or ion gauge in the test chamber can cause extra outgassing; thus the measuremenith a spinning rotor gauge or with no gauge in the test chamber should be more reliable. The low outgassing rates observed with17] and with stainless steel after rigorous vacuum furnacing [119] are noteworthy.





1.5HV/XHV Hardware

he expanding use of UHV technology in the 1960s depended on the development of demountable metal systeequired reliable all-metal valves, motion transmitters, demountable flanges, and other demountable componen

were free from any leakage. Previous versions of these devices used at higher pressures, which relied on greaselastomers to achieve a vacuum-tight seal, were not applicable at UHV where high bakeout temperatures were he vapors from the greases and elastomers were not tolerable. The various methods that had been developed part of UHV technology for making permanent joints between metal parts and between metals and ceramics or

were in general suitable for use at UHV/XHV, provided that sufficient care was taken to produce clean, leak-freungsten-inert gas welding and electron beam welding have proved very effective for UHV/XHV systems. Theistorical development of vacuum hardware has been described by Singleton [123], and the various types of se

methods and the theory of metal gasket seals have been described by Roth [124].

he early types of metal gasket seals using aluminum or gold wire and flat flanges were compatible with UHVot very reliable. More consistency was achieved in 1954 with copper gaskets compressed between knife edgearder metal [125]. The development of the captured copper gasket seal by Wheeler [126] in 1962 led to a thoreliable seal for UHV/XHV and is now almost universally used in a wide variety of commercially available siz

Alpert described the first all-metal valve in 1951 that was both bakeable and suitable for UHV use [127]; this vclosed conductance of 1013 m3·s1. Bills and Allen [128] developed in 1955 an improved valve with a constrlver insert as the sealing element which achieved a closed conductance of 1017 m3·s1. Another type of seal f

UHV valves, using a hard knife-edge driven into a copper gasket by pneumatic pressure, was developed [129]

A wide variety of demountably flanged components compatible with UHV/XHV are now available such as winlectrical and liquid feed-throughs, and motion transmitters (using both metal bellows and magnetic coupling)

which complex UHV/XHV systems can be built.

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9. T. Koizumi, Y. Kawasaki, T. Kurita, M. Kondou, and Y. Hayashi, J. Vac. Soc. Jpn . 34, 505 (1991).

0. C. Hayashi, J. Vac. Sci. Technol . 3, 286 (1966).

1. E. V. Kornelsen,Trans. Natl. Vac. Symp . 7, 29 (1960).

2. S. Komiya, N. Takahashi, and M. Xu, J. Vac. Soc. Jpn . 36, 125 (1995).

3. M. Xu, N. Takahashi, and S. Komiya, J. Vac. Soc. Jpn . 36, 271 (1995).


4a. C. Benuenuti and P. Chiggiato,Vacuum , 44, 511 (1993).

5. J. P. Hobson, Proc. Int. Vac. Congr . 9, 35 (1983).

6. J. P. Hobson, J. Phys. Chem . 73, 2720 (1969).

7. J. P. Hobson, J. Vac. Sci. Technol . 3, 281 (1966).

8. W. Thompson and S. Hanrachan, J. Vac. Sci. Technol . 14, 643 (1977).

9. M. G. Rao, P. Kneisel, and J. Susta,Cryogenics 34, 377 (1994).

00. L. E. Bergquist and Y. T. Sasaki, J. Vac. Sci. Technol. A 10, 2650 (1992).

01. G. R. Mynemi, U.S. Pat. 5,343,740 (1994).02. B. S. Barton and B. P. Govier,Vacuum 20, 1 (1970).

03. A. G. Mathewson, J.-P. Bacher, K. Rooth, R. S. Calder, G. Dominichini, A. Grillot, N. Hilleret, D. LatorreeNormand, and W. Unterlerchner, J. Vac. Sci. Technol. A 7, 77 (1989).

04. M. Suemitsu, H. Shimoyamada, N. Miyamoto, T. Tokai, Y. Moriya, H. Ikeda, and H. Yokoyama, J. Vac. Sci.echnol. A 10, 570 (1992).

05. H. F. Dylla, D. M. Manos, and P. H. LaMarche, J. Vac. Sci. Technol. A 11, 2623 (1993).

06. M. Li and H. F. Dylla, J. Vac. Sci. Technol. A 13, 571 (1995).07. S. Kato, M. Aono, K. Sato, and Y. Baba, J. Vac. Sci. Technol. A 8, 2860 (1990).

08. M. Miki, K. Itoh, N. Enomoto, and H. Ishimaru, J. Vac. Sci. Technol. A 12, 1760 (1994).

09. R. Calder and G. Lewin, Br. J. Appl. Phys . 18, 1459 (1967).

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11. K. Odaka and S. Ueda, J. Vac. Sci. Technol. A 13, 520 (1995).



12. T. Ohmi, A. Ohki, M. Nakamura, K. Kawada, T. Watanabe, Y. Nakagawa, S. Miyoshi, S. Takahashi, and Mhen, J. Electrochem. Soc . 140, 1691 (1993).

13. M. Saitoh, K. Kanazawa, T. Momose, and H. Ishimaru, J. Vac. Sci. Technol. A 11, 2518 (1993).

14. N. Ota, M. Saitoh, K. Kanazawa, T. Momose, and H. Ishimaru, J. Vac. Sci. Technol. A 12, 826 (1994).

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2alibration and Standards

Karl Jousten

he pressure p in an enclosed gaseous system is basically defined as the forcedF per areadA exerted by the gas in hamber:

he SI unit of pressure is the pascal (Pa),

which will be used throughout this chapter. The pressures in vacuum are divided into various ranges by the scan Table 12.1 [1].

ince in the vacuum range <10 Pa for practical areas of a few square centimeters the force becomes very smallifficult to measure, in most vacuum gauges other pressure-dependent physical properties of the gas such as vishermal conductivity, or particle density are being used to indicate pressure. For these gauges it is generally noto state an equation by which the pressure can be calculated from well-known parameters of the gauge. In thesealibration of the gauges is needed, by which the gauge's indication is related to the true pressure applied to it. lso true for gauges which still use the mechanical force of the gas, but the magnitude of the force or the area c

uantified absolutely. Practically, two calibration methods exist: Foundations of Vacuum Science and Technology , Edited by James M. Lafferty.ISBN 0-471-17593-5© 1998John Wiley & Sons, Inc.





Table 12.1. Classification of Vacuum Ranges from AVS [1]Vacuum RangeDegree of Rarefication)

Pressure Range (in pascals)

Low (rough)3.3 × 103 to 105

Medium101 to 3.3 × 103

High104 to 101

Veryhigh107 to 104

Ultrahigh1010 to 107

Extreme ultrahigh

< 1010

. The more accurate calibration method is to subject the gauge head to a pressure generated by a primary standrimary standard is defined [2] as standard that is designated or widely acknowledged as having the highest

metrological qualities and whose value is accepted without reference to other standards of the same quantity. Sacuum primary standards provide the most accurately known pressures in vacuum, and they deduce pressure dom other units as mass, length, and time according to Definition 12.1 and basic laws of physics. Not all vacuu

anges can be covered by a single primary standard, so that various methods of generating pressures and also vealizations of these methods exist (Section 12.1). The most accurate and well-known vacuum primary standareen established by the vacuum sections of some National Metrological Institutes, among them the NIST (Natinstitute of Standards and Technology) in the United States, PTB (Physikalisch-Technische Bundesanstalt) in G

NPL (National Physical Laboratory) in England, IMGC (Istituto di Metrologia ''G. Colonnetti") in Italy, and thndia.

. With less accuracy the reading of a gauge may be compared to the reading of a stable gauge, called secondaryandard or reference standard , which was calibrated on a primary standard. This method is known as thecomparison

method (Section 12.2).

n both calibration methods, it is a crucial point that the generated pressure in the primary standard or the presspplied to the reference gauge is identical to the pressure applied to the gauge to be calibrated. This means thatalibration chambers the pressure has to be as homogeneous as possible, and this is one of the main criteria for esign of a calibration system for pressures in vacuum.

According to the kinetic theory of gases the momentum of gas molecules depends on temperature and so does

ressure. Although this is well known, it is an often forgotten fact that, when pressure values are being comparhe temperature of the gas of which the pressure was measured has to be named. It is mostly tacitly assumed thressure was measured at room temperature whatever this exactly was. In this chapter, pressure will always be o a temperature of 23°C, if not specified otherwise.

2.1rimary Standards

Above about 10 Pa, it is possible to measure directly the force exerted by the gas, for example in a liquid mano





elow 10 Pa, the idea of all vacuum primary standards used today is the following: The gas is measured at a prigh as possible and then expanded in a calculable manner to the desired pressure. The initial pressure of the gae as high as compatible with the expansion method, because the accuracy of pressure measurement increases ressure, but low enough that the gas can still be considered as ideal (practically less than 300 kPa; see Sectionhe expansion is carried out mainly in two ways: statically or continuously.

n the static expansion, the BoyleMariotte law

used and the gas is expanded from a small volume into a large volume.Static means that no pump is used for thexpansion itself. Under isothermal conditions, the ratio of the small volume to the arithmetic sum of the small aolume gives the factor by which the initial pressure is being reduced (see Section 12.1.2).

n the continuous expansion, the gas at the high pressure is continuously pumped through two orifices, the firstery small conductance, the second of much larger conductance. The ratio of the two conductances gives the fa

which the initial pressure is being reduced (Section 12.1.3).

here is another expansion method, which is rarely used: the expansion by molecular beam. Herein, a molecul created by the exit orifice of an effusion cell and by the entrance orifice of a calibration chamber. From the sngle of the entrance orifice of the calibration chamber with respect to the exit orifice of the effusion cell and th

Maxwellian velocity distribution, the ratio can be calculated by which the initial pressure in the effusion cell is educed (Section 12.1.4).

n this sense, realizing the vacuum pressure scale is like stepping down a ladder. Each step refers to an expansioigher pressure to a lower one, and this lower one may serve again as a starting point for a further expansion, a

2.1.1iquid Manometers and Piston Gauges

he initial step of this ladder and the starting point for all vacuum primary standards are the instruments whichmeasure the pressure as force per unit area at a specified temperature. These are the liquid manometers (describection 6.2) and the piston gauges (described in Section 6.4).

igure 12.1 shows the principle of a gas-operated piston gauge (also called pressure balance). A cylindrical pisotates in a closely fitted circular cylinder. The pressure at the base of the piston is defined as the ratio of the toownward force on the piston to the effective area of the gauge when floating at its operation level.

As with many vacuum primary standards, a piston gauge is basically a pressure generator, not a vacuum meter.e even more specific, it generates a pressure difference between the piston's bottom and the volume above theistoncylinder assembly. If this volume is enclosed by a bell jar and evacuated to <0.1 Pa, the piston gauge cans an absolute pressure generator. Typical pressure ranges of piston gauges used for vacuum gauge calibrations kPa to 300 kPa.

he gap between piston and cylinder is typically a few tenths of a micron at a cross section of 10 cm2 of the pilear from this that manufacturing a





Fig. 12.1The principle of piston gauges. Theweight force acting on the base of a

rotating piston in a closely fitted cylinderdefines the pressure underneath.

istoncylinder assembly requires elaborated precision techniques and materials (often tungsten carbide and in rmes also ceramics).

he accuracy with which the pressure can be generated depends on the accuracy with which measurements of borce and effective area can be performed. If magnetic forces between piston and cylinder can be excluded andiction effects are considered [3], the effective area can be determined by dimensional measurements which ag

with values received from pressure comparisons with liquid manometers [37]. Comparisons with liquid manommore convenient and more precise in determining effective piston areas, because disturbing effects such as inclf the piston axis against the cylinder axis, unroundness of the parts, frictions effects, and so on, are calibrated ffective area. Also, possible dependencies of the effective area on gas species, operation height, and pressure e easily determined by comparisons with liquid manometers.

he force can be calculated from the product of the sum of all massesmi acting gravimetrically on the piston's bottnd the local acceleration constant g local due to gravity, reduced by the buoyancy of the masses in the surroundi

f there is vacuum in the bell jar surrounding the masses, the latter influence can be neglected, and the generateressure is calculated from

where A0 is the effective area of the piston, (α pist +αcyl) is the sum of the linear thermal expansion coefficients iston and cylinder,T 0 is the temperature at which A0 was determined, the actual temperature and pres the residualressure in the bell jar.







he uncertainties (approximately 95% confidence internal) of the pressure generated by a piston gauge are givressure-independent term and a pressure-dependent one with typical values of

he piston gauges are used to calibrate vacuum gauges from 2 kPa up to 100 kPa or for generating accurate iniressures for static expansion systems.

2.1.2tatic Expansion

he principle of the static expansion is as follows (Fig. 12.2): Gas contained in a small volume, whose pressure p1 wccurately measured (or generated with a piston gauge), is expanded into a large evacuated volumeV 2 by opening aalve in between. To apply the BoyleMariotte law [Eq. (12.3)] it must be assumed that the expansion is isother

meaning that both vessels and the intermediate tubing are at equal temperatures and the gas temperature does nhange during the expansion. Since these assumptions are usually not realized [9], we will apply the more geneaw pV/T = const. IfV 1 is at temperatureT 1 and V 2 at T 2, we receive the following for the pressure p2 in V 2 after

xpansion:



Fig. 12.2The principle of static expansion used for generating low pressures in the vacuum regime.Gas contained in a small, enclosed volumeV 1 is expanded into another enclosed volume

V 2 which is much larger Under isothermal conditions the pressure inV 1 isreduced byV 1/(V 1+V 2).





he ratioV 1/V 1 + V 2 is called theexpansion ratio and is a constant for each expansion system. Hence, to determi he expansion ratio has to be known, and the initial pressure p1 and the temperaturesT 1 and T 2 of the two vessels ho be measured. This method was first used by Knudsen in 1910 [10].

he initial pressure, which ranges typically from 1 kPa to 200 kPa, is measured either with a liquid manometeriston gauge, or a suitable secondary standard like a quartz Bourdon spiral manometer (QBS; see Section 6.5).ood idea to design the expansion ratio such that an expansion from the highest measurable pressure p1 gives a p2arger than the lowest pressure measurable with the gauge for initial pressure measurement. By this overlap it iso check if pressures generated by the expansion are consistent with the pressures directly measured with the inressure measurement device.

he gases which can be used for the static expansion method have to meet two requirements: Their virial coeffhould be small (no significant deviations from ideal gas law) and they should not be adsorbed on the walls of tacuum vessel. In practice, this limits the application of the static expansion method to the rare gases, N2 and C1114]. H2 can be used for p2 > 102 Pa, while oxygen or oxygen containing diatomic gases are hardly manageabatic expansion systems [14].

hree methods are applied to determine the expansion ratio: the gravimetric technique and the constant pressur

echnique, with which the absolute volumes are determined, and expansion techniques, with which the expansi determined.

. Gravimetric Technique . For volumes >0.1 liter, this is the most accurate method. Highly distilled water (4×) oquids like alcohol or mercury [15] is filled into the volume and its weight is measured. To remove all air from

water and air bubbles sticking to the wall, the volume has to be evacuated. With fiber optics it may be checkedubbles have been removed. When the water temperature including eventual temperature gradients in larger veccurately measured and buoyancy corrections are applied, volumes can be determined with relative uncertaintow 104 range.

. Constant Pressure Technique (Fig. 12.3). Volumes <0.11 are best measured with the constant pressure techniq16]. A known variable volume (for example, a precision piston driven into a vacuum cylinder) and a stable vaauge are connected to the small volume to be measured. After an expansion into the small evacuated volume t

measured, the variable volume is adjusted such that the gauge shows the same reading as before the expansionhe valve to the small volume has to be carefully (slowly) closed again in order to remove the effect of the movolume in the valve. The size of the change of the known variable volume is identical to the size of the volume

measured.

. Expansion Technique . In this technique the pressures before and after the expansion are used for the determinhe expansion ratio. This has the advantage that the measurement is carried outin situ . The point is that the pressuratio has to be measured with high accuracy. For this it is possible to use two calibrated gauges (or primary stanke liquid manometers) or to use a single uncalibrated gauge with a strictly linear pressure response.





Fig. 12.3The measurement of small volumes enclosed between two valves: A certain pressure is set in the volume of the cylinder and the differential gauge with the bypass valve open. After closing the bypass valve, a piston of known volume

is driven into the cylinder, until the pressure on the gauge shows the samereading both before and after expansion of the gas into the volume to be measured

( L1 L2) times the piston cross section area gives the unknown volume.

lliott and Clapham [17] used a piston gauge to generate the initial pressure and a calibrated QBS for the pressmeasurement of the expanded gas. The idea of their experiment was to repeat the expansion until a sufficiently

ressure is built up in the large vessel (no pumping between the expansions) which could accurately be measurQBS as secondary standard. When taking corrections due to temperature gradients between the vessels, temperrift, and departures from the ideal gas law into account, it is possible to determine expansion ratios of 1 : 100 welative (one standard) uncertainty of close to 1 × 103. The determination of even lower expansion ratios down000 with this method has been reported [18].

erman and Fremerey [19] used a single expansion where both the initial pressure p1 and the final pressure p2 wasmeasured with the same spinning rotor gauge. Since the pressure response of the spinning rotor gauge is not str

near above 102 Pa, they applied a linearization procedure; and by repeating the expansion over a range of initressures and for three gases, they were able to measure an expansion ratio of 1 : 250. This is about the upper l

which can be determined with sufficient accuracy with this expansion technique.

he disadvantage of the expansion techniques is that the volumes are not determined to their absolute values, wnconvenient when volumes have to be added







Fig. 12.4A multiple-stage static expansion standard in use at the National Physical Laboratory

(NPL), United Kingdom. (By courtesy of NPL, UK.)

o the system (for example, the volumes of gauges to be calibrated), and the expansion ratio must be corrected herefore the small volume is often determined with one of the first two methods, or the expansion ratio is deli

hanged by inserting an object with known volume into the system [19] to determine the absolute values.Although it is possible to determine expansion ratios up to the order of 1 : 10,000 with the gravimetric and con

ressure technique, in practice mostly expansion ratios up to 1 : 250 are realized, since the expansion techniqueasier to use than the absolute techniques. Therefore, it is necessary to use multiple expansions to generate lowressures. This can be accomplished by designing a system either with a series of small and large volumes, cal sta11, 20] (Fig. 12.4), or with repeated expansions with the large volume being evacuated after each expansion [2

with a combination of both. It is advisable that there be an overlap in the calibration pressures generated by a halued expansion ratio with a small initial pressure p1 and the ones generated by the next lower-valued expansion

with a high initial pressure p1 in order to check whether the determined expansion ratios are consistent with each

n one of the NPL primary standards [11, 20] a five-stage expansion system (Fig. 12.4) is used, while in one of TB static expansion standards [2224] only a two-stage system is used (Fig. 12.5), so that for lower pressures rxpansions have to be applied.

he lower limit of calibration pressures, which can be generated in a static expansion system, is determined byowest residual pressures in the chambers, the outgassing rate of the inner walls of the system, and adsorption e

which become significant below 104 Pa even for the gases mentioned above, as investigated





Fig. 12.5A static expansion system used at the Physikalisch-Technische

Bundesanstalt (PTB), Germany.Reprinted from [22], Copyright 1990, with kind permissionfrom Elsevier Science Ltd., Kithington, UK.

y Messer [14]. Typically, a lowest calibration pressure, 106 Pa, can be achieved in a well-baked-out stainless ystem with a specific outgassing rate of <1011 Pa · liter/s · cm2.

he uncertainties of the generated pressures in static expansion systems are mainly determined by the uncertainhe expansion ratios and by the uncertainties in the determination of the temperatures. The uncertainties of the TB are shown in Fig. 12.6.

No national or international written standards have so far been implemented for the realization of this sort of ex

echnique for vacuum primary standards.2.1.3ontinuous Expansion

n the continuous expansion method, also called "orifice flow method" or "dynamic method" [11,25,26], the caas is continuously expanded from a volume at high pressure through at least two conductances into the vacuun between the two conductances is the calibration chamber (Fig. 12.7). When there are no sinks or sources of etween the two conductances, the equation of continuity holds and the net flow through the two orifices must sothermal conditions):







Fig. 12.6Uncertainties of the generated pressures in the static

expansion system shown in Fig. 12.5. The main contributionsto the total uncertainty (2σ) are also shown: 1, uncertainty

of expansion ratio; 2, uncertainty of temperature due togradients; 3, uncertainty of gas temperature due to expansionitself; 4, uncertainty of initial pressure generated by a piston

gauge; 5, uncertainty of temperature measurement due todrift; 6, uncertainty of pressure due to outgassing.

Fig. 12.7The principle of continuous expansion for generating pressures in the

high and very high vacuum regime. The gas which is initially on pressure p1 is continously expanded through two conductances of

largely different size and pumped away. The calibration pressure p2 is given by p2= p1·C 1/C 2.



where ( p1 p2) is the pressure drop across conductanceC 1, and ( p2 p3) is the pressure drop acrossC 2. If p2 is muchmaller than p1, and p3 is much smaller than p2, we can approximate

where p2 is the calibration pressure. This is the basic equation of the continuous expansion method. Instead of tolumes as in the static expansion, two orifices of





Fig. 12.8One of the flowmeters used at the Physikalisch-Technische Bundesanstalt.

Flowmeters generate precisely known low flow rates for vacuum metrology.Reprinted from [31], Copyright 1993, with kind permission from Elsevier

Science Ltd., Kithington, UK.

argely different size are used to reduce the initial pressure p1. The typical range of values forC 1 is 106105 liter·s1,hat forC 2 is 10100 liter·s1.

he gas flow with the throughput

t a specified temperature is usually generated in a separate device, called a flowmeter , which is actually also a flowenerator. Herein, p1 (10 Pa to 100 kPa) is measured by a suitable secondary standard such as a QBS or a capaciaphragm gauge (CDG). The conductance is mostly determined by measuring the volumetric speed∆V /∆t to keep ponstant (constant-pressure flowmeter). A review of several types of flowmeters has been given by Peggs [27].

A few written standards exist for calibration systems based on this method [2830]. As an example of a flowmetcheme of the constant pressure flowmeter used at PTB [31] is shown in Fig. 12.8. The gas reservoir consists oections, the reference volume and the working volume, which are separated by valve V3 and the diaphragm oensitive CDG (A). The working volume is enclosed additionally by the valves V4 (constant conductanceC 1) and Vvariable conductanceC 1), and it includes a displacement bellows as a variable volume. The reference volume ealve V2.

n the beginning of the operation, both volumes are equally pressurized with V3 open. After closing V3, gas wut of the working volume through the open valve V4 (or V5) and a pressure difference across CDG (A) will dhis signal is used to drive the bellows such that the pressure remains constant inside the working volume. In p

he bellows can be driven continuously with constant speed or from time to time so that the pressure will slight±5×104) in a sawtooth-like manner. The measured volume speed of the calibrated bellows is identical to theonductanceC 1 of valve V4 (or V5) at this pressure.







Fig. 12.9One of the calibration systems based on the

continuous expansion method used at the NationalInstitute of Standards and Technology, USA. Thechamber above the orifice plate is the calibration

chamber, Reprinted from [40], Copyright 1988, withkind permission from AIP, Woodbury, New York.

A similar flowmeter used at NIST has been described in McCulloh et al. [32].

rom the flowmeter, the gas is injected into the calibration system. This consists of (1) the inlet system, (2) the

alibration chamber, (3) the pump orifice with conductanceC 2, and (4) the pumping system (Fig. 12.9).. Inlet System . The inlet system has to be designed such that any beam effect of the molecular flow through theom the flowmeter is transformed to a Maxwellian distribution inside the calibration system. This can be accomy building a separate chamber with a small orifice to the calibration chamber. A simpler solution is to form thubing such that the outcoming particle will hit a portion of the wall of the calibration chamber far away from trifice, or hit a baffle plate.

. Calibration Chamber . The Maxwellian distribution in the calibration chamber is disturbed by both the gas inlhe pump orifice. To minimize these disturbances, the following precautions have to be taken concerning (a) thnd the size of the chamber and (b) the position and orientation of the flanges.



• The ideal shape of the chamber is the sphere, but a more practical approach is the cylinder with equal lendiameter. These shapes minimize pressure gradients inside the vessel and also minimize the ratio of inner sto volume.





According to the German Industry Standard DIN 28416 [29], the surface of the largest inscribed sphere in chamber should be at least a factor of 1000 larger than the orifice area. This is to ensure that the pressure wchamber is homogeneous to within about 1×103. However, by means of Monte Carlo simulations of molescattering in the chamber, it is possible to estimate the particle density distribution in the chamber and to dcorrections for the pressure at the position of the flanges used for the gauges under calibration. If this is domeasurements of the density distribution inside the chamber are carried out [33, 34], orifice areas larger th1/1000 of the largest inscribed sphere may be used. The volume of the chamber should be much larger (a f50) than the sum of all volumes added by the gauges to be calibrated.

• The position and orientation of the flanges where the gauges to be calibrated are mounted on (called testhave to meet the following requirements:

No direct interaction between attached gauges should be possible.

Only a small fraction, if any, of incoming particles should be allowed to hit a test flange directly.

No direct path of molecules from the test gauge to the exit orifice should be possible.

. Pump Orifice . Since only the molecular flow of particles through orifices can be mathematically described wccuracy, the pump orifice and the input flow rate should be sized such that only pressures in the molecular regevelop in the calibration chamber. The conductanceC 2 of a circular pump orifice with open area A and a thin edgeiven by

where is the mean velocity of the gas particles. Particle scattering on the edge is considered by the correctio1, which is [35]

whered is the diameter of the circular orifice andt is its much smaller thickness (t <<d ). It is advantageous to instalrifice on the surface of the largest inscribed sphere of both the calibration vessel and the pump chamber to ens

molecular flow through the orifice in both directions. If this is not the case, a further correction has to be applieetermination ofC 2.

ntermolecular scattering is accounted for by the Knudsen correction factor K 2:

where a is a constant and the mean free path length of the molecules. The value ofa lies between 0.07 and 0.125ccording to older literature [26,36,37]; experimental data recently obtained at NIST, however, suggesta = 0.08 [38

. Pumping System . One of the assumptions in deducing Eq. (12.8) is that the pressure p3 downstream the pump orn the pumping system can be neglected





gainst the pressure p2 in the calibration chamber, or in practice should be p3<104 p2. This is true if a cryocondensump directly behind the orifice is used [34]. If turbomolecular pumps or diffusion pumps are being used, theonductanceC 2 has to be corrected to

nd p3/ p2 is in the range from 103 for heavier gases up to 0.2 for light gases. To measure this ratio [3942], whicometimes called thebackstreaming factor , it is necessary to have built another chamber behind the pump orificebout the same size as the calibration chamber in order to receive a more uniform pressure distribution in this phamber [43].

ince isothermal conditions rarely exist in practical systems, corrections for the temperature differences between the flowmeter and in the calibration chamber are necessary. DIN 28416 recommends to refer both temperatuommon temperature of 23°C and calculates different correction terms for gauges which respond directly to gand gauges which respond directly to pressure.

n continuous expansion systems a stationary equilibrium is established: Depending on the gas species, after a

quilibrium time the number of particles leaving the calibration chamber will balance the number entering it. Td- and desorption effects are only important until this equilibrium is reached, and more gases are applicable wmethod than with the static expansion. Even water vapor has been used with at least some success [44].

he lower limit of calibration pressure in continuous expansion systems is determined by the residual pressure alibration chamber and by the lowest flow rate which can be generated in the flowmeter with sufficient accuraypical value of the lower limit is 1×107 Pa. It can be further reduced if flow divider or multiple stages techniqused [45,46].

he upper limit of calibration pressure in the continuous expansion is determined by the transition from the moow to the viscous flow regime. In principle, this can be shifted to quite high values as recently demonstrated ay using small capillaries of a few-micron diameters of a channel plate structure for the realization ofC 2; the typicaalue for the upper limit, however, is 102 Pa.

he uncertainties which can be achieved in a primary standard of this type are illustrated in Fig. 12.10.

2.1.4Molecular Beam Expansion

or the last step of the pressure realization toward XHV, it is no longer possible to deduce the pressure directlyI units. Instead, an ionization gauge, calibrated with one of the two methods described above, is used for the

measurement of the initial pressure before expansion.

he method of attenuating the pressure is the following (Fig. 12.11): A stable, but adjustable, pressure of calibr established in an effusion cell measured with the calibrated ionization guage. Gas effused out of the circular

open area A1) of this cell is mostly pumped away by a cryo-panel. Only a small fraction of it is formed into a meam by another circular orifice ( A2), which is the entrance to the calibration chamber. The gauge head to be cal mounted in a position so that





Fig. 12.10Total uncertainty (2σ) of nitrogen pressures generated in one

of the continuous expansion systems in use at the Physikalisch-echnische Bundesanstalt. Also shown is the uncertainty of the

generated flow rate of the flowmeter, which dominates theuncertainty below about 105 Pa. The major contributions

above 105 Pa are uncertainties due to pressure inhomogeneitiesin the calibration vessel and due to temperature measurement.

Fig. 12.11Principle of molecular beam expansion. The pressure is reduced by forming a

molecular beam defined by the exit orifice of an effusion cell and the entrance orifice ofa calibration chamber. The remainder of the molecules effused is pumped by a cryo-panel.



is not hit by the molecular beam directly. Both orifices have to be small enough to ensure a homogeneous Maistribution inside both chambers.

n equilibrium, the same number of particles will enter and leave the calibration chamber per unit time:





he number of particles per unit time leaving the effusion cell orifice in solid angle∆Ω at angleθ normal to the oriflane is

wheren1 is the particle density and 1 the mean velocity in the effusion cell. Molecular beam systems are des= 0°. The solid angle of the entrance orifice of the calibration chamber is

where l is the distance between A1 and A2 and we obtain for the gas flow rate into the calibration chamber

while the flow out is

wheren2 is the particle density and the mean velocity in the calibration chamber. Equalizing these two equ

ccording to Eq. (12.14) and assuming results in

or typical valuesl = 100 mm and A1 = π·1 mm2, it isn1/n2 = 10,000 and so p1/ p2, since we have assumed equalemperatures in the effusion and calibration cell.

n practice, the ratio p1/ p2 is determined experimentally by using two calibrated ionization gauges. This is possiecause in the molecular regime the ratio is pressure independent, so that for the lower p2 a value > 107 Pa can behosen, for which the gauge can be calibrated. This experimental approach in determining the pressure attenua

he advantage that a number of idealizations in the theory, such as thin orifices, well-defined temperatures, andomogeneity, do not have to be realized in the apparatus.

ince practically the conductance of A2 has to be of the order of 1 liter·s1 (nitrogen), outgassing of the ionizationecomes a problem for the residual pressure in the calibration chamber. Typical outgassing rates of ionization gre in the range 109106 Pa·liter·s1. So even for ionization gauges with very low outgassing rates, the residual p limited to about 109 Pa nitrogen equivalent. This problem can be overcome if the calibration chamber is layetanium, which effectively pumps the outgassing gas species but does not pump the rare gases,





Fig. 12.12The calibration system based on molecular beam expansion used at the Physikalisch-

Technische Bundesanstalt. The effusion cell is called the Knudsen cell herein. (From [48].)

which are used as calibration gas. It has also been shown [47], however, that, when the residual signal is carefuetermined and subtracted from the signal at calibration, the gauge can be calibrated for partial pressures even han the residual pressure.

he calibration system designed by Grosse and Messer [48] is illustrated in Fig. 12.12. The recently estimated r

ncertainty (2σ) of the calibration pressure between 1010 Pa and 107 Pa is somewhat below 7% [24].2.2alibration by the Comparison Method

f the vacuum gauge to be calibrated is not exposed to a calculable pressure generated in a primary standard, bueading is compared to the pressure indicated by a so-called reference gauge (secondary standard; see next sectalled calibration by comparison .

n the viscous flow regime (> 100 Pa) the setup for the calibration by comparison is relatively simple, since disuch as residual pressure, outgassing, adsorption, desorption, temperature gradients, and so on, are usually of ngnificance. The







eference gauge and the device to be calibrated will be connected to the same vacuum pipe, evacuated by a simumping system (in many cases a roughing pump will do the job); and via a gas inlet system a constant pressurpplied to both gauges. Usually, it is sufficient to adjust a static equilibrium in the calibration system. The inneiameters of the connecting tubes just have to be large enough that no pressure gradients in the tubes with evenarge relaxation times will occur. If the calibration system has to be pumped continuously for a stationary equilare has to be taken that there are no pressure differences between the gauges. This can be accomplished by aymmetrical arrangement of the test gauge and the secondary standard to gas sinks and sources.

n the molecular and transition flow regime, where the pressure at specific points in the calibration system mayependent on the local temperature, a much greater effort has to be made. In the molecular flow regime (< 0.1 alibration pressure is usually established by a continuous, stationary flow. The DIN standard 28418 [49] and aSO [50] exist as guideline for the realization of this method. According to them, the calibration system must fuollowing requirements, which are very similar to the requirements for a continuous expansion primary standar

The volume of the calibration chamber should be large compared to the sum of all volumes added by the devalibrated. DIN 28418 requires a factor of 50.

To minimize the effects of outgassing and sorption, the ratio of inner surface to volume should be as small as deally, the shape of the calibration chamber would be a sphere. A reasonable choice is also a cylinder with eqund diameter. DIN 28418 requires that the ratio not exceed the one of a straight cylinder whose length is four tiiameter, which may be a length value too high.

The gas inlet system must be designed such that a significant fraction of the incoming gas particles will neithirectly any gauge nor hit the orifice of its tubing.

Similarly the pump system should be designed such that there is no direct path of molecules from the vacuumnto the pump system possible (or only with a very small probability).

The ports for the secondary standards and the test gauges should be arranged symmetrically to the pump outlenlet. Also, they should be arranged such that no direct interaction between each two gauges can occur. Interact

e thermal radiation, direct gas or charged particle flow from one gauge to the other, electromagnetic disturbano on.

The tubing to the gauges must be of a conductance that will not build up significant pressure gradients due toutgassing or pumping of the gauge.

DIN 28418 requires that the base pressure in the chamber not exceed 2% of the lowest calibration pressure. Tonsidering the expected outgassing from the walls (after a bake-out, if necessary) and vacuum gauges, the effeumping speed to the calibration chamber must be sized accordingly. Besides this, it is always a good idea to sny residual signal from the measured signal to minimize disturbances from that.





Fig. 12.13A commercially available calibration system (Balzers PSK 110)

based on the comparison method. This system also has theoption to apply the continuous expansion method according toEq. (12.7) with the use of the conductancesC 1 and C 2. TheCDG and the SRG on the left-hand side are used to measure

the pressure beforeC 1.(By courtesy of Balzers Instruments, 1996.)

n commercial calibration systems the calibration procedure is preferably automized. The pressure is steadily inn the system, and the reference and the test gauge readings are taken at several set points per decade. Since in ases the pressure is changing in time, it is important that, when taking the readings at the set points, the pressuonstant to approximately within ± 0.5% for 510 min to ensure that a stationary equilibrium is established in boessel and the gauge heads, and no errors occur due to a dynamic measurement.

he temperature of the calibration chamber should be measured on several points to get a reasonable estimate omean temperature, because temperature gradients, especially in stainless steel chambers, are always present.

A gas impurity of 0.1% at the inlet into the calibration chamber (impurities of the gas inlet system as well as thmpurities in the reservoir have to be considered) is acceptable.



A typical comparison calibration system as commercially available is shown in Fig. 12.13.

We should note at the end of the sections describing the systems for calibration that also other methods or signiariations of it existfor example, so-called





ressure-time dependence methods as reviewed by Kuz'min [51], which, however, are not used by the widely kNational Metrological Institutes and which usually can be considered of less accuracy than the described ones.

2.3alibration of Vacuum Gauges and Mass Spectrometers

n this section we will describe specific points to consider, when vacuum gauges which are suitable as secondaandards and mass spectrometers are calibrated. A secondary standard is defined as a standard whose value is y comparison with a primary standard. After calibration they are often used as reference standards in comparialibration systems.

he most accurate and stable gauges in the specific vacuum range are used as secondary standards. Nowadays he Quartz Bourdon spiral manometer (QBS) from 1 kPa up to 100 kPa, the capacitance diaphragm gauges (CDom 0.1 Pa up to 1 kPa (sometimes also up to 100 kPa), the spinning rotor gauges (SRGs) from about 103 Pa tnd below 103 Pa the ionization gauges (IGs).

n Chapter 5 the physical basis and technical details of these instruments have been described, and we will thereestrict ourselves to the points important for the calibration and stability of them.

he quartz Bourdon spiral manometer is quite straightforward to calibrate in the pressure range 1 kPa up to 100see previous section), so that we will start our notes with the CDGs.

2.3.1apacitance Diaphragm Gauges

A CDG sensor [52] is a two-sided cavity, separated by a nonporous diaphragm. The side which is exposed to thas is called thetest side , the other thereference side , of the CDG. The diaphragm forms the movable side of a vaapacitor. The change of capacitance will give an indication of the pressure exerted on the diaphragm. The cap measured by means of an oscillator whose frequency is converted to a voltage, amplified, and sometimes cor

or predictable system errors (linearization).

he zero stability and the accuracy of the instrument is improved when the diaphragm serves as electrode for twapacitors, which change their capacitance differently under pressure. Since the dielectric constant is dependenpecies and pressure, today's gauges operate in a ''bull's-eye" configuration; that is, both capacitors plates are lohe reference side of the CDG, one electrode being opposite to the center of the diaphragm, the other being ringnd concentric to it. This also has the advantage that corrosive or dirty gases do not deteriorate the sensing capnd the lifetime of the sensor head is increased.

wo configurations are commonly used (Fig. 12.14):

. Absolute-Type : The sensor is permanently vacuum-sealed on the reference side (usually with a getter materialnd the inlet port (test port) on the other side allows for absolute pressure measurement. The vacuum on the seaas to be smaller than the lowest detectable pressure, by a factor of 102 or less.





Fig. 12.14The two important types of capacitance diaphragm

gauges. In the absolute type the reference chamber is

evacuated and only absolute pressure can be measured;with the differential type, also differential pressurecan be measured.

. Differential-Type : The sensor has two inlet ports, a test port and a reference port, to allow for differential presmeasurements between the ports. If the pressure on the reference port (called line pressure) is low enough, typic

a, the test port may be used for absolute pressure measurement also.



ince the modulus of elasticity is temperature-dependent and also the geometry is changing with temperature (e noted here that CDGs sense diaphragm deflections as low as 0.5 nm), CDGs respond to temperature changeead. To minimize the effect on pressure indication, CDGs are available with temperature control units, which he sensor head temperature to typically 45°C to within 0.1°C or, for high-accuracy models, even to within 0.02onsequence, as soon as the pressure drops below the viscous flow regime at about 100 Pa, the





igher temperature (T 2) volume inside the head will be at higher pressure than the lower temperature (T 1) volume ohamber which is usually at room temperature. In the molecular flow regime the ratio p(T 2)/ p(T 1) will be a constan

n the transition range between viscous and molecular flow the ratio has to be calibrated, and it depends not onressure and on the geometry and the surface of the tubing but also on the gas species (See Section 1.10. on theanspiration).

n the other regimes the indication of a CDG is independent of the gas species if the dielectric constant of theapacitance is not changed, which occurs when the capacitance is measured on the reference side only. Severalave published equations to describe p(T 2)/ p(T 1) in the transition regime [5355]. The theory behind these equatioowever, is not complete and based on assumptions, so that experimentally determined parameters have to be uherefore, if CDGs are used as reference standards, they should be calibrated also in the transition regime inste

elying on equations with relatively uncertain parameters. Figure 12.15 shows a typical calibration curve of a 1ull-scale CDG for two gases. The molecular regime of helium is larger than that for nitrogen, because the meaath length of helium is larger at the same pressure and temperature.

A valuable guide on the calibration and use of CDGs has been published by a subcommittee of the "Recommenractices" committee of the American Vacuum Society [56]. According to these recommendations, before a CDalibrated, the following precautions should be honored (Table 12.2):

Fig. 12.15A typical calibration curve (carried out at the

Physikalisch-Technische Bundesanstalt, PTB) of a 133-Pafull-scale CDG (MKS-Baratron) at elevated temperature

for helium and nitrogen. Three regimes can bedistinguished: the molecular regime below 1 Pa, theviscous flow regime above 100 Pa, and the transition

regime in between.







Table 12.2. Points to Consider when Calibrating Capacitance Diaphragm Gauges (CDGs)CDG CalibrationsFor installation consider:VibrationsLocal air currentsOrientation of sensor headConnections to differential gauge headssolation valves for absolute-type CDG with full scale <100 kPa

Leak test

Before calibration consider:Warm-up period ~ 24 hZeroingPrecycling

During calibration consider:Pressures from low to highHysteresisZero checks

After calibration consider:Close isolation valve (if existent) before airingSwitch off heater one hour before airingDisconnect measurement port of differential-type CDG first

he CDG sensor head should be installed such that it is not subject to vibrations, and it should be protected froir currents. Since also the gravitational field is acting upon the diaphragm, the orientation of the sensor shouldame during calibration and use. It is advisable to use the test port for the connection to the calibration system,

most CDGs are linearized only in this direction and since the reference side should be kept as clean as possiblealibration system should be leak tested.

f temperature-controlled CDGs are being used, a warm-up period of 24 h is recommended. After this period thnstrument, including the signal conditioner, has to be zeroed. With single-sided CDGs, one has to apply a baseower than the smallest detectable pressure. The base pressure should be measured with an independent high- oltrahigh-vacuum gauge. For zeroing a differential CDG, the two ports should be "short-circuited" (Fig. 12.16)hat the zero indication is a function of line pressure, and for absolute pressure measurement the base pressure eference side should be applied also to the test side for this reason.

o minimize hysteresis effects, it is recommended that CDGs be precycled from zero to full scale and back befalibrations.

he calibration should proceed from the lowest to the highest pressure and then return, if any hysteresis effectsxpected. The calibration consists of applying pressure, waiting an appropriate time for thermal equilibrium to chieved, and recording the pressure indications of the standard and device under calibration as





Fig. 12.16The experimental setup for calibrating a differential CDG for absolute pressures. The isolation valve is closed and the bypass valve open forzeroing the instrument. Another gauge (not shown) should be used to

check the pressure, pR, on the reference side.lose to simultaneously as possible. When the CDG is calibrated for pressures below the viscous flow regime, aemperature of the gas in the primary or secondary standard has to be recorded. This is important, since when das temperaturesT 1 will exist when the calibrated gauge is used, corrections have to be applied [see Eq. (12.20)est accuracy, zero- and full-scale indications should be checked after each calibration point, if possible.

Although most commercial absolute-type CDGs are safe against atmospheric overpressure, one should be awaract that overpressurizing CDGs with full scales < 133 kPa may seriously change the calibration curve. Therefoecommended that an isolation valve is used to prevent the sensor from being exposed to pressures higher than cale.

he accuracy of a CDG calibration is mainly determined by the uncertainty of the generated or measured pressrimary standard. It can be as low as 0.01% at 100 kPa, but as high as 0.3% at 0.1 Pa ((2σ) uncertainties).he long-term stability of all types of vacuum gauges is within a certain range an individual value of each specauge. It is best estimated by frequently (at least no more than a year apart) recalibrating a gauge over a long pme to determine a standard deviation and/or drift of the calibration factors. For instruments with a long metroistory (and these instruments are quite rare and very precious) the future stability can then be predicted withinort of confidence interval (there will never be a "guarantee"!). Typical for all kinds of vacuum secondary standhis chapter are discontinuous shifts in calibration factors rather than a steady drift.

DG stabilities depend on their full scale, and the stability is much better in the viscous flow regime than in theypical values of long-term instabilities for good instruments over a one-year period in the viscous flow regime

heir full scale are: 0.1% for 100 kPa and 10 kPa full scale and 0.30.4% for 1 kPa and 100 Pa full scale [57, 58]

2.3.2pinning Rotor Gauges

pinning rotor gauges (SRGs) [5961] are the preferred secondary standards from 103 Pa to 1 Pa. They can be uecondary standards even down to 104 Pa, if the residual drag and the single scattering of the data is low.





n the SRG a steel (often stainless steel) sphere of 4.5 mm or 4.76 mm diameter is magnetically suspended in a ube, called athimble , and put into rotation of about 400 Hz. Due to gas friction the rotor will slow down and th

elative deceleration rate is proportional to the pressure in high vacuum.

he SRG can be used for pressure measurement > 1 Pa [62, 63], but it is less suitable as secondary standard coo CDGs in this pressure range.

he pressure in the high-vacuum regime measured by an SRG is calculated from [60, 61]

where the square root is the mean thermal velocity of the gas species with molecular massm and temperatureT ; d anre the diameter and density of the rotating sphere;σ is the dimensionless accommodation coefficient of tangentia

momentum of the gas particles on the rotor surface; is the deceleration rate of the rotor due to pressuRD (residual drag, also called offset) is the deacceleration (in s1) caused by induced eddy currents and possiblerifts. RD is measured at p≤ 106 Pa.

he accommodation coefficientσ is the parameter to be calibrated in an SRG. It is basically an effectiveccommodation coefficient, because not only the surface itself but also the surface roughness contributes to its or this reason,σ can be larger than 1.σ may vary from slightly below 1.0 to up to 1.27 for very rough rotor surf60]. It depends slightly on gas species, where the lightest gases hydrogen or helium give usually either the min

maximum value ofσ , depending on the rotor.

After calibrating,σ can be stored into the SRG control unit and the pressure indication will be correct accordingalibration.

he deceleration rate versus pressure characteristic is, according to our recent knowledge, linear for pressures <Above 0.1 Pa it becomes increasingly non-linear due to the nonisotropy of incident molecules which have beenp by collisions with molecules coming from the rotor. This can be considered by introducing a (slightly) pressependentσeff( p) or (as is done in the commercial control units) by a linearization procedure which includes gaiscosity.

rom zero up to 2 Pa,σeff is a strictly linear function of p, as was shown in Messer and Röhl [64] (Figure 12.17).herefore, two possibilities exist for determiningσ:

σ eff vs. p is determined for 0.1 Pa < p < 2 Pa and extrapolated to p = 0: σ = σeff( p = 0).

A pressure p significantly below 0.1 Pa is applied to the SRG and the reading pind of the SRG compared to the trressure p will giveσ = pind/ p.

n both cases,σ = 1 has to be entered into the control unit before calibration; in the first case also the viscosity vo be set to zero so that no linearization procedure is performed for the pressure indication. We note that for thend the density of the rotor, usually nominal values are entered into the controller, and also for this reason the calue ofσ will be only "effective."





Fig. 12.17The pressure dependence of the (effective) accommodation coefficient for a

special sphere. It is generally linear up to 2 Pa. From [64].

Table 12.3. Points to Consider when Calibrating Spinning Rotor Gauges (SRG)SRG CalibrationsConsider:VibrationsBaking (may change accommodation coefficient)Stable temperature around gauge headWarm-up period ~ 6 hOffset measurementFrequency-dependence of offsetTransport: Rotor fixed and save from corrosion

verything that changes the surface of the rotor may change its (effective) accomodation coefficientσ and mayherefore invalidate the calibration. The rotor surface may be subject to corrosion, so that keeping the rotor undacuum all the time is certainly a good idea. Mechanical friction may change the surface roughness so that the hould be fixed during transporation. Both requirements can be accomplished by a special transport device as dy Röhl and Jitschin [65]. Also, adsorbed molecules on the rotor surface may change the accommodation coeff

may be different by 2% for a rotor after baking compared to the same rotor before baking. Some rotors, howevhangeσ after baking [66].

During the calibration procedure of an SRG, the following should be considered (Table 12.3):







The gauge head must not be subject to significant vibrations.

Before calibration, the rotor should run for at least 6 h. This is because after start-up of the SRG, the temperatf the rotor caused by the eddy currents will give a systematic drift of the residual drag in the first hours.

Since temperature drifts will falsify the RD measurement, temperature drifts of the thimble (and rotor) shouldvoided.

The residual drag may be frequency-dependent due to frequency-dependent changes in the axis of rotation anhe frequency-dependence of the eddy currents [67]. The size of this frequency-dependence (020% for |∆ f| = 10 Hz)ifferent from rotor to rotor, and also it is dependent on the orientation of the rotor in the magnetic field. The frependence of the residual drag should be carefully determined when high accuracy of the calibration is requirgnals close to the offset value are taken.

It is recommended that the residual drag be measured over a longer period of time (12 h) before calibration toetermine its value with a small uncertainty due to random effects. If the temperature of the thimble does not chgnificantly and the rotor is continuously kept in the same orientation in the same magnetic field, the offset va

will be stable [68]. If, however, the temperature is not stable, the offset is better measured immediately before ahe calibration.

he relative uncertainty of a primary SRG calibration is typically 0.30.5%, which includes the uncertainty due act thatσ also depends slightly on the orientation of the rotor in the magnetic field, typically by 0.00.2%.

he long-term instability over a one-year period of theσ of a well-handled SRG is typically 0.30.5% [69], but cane much better. Shifts of 1%, however, after a one-year period have been observed, and this value should be usrst-time calibrated rotor.

2.3.3onization Gauges

Although, in general, ionization gauges (IGs) have only a modest stability, they have to be used as secondary selow 103 Pa, since for now there is no alternative in this pressure range.

he most common type of ionization gauges nowadays is the BayardAlpert gauge [70], where a hot cathode ouylindrical anode grid provides the electrons for ionization and the thin ion collector wire is centered in the cylinode. They are mainly available as nontubulated systems ("nude"-type) or as systems within a glass enclosure

German Calibration Service (DKD), some nude ionization gauges have been successfully used as reference stan

xtractor gauges, which have the ion collector outside the anode grid to reduce the x-ray limit due to high-enerhotons generated at the anode, may also be used as secondary standards.

old-cathode gauges, on the other hand, have been found less suitable as secondary standards [71, 72].

ommon to all types of ionization gauges is the measurement of an ion current, which ideally should be linearlroportional to the molecule density in the gauge.





Table 12.4. Points to Consider when Calibrating Ionization Gaugesonization Gauge Calibrations

Consider:Tubulation of nude gaugesOrientation of gauge headWarm-up period ~ 12 hConditioning procedure of gauge headsCathode heating and electron emission regulationResidual current measurementPressures from low to high

herefore, in a calibration of an IG, the sensitivityS (also called the vacuum gauge constant) is determined:

where p0 is the pressure due to residual gases in the calibration chamber, p is the pressure due to the residual gaseshe calibration pressure pcal generated by the standard, Ic is the collector current at pressure p, Ic0 is the residualollector current at residual pressure p0, and Ie is the emission current measured on the anode.

ince physically in an ionization gauge the gas density is being measured, while the sensitivity is determined bressure, it is always necessary to state the temperature at which the calibration was performed. For clarity,S shouldlways be corrected for and stated for a temperature ofT 0 = 23°C. IfS was determined for a temperatureT 1, it isxpressed as

When ionization gauges are being calibrated as secondary standards, the following should be considered (Table

The potential distribution inside the gauge head depends on its surrounding. If a nude gauge is calibrated, it isherefore advisable to calibrate the gauge in the same configuration as in use or to surround the gauge head at iength with a tube which will not be removed. Recently, Bayard-Alpert gauges completely immersed in a stainlube have become commercially available.

The orientation of the gauge head should be identical during calibration and use, since geometrical deformatio different orientations may affect the potential distribution and the electron trajectories in the gauge head.

Due to the hot cathode, the temperature of the gauge head (T ga) is higher than the temperature of the vessel (T ch), herefore gas pressure and particle density will be different in the gauge head and the vessel (see Section 1.10 o





hermal transpiration). This difference is dependent on the special geometry, the flow conditions, temperature gccommodation coefficients, and so on, and cannot be calculated. At most the pressures will differ by the facto

assuming molecular flow and complete accommodation of the gas particles to eitherT ga or T ch. If theifference is smaller, it will be proportional to the square root factor with a proportionality constant < 1. Hencehe calibration as valuable as possible, the ratioT ga/T ch should be as close as possible during calibration and furtse. This can be accomplished when the ionization gauge is always enclosed in the same tube, so that the heatonductivity to the immediate environment will be the same, and when the vessel temperatures are very similaralibration and use. Additionally, the emission current (heating power) should not be changed significantly fromalibration to use.

Since effects like the secondary electron and photon production in IGs depend on the surface state, the surface as clean as possible to obtain reproducible results from these effects [73, 74]. Therefore the calibration systencluding the IG should be baked out to obtain a residual pressure of at least a factor of 10 lower than the lowesalibration pressure. The cathode should be cleaned by applying a higher temperature than during operation, annode should be cleaned by electron bombardment. Both procedures are usually done in the "degas" mode ofommercial control units. Longer degas operating periods than stated in the manual for the specific gauge, how

must be avoided, since excessive heating will irreversibly damage the electrodes. The ion collector, whose surf

ritical due to the secondary electron production on it, can be cleaned by ion bombardmentthat is, operating theonization gauge at a high pressure (102 Pa or more, if possible) for about 1 h [75, 76]. After these conditioningrocedures, the gauge has to be operated in normal mode (regular emission current) for 12 h before calibration

Whenever an ionization gauge is being calibrated, it should be operated either with its control unit or at least ame cathode heating power supply and electron emission regulations. It has been found that different cathode hough stated with the same nominal data, may result in different sensitivities, possibly because the electron emistribution on the cathode is changed.

Instabilities in determined sensitivities of IGs may be due to either changes in the gauge head or changes in thontroller. To distinguish between the two, the controller has to be calibrated separately (emission and ion curre

meters, voltages).

Although in principle it should be possible to calibrate a gauge for one gas and use this calibration for another ghe ionization probability ratio for the two gases as scaling factor [77], investigations have shown [78, 79] that ot the case if high accuracy (uncertainty < 10%) is required. Even for isotopes of the same gas speciesfor examydrogen and deuteriumsignificant differences in sensitivities can be found [80].

f the sensitivity is determined according to Eq. (12.22), the residual current in the IGcaused by outgassing, elehoton-stimulated desorption, or x-ray-induced photoelectronsis subtracted from the signal. A user should be a





his, because, when the gauge is in use, its residual current reading (or the equivalent pressure reading) has to bubtracted from the signal as well.

or high accuracy, IGs should be calibrated with three points per decade over their operating range, because inases the sensitivity is at least slightly pressure-dependent (with about a few percent over several decades), eve03 Pa [81].

he relative (2σ) uncertainty of sensitivity determination, which can be reached at the time of calibration of an ncreases with decreasing pressure and has typical values of 0.51% at 102 Pa, 23% at 106 Pa, and up to 40% at

he long-term instability of any IG as for other gauges is a very individual feature [82]. For an IG that is of hignd is carefully treated, a value of 36% over a one-year period may serve as reasonable estimate for its instabilhis period [83].

2.3.4Mass Spectrometers

Mass spectrometers are used extensively for the qualitative and quantitative analysis of gas mixtures in manypplications in industry and research. As an example, in the microelectronic industry the purity of gases has beontinuously improved for the higher integrity of the devices, and a check of impurities in the process gases haone on a routine basis.

oday most of the mass spectrometers for general purposes are of the quadrupole-type, dominating with about he market; the magnetic sector type has a significant fraction of the remaining 5% [84]. Therefore, in the follo

will mainly refer to quadrupole mass spectrometers (the calibration methods, however, are independent of thepectrometer type).

Quantitative interpretation of the mass spectrum can be obtained if the mass spectrometer has been calibrated bseful factor to define for calibration purposes is a sensitivity for each gas component x measured:

x) is the ion current at partial pressure p( x) when the instrument is tuned to the molecular peak of component x, andx) is the corresponding value at some reference pressure p0( x). A number of investigations, however, have shown

mass spectrometers cannot be calibrated absolutely in a manner, which would allow quantitative interpretation ossible mass spectrum [8588]. For example, if the sensitivity for a gas component x was determined by a calibrati

which x was the only component in the system, this sensitivity for x may be very different if another gas componewith a much higher partial pressure (sometimes called ''matrix gas") is present. This is because at higher pressupace charge in the ion source can alter ion extraction efficiencies and ion-molecule collisions can alter ion speatios by charge transfer [85]. In this case, for calibration the specific gas mixture very similar to the one when pectrometer is in use has to be applied. For calibrations of relatively low total pressures (< 104 Pa), however, isually sufficient to calibrate for each gas species separately.





Table 12.5. Some Specific Points to Consider when Calibrating Quadrupole Mass SpectrometersQuadrupole Mass Spectrometer CalibrationsBefore calibration consider:Cleanliness of gauge head and calibration systemUniform bake-out (no localized sources of outgassing)Background partial pressure < 10 times calibration partial pressureGroundingWarm-up of instrumentation (6 h)Regular peak shape of mass peaksStable ion currents (repeatibility of mass peaks)Tuning adjustments (set resolution, scan speed, etc.)

During calibration consider:Protocol of all settingsBackground scannstability of background signal

Outgassing of mass spectrometerFragmentationLinearityDependence of sensitivity on presence of other gas species

he settings of voltages and resolution have a significant influence on the sensitivity and must be clearly stated at the alibration so that they can be reset when using the calibration data.

dditionally the stability has been found to be very poor in an investigation of a group of mass spectrometers, where tensitivity for a single-component gas varied up to a factor of two over a 220-day period [85]. The use of electron mularticularly critical for the stability of mass spectrometers due to aging, especially of new multipliers units, and sensithanges after bake-outs [89]. For these reasons, the use of quadrupole mass spectrometers as reference standards is pr

nother problem is that the outgassing of mass spectrometers is quite high and many components measured in a residpectrum are being produced by the mass spectrometer itself. It was shown by several authors [9092] that the productiome gases such as methane, water vapor, carbon monoxide, and carbon dioxide is enhanced when hydrogen is introde mass spectrometer.

subcommittee of the "Recommended Practices" committee of the American Vacuum Society has published recommor the calibration of mass spectrometers for partial pressure analysis [93], which we will partly refer to in the followinso Table 12.5).

he most accurate calibration method of partial pressure analyzers is the use of two or more flowmeters in a continuourimary standard (Section 12.1.3). Each flowmeter injects a well-known gas flow of different species into the calibratihamber at which the mass spectrometer is installed. Each partial pressure is then given by Equation (12.8), when eacevaluated for the specific gas component. Due to the use of a primary standard and at least two





owmeters, this calibration method is probably restricted to the National Metrological Laboratories.

Useful calibrations can also be obtained using ionization gauges as reference standards, since ionization gaugesmuch more linear, stable, and predictable than partial pressure analyzers [85]. It is even possible to calibrate a mpectrometer with an IG for gas mixtures with components in moderate ratios from about 1:1 to 1:10 if each coan be separately injected in the gas chamber, since for p < 103 Pa IGs react quite linearly on the addition of anotomponent. Only the specific sensitivity value of each gas species of the IG has to be considered in the calculaartial pressure. For the calibration of mass spectrometers with ionization gauges it is necessary to obey the rulated for general comparison calibration systems (Section 12.2).

n principle, it is also possible to calibrate a mass spectrometer with a spinning rotor gauge. The useful overlap 04 Pa up to 102 Pa, however, is generally too small to obtain useful results due to the often observed nonlineapace charge effects of quadrupole mass spectrometers in this range, so that it is not possible to extrapolate senower pressures.

Another possibility of calibrating mass spectrometers is the use of reference leaks [94] or calibrated capillaries When the flow rate through these devices and the effective pumping speed in the chamber is known, the partialan be calculated [96]. This calibration method is particularly useful when a small trace gas pressure in a large

as pressure (this pressure can be measured by an IG) has to be established for calibration, but also if gas sampifferent species are mixed in the reservoir for the capillary by the use of CDGs at relatively high pressures.

f no calibrated leak is available, it is also possible to measure the ratio of the upstream and downstream pressueak or small conductancein situ by a secondary standard. The principal experimental setup for this kind of calib shown in Fig. 12.18. CDGs, SRGs, or IGs can be used as secondary standards, dependent on the upstream pr

which have to be established for the desired calibration pressure.

Fig. 12.18The principal experimental setup for calibrating massspectrometers according to a pressure divider method.The ratio of up- and downstream pressure of the small

conductance can be measured with the secondarystandard. It is possible to expand this setup also for

generating gas mixtures in the main chamber (see text).





he small conductance can also consist of a leak valve; however, the stability of the leak has to be verified. If tressure ratio shall be independent of gas species and pressure, it must be ensured that the flow through the con in the molecular regime, since the flow through the pump orifice of much larger conductance will automatica

he molecular regime. As in all calibration systems, the size of the pump orifice must ensure a homogeneous pristribution in the chamber.

is possible to expand the setup of Fig. 12.18 for generating gas mixtures in the main chamber by adding a sepnlet system for each gas symmetrically to the axis of the main chamber.

he accuracy of the calibration of a quadrupole mass spectrometer depends strongly on the instrument itself. Dheir poor stability a very accurate calibrationfor example, on a primary standard with two flowmetersis very ofot worth the effort. Uncertainties which include the instrument and instability effects smaller than 10% shouldxpected when the mass spectrometer is removed from the calibration system. Only when mass spectrometers aalibrated in regular and frequent mannerin situ is an improved accuracy possible.

2.4alibration of Test Leaks

he calibration of test leaks with secondary methods is treated in Chapter 6 of this book, while in this section wescribe the calibration of test leaks with primary methods, which was also covered by recommendations of aubcommittee of the AVS "Recommended Practices" committee (see page 678) [97].

est leaks provide a stable gas flow, usually of helium, since leak detectors are calibrated with helium. Commore permeation leaks (also called diffusion leaks) and capillary leaks. The latter can be used for all gases, whichlog or etch the capillary, while the permeation type is only applicable to a few gases, mainly helium and hydro

or users of test leaks the most convenient unit for the leak rate is Pa·liter·s1 or similar units. We have to note, hhat this unit will not give the complete physical information if two temperatures are not stated at the same timere the temperature of the permeation material or the capillary and the temperature at which the gas pressure or

was measured. To avoid confusion, it is recommended that the unit moles per second (mol·s1) is used for test le9].

Differentiation of the ideal gas law with respect to timet at constant temperature yields an expression that is usefuvaluating molar leakage ratesqv:

where ν is the number of moles andT is the temperature of the gas at which pressure p was measured, and R is theniversal gas constant.

wo main primary calibration methods can be deduced from this equation:. The pressure is held constant so that the second term is zero.

. The volume is held constant so that the first term vanishes.





Fig. 12.19The principal experimental setup for primary calibrations of test

leaks. On the mass spectrometer the signal from the test leak iscompared to a similar flow rate generated and measured by theflowmeter, which can be "switched on" and "off."

ince both methods are also used for generating and measuring gas flows in a flowmeter (Section 12.1.3), it isbviously convenient to use a flowmeter, if available, to calibrate leaks by comparison with a known gas flow fowmeter. A typical experimental setup is shown in Fig. 12.19. The signal to be compared is the helium partia

eading on a mass spectrometer, which has to be installed such that identical gas flows from the flowmeter or theak will give identical signals; that is, the mass spectrometer should be symmetrical to the flowmeter, and the tnd/or the tubing to the both gas sources should not be too short. The flow rate from the flowmeter is adjusted he one from the test leak. In practice, two points of the flow rate from the flowmeter may be adjusted slightly hhan, one close to, and two points slightly lower than the leak rate, and the zero crossing of the five differenceseak rate is taken.

eak rates are often below the lower limit of flow rate of a constant pressure flowmeter of about 1011 mol·s1 (a·liter·s1 at 23°C). In these cases the flowmeter is either operated in the constant conductance mode down to 1

mol·s1 [31] or flow-division techniques are used to further reduce the flow rate [40].

f no flowmeter is available, a direct realization of either method (1) or (2) is necessary.

. In the constant pressure method the gas from the leak is allowed to flow into a volumeV 1 in which the pressure imeasured by a secondary standard. After a while, at pressure p1 ( p1 has to be negligible compared to the upstream

ressure of the leak) a second known evacuated volumeV 2 is added by opening a valve, similar to a stxpansion, and the time∆t is taken for the pressure to recover to the same value p1 before the expansion (Fig. 12.2he flow rateqv is given by





Fig. 12.20Test leak calibration by the constant pressure method:The gas from the test leak is expanded into volumeV 2,

and the time is measured until the pressure hasrecovered to its original value.

Fig. 12.21Variation of test leak calibration by the constant pressure

method: The volume displacer is moved such that thesignal on the mass spectrometer remains constant. Thevolume speed and the measured partial pressure will

determine the leak rate.

whereT is the average temperature in the volumesV 1 and V 2 at the time of the second measurement of p1. In case ony significant temperature drift, p1 has to be corrected.



nstead of using a fixed volumeV 2, a calibrated variable volume like a pistoncylinder assembly, conveniently drstepping motor, may also be used [100] (Fig. 12.21). Table 12.6 lists the main possible errors which may be muring a calibration of test leaks which should be accounted for.

f a permeation leak was closed with a valve for a long time, higher partial pressures will build up on the low prde of the leak and change the concentration gradient in the permeation element. After opening the valve, one ware of





able 12.6. Possible Effects Which May Falsify Leak Rate Calibrationseak Calibrationsossible problems of vacuum system:eak of vacuum systemutgassing of inner surfacedsorption of leaking gas speciesesorption from inner surface

nstability of background pressureemperature gradients and drifts

roblems of vacuum gauge (secondary standard):umping effectutgassing

nstability of background signal

roblems of leak:eak rate in stationary equilibrium?

e time to reach equilibrium with the new boundary conditions. Capillary leaks on the other hand have quite fast equilibrium times.

The same precautions of Table 12.6 must be honored if the pressure rise with time is measured in a constant and known volume whicnot too small (at least 50 cm3 [101]). It is advisable that all calibrations of leaks should start and also end with a "blind" experiment;

e measurement is repeated with the leak valved off. When small, well degassed volumes with the pressure measured by the non-gas-nsuming spinning rotor gauge are used, molar flow rates as low as 1018 mol·s1 can be measured. The uncertainties of the measured lth the above methods are rising with decreasing leak rates. The uncertainties vary typically from 0.5% to 1% at 106 mol·s1 to 8% at ol·s1 [102].

nce the permeation and the conductance of a capillary are temperature-dependent, the test leaks have to be temperature-conditioned tothin ±0.1°. A typical permeation leak changes its leak rate near 23°C by 3%/°C, so that an uncertainty of 0.3% can be expected for ±

5easurement of Pumping Speeds

he pumping speed of a pump is defined as the volume of gas removed by the pump per unit of time, for which reason the pumping speso called volumetric speed. Although the pumping speed usually depends on the inlet pressure of the pump, the above definition is cocause this pressure-dependence is rather small (< 30% over several decades) for many pumps in their regular operating range. Slidingtary pumps, for example, have a well-defined displacement volume, in which the sucked in gas is compressed and then exhausted atmospheric pressure.





he displacement volume times the rotor frequency will give the maximum pumping speed in this case.

he volumetric speed of a pump can be determined by measuring gas flowqpV injected through the inlet port of the pumpe pressure p in front of it at a certain temperature:

here p0 is the pressure forqpV = 0. For the application of Eq. (12.27) p should be significantly greater (about a factor ofan p0.

While the quantityqpV can be reliably measured, the measurement of p is rather difficult. Due to the pump there is a stronressure gradient in front of the inlet port, and the movement of the gas particles is far from being isotropic or Maxweeal physical concept has to use a chamber of infinite volume and surface area, where the pump inlet port has a negli

ffect on the Maxwellian distribution inside [103, 104]. Since inlet ports are of significant size and practical vessels capproximate the ideal chamber according to the above concept, written standards have been made which state how thexperimental system (called test dome) has to be designed and at which position and orientation relative to the inlet poressure p has to be measured. The original idea of the first standards was to find a position for the measurement of p in theome, so that p would have a very similar value as in an infinitely sized test dome [103105]. On the other hand, the teshould be similar to a practical vacuum chamber, so that the measured pumping speed is actually a useful value for a u

designing a vacuum system.

able 12.7 shows existing standards for the calibration of pumps. The American Vacuum Society (AVS) replaced theiro-called "standards" 4.1, 4.2, and 4.8 and also 5.1, 5.2 and 5.3 by new recommended procedures published in 1987 [1

Table 12.7. The Existing Written Standards for the Measurement of Pumping Speed and Acceptance Specificationsor Several Pump Typesa

Written Standard Type of Vacuum PumpDIN 28426, Part I,PNEUROP, ISO 1607/1,2 Rotary plunger, sliding vane rotary

rotary piston

DIN 28426, Part II,PNEUROP, ISO 1607/1,2 Roots

DIN 28427PNEUROP, ISO 1608/1,2 Diffusion, vapor jet

DIN 28428, PNEUROPTurbomolecular

DIN 28429, PNEUROP Getter ion

PNEUROP PN5 ASRCC/5Cryo-refrigerator

For addresses for ordering these standards see end of References.





nd 1989 [107] in order to have agreement with the ISO, DIN, and PNEUROP standards. The location of the gmeasuring p was moved away from the pump inlet from one-quarter to one-half of the pump inlet diameter, resu

reduction of 1015% of the measured pumping speed compared to the old AVS "standard."

n all written standards or recommendations of Table 12.7 the internal diameter of the test dome (Figs. 12.22 anmust be the same as the pump inlet diameter. The AVS procedure requires this down to 50-mm internal diametewhereas the other standards require it down to 100 mm, but with a well-described adapter from the test dome to

ump if the pump diameter is < 100 mm. The top of the test dome should be rounded, conical, or inclined. Thiswas chosen to ensure that any oil, when condensing on this surface, will run down the sides of the domes ratherop down onto the pump stack and cause erratic pressure bursts. In today's completely oil-free pumps (e.g., ior magnetically levitated turbomolecular pumps) or nearly oil-free pumps, this is of no importance and the top hosen to be flat.

Depending on pressure p, two methods are defined by the standards to measure the flow rateqpV . In the molecularegime (AVS recommendation) or p < 104 Pa (DIN/ISO/PNEUROP) the orifice flow method with the twin dome2.23) should be used where the pressure drop across a suitable designed orifice is measured. At higher pressurngle-dome configuration (Fig. 12.22) is used withqpV being measured by some type of flowmeter (for details se

pecific standards). Also a flowmeter as described in Section 12.1.3 may be used. Unfortunately, it has been



Fig. 12.22Design of a single test dome for pumping speed measurementaccording to DIN/ISO/PNEUROP standards (see Table 12.7).

The diameter of the inlet flange of the pump must be D . Pressureis measured at flange 2. A known gas-flow rate is injected intothe dome. Reprinted from PNEUROP, 1972, Vacuum Pump

Acceptance Specifications Part II, p. 8, with permissionof VDMA, Frankfurt, Germany.





Fig. 12.23Design of a double test dome for pumping speed measurementaccording to DIN/ISO/PNEUROPstandards (see Table 12.7). The

diameter of the inlet flange of the pump must be D . The gas-flow rate

is measured by the pressuredifference p1 p2 across theorifice between the domes.

Reprinted from PNEUROP, 1976,Vacuum Pump Acceptance

Specifications Part IV, p. 11, with permission of VDMA, Frankfurt,

Germany.

ound that the orifice flow method and the flowmeter method do not agree within their uncertainties for an overessure range [108], which is not too surprising because the molecular flow conditions are different in the singwin-dome configurations. With a flowmeter of wide range down to about 105 Pa·liter·s1 as available in the Naaboratories, it is possible to calibrate high- and ultrahigh-vacuum pumps over their entire operating range withsing the orifice flow method. This is of great convenience, since only one experimental setup and the simpler ome configuration can be used. To avoid the described ambiguities between the two methods, it may be advanne day to recommend only the flowmeter method in the written standards.



Although other methods for measuring pumping speeds exist, we mention the conductance modulation method10], it is recommended that only the written standards be used, even if drawbacks exist with them, in order to omparable results of pumping speed.

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SO standards are available from :

SO Central Secretariat, 1 Rue de Varembé, CH-1211 Genf 20; or from the National member of ISO respectivelublisher of National Standards.

IN standards are available from :

euth Verlag GmbH, D-10772 Berlin

NEUROP are available from :

ritish Compressed Air Society, PNEUROP General Secretariat 8, Leicester Street, GB-London WC 2H 7BN





Appendix

Graphic Symbols for Vacuum Components DIN 28 401

Vacuum Pumps

Vacuum pump, general

Positive displacement pump

Positive displacement pump, oscillating

Piston vacuum pump

Diaphragm vacuum pump

Rotary positive displacement pump



Rotary positive vacuum pump

Sliding vane rotary vacuum pump

Rotary piston vacuum pump





Liquid ring vacuum pump

Roots vacuum pump

Turbine vacuum pump, general

Radial flow pump

Axial flow pump

Gas ring vacuum pump

Turbomolecular pump

Ejector vacuum pump

Diffusion pump



Adsorption pump

Getter pump

Sublimation (evaporation) pump





Sputter ion pump

CryopumpVacuum Pump Accessories

Condensate trap, general

Condensate trap with heat exchange (e.g., cooled)

Gas filter, general

Filtering apparatus, general

Baffle, general

Cooled baffle



Cold trap, general

Cold trap with coolant reservoir

Sorption trap





Vacuum chambers

Vacuum chamber

Vacuum bell jar Isolation devices

Shut-off device, general

Isolating valve

Right angle valve

Stop cock

Three-way stop cock

Right-angle stop cock

Gate valve



Butterfly valve

Nonreturn valve

Safety shut-off device





Valve Modes of Operation

Manual operation

Variable leak valve

Electromagnetic operation

Hydraulic or pneumatic operation

Electric motor operation

Weight-operated

Connection and Tubes

Flange connection, general

Bolted flange connection



Small flange connection

Clamped flange connection

Threaded tube connection





Ball-and-socket joint

Spigot-and-socket joint

Connection by taper ground joint

Change in the cross section of a duet

Intersection of two ducts with connection

Crossover of two ducts without connection

Branch-off point

Collection of ducts

Flexible connection (e.g., bellows, flexible tubing)

Linear motion leadthrough, flange-mounted



Linear motion leadthrough, without flange

Leadthrough for transmission of rotary and linear motion

Rotary transmission leadthrough

Electric current leadthrough





Vacuum Gauges

General symbol for vacuum

Vacuum measurement, gauge head

Vacuum gauge, gauge control unit

Vacuum gauge, control unit recording

Vacuum gauge control unit with dial indicator

Vacuum gauge control unit with digital indicator

Measurement of throughput





able of Conversion Factorsn for Pressure Unitsa

xµbar Pa

(N/m2)mbar Torr atm lbs/in2

bar 1 0.1 0.001 7.50 × 104 9.87 × 107 1.45 × 105

a (N/m2) 10 1 0.01 7.50 × 103 9.87 × 106 1.45 × 104

mbar 1000 100 1 0.750 9.87 × 104 0.01450

orr 1333.22 133.322 1.33322 1

1.316 × 1030.01934

m1,013,250 101,325

1,013.25 7601 14.696

s/in.268,947.6 6,894.76 68.9476 51.715 0.0680 1

Pressure in x units =n × pressure in y units.





Vapor pressure curves of common gases. (To convert Torr to Pa, multiply by 133.)Reprinted from R. E. Honig, RCA Review 13, 567 (1962).





Pa

Vapor pressure curves of common gases. (To convert Torr to Pa, multiply by 133.)Reprinted from R. E. Honig, RCA Review 13, 567 (1962).





Vapor pressure curves of solid and liquid elements. (To convert Torr to Pa, multiply by 133.)Reprinted from R. E. Honig, RCA Review13, 567 (1962).





Vapor pressure curves of solid and liquid elements. (To convert Torr to Pa, multiply by 133.)Reprinted from R. E. Honig, RCA Review 13, 567 (1962).





Pag

Vapor pressure curves of solid and liquid elements. (To convert Torr to Pa, multiply by 133.)Reprinted from R. E. Honig, RCA Review 13, 567 (1962).





General Reference Books on Vacuum Science and Technology

A. Berman,Total Pressure Measurements in Vacuum Technology . Academic Press, Orlando, FL, 1985.

R. L. Boxman, D. M. Sanders, and P. J. Martin, Handbook of Vacuum Arc Science and Technology . Noyes Publicat

ark Ridge, NJ, 1995.A. Chambers, R. K. Fitch, and B. S. Halliday, Basic Vacuum Technology . Adam Hilger, Bristol and New York, 19

H. DeBoer,The Dynamical Character of Adsorption . Oxford University Press (Clarendon), Oxford, 1953.

. Dushman and J. M. Lafferty,Scientific Foundations of Vacuum Technique . Wiley, New York, 1962.

D. Fast, Interactions of Metals and Gases . Vols.1 and 2. Macmillan, London, 1971.

. J. Gregg,The Surface Chemistry of Solids . Chapman & Hall, London, 1965.

A. Guthrie,Vacuum Technology . Wiley, New York, 1963.M. Hablanian, High-Vacuum Technology . Dekker, New York, 1990.

N. Harris, Modern Vacuum Practice . McGraw-Hill, 1989.

D. M. Hoffman, B. Singh, and J. Thomas, Handbook of Vacuum Technology . Academic Press, San Diego, CA, 199

H. Leck,Total and Partial Pressure Measurement in Vacuum Systems . Blackie, Glasgow and London.

R. I. Masel, Principles of Adsorption and Reactions on Solid Surfaces . Wiley, New York, 1996.

F. O'Hanlon, A User's Guide to Vacuum Technology , 2nd ed., Wiley, New York, 1989.

V. Ponec, Z. Knor, and S. Cerny, Adsorption on Solids . Butterworth, London, 1974.

W. Pupp, Vakuumtechnik, Grundlagen und Anwendungen . Thieme, Munich, 1972.

A. Redhead, J. P. Hobson, and E. V. Kornelson,The Physical Basis of Ultrahigh Vacuum . Chapman & Hall, Lon968. (and AVS reprint 1993).

R. W. Roberts and T. A. Vanderslice,Ultrahigh Vacuum . Prentice-Hall, Englewood Cliffs, N.J.

A. Roth,Vacuum Technology . North-Holland Publn., Amsterdam, 1982.

G. L. Saksagansky, Molecular Flow in Complex Vacuum Systems . Gordon & Breach, New York, 1988.

G. L. Saksagansky,Getter and Getter-Ion Vacuum Pumps . Harwood Academic Press, New York, 1994.

. M. Trapnell,Chemisorption . Butterworth, London, 1955.

K. M. Welch,Capture Pumping Technology . Pergamon, Oxford, 1991.

M. Wutz, H. Adam, and W. Walcher,Theory and Practice of Vacuum Technology . Vieweg, Verlagsges., Braunschw989.







ndex

AAbsolute reaction rate theory, 549-550

Absolute temperature, 3, 6

Absorption, 589-605

diffusion rates, 590-591

equilibrium solubility, 590

kinetics, 591 permeation, effect of desorption kinetics, 600-605

steady-state permeation, 592-595

transient permeation, 595-600

Accommodation coefficient, 47-50, 572, 579

values, 50

Activation, getter materials, 273-274

Activation energy, 607, 612, 615

diffusion, 592

permeation, 602

Adsorption, 261, 263-265, 548-588

capillarity effects, 584-588

dissociative, 576, 607

equations, 548-551

heat, 562, 566-567

immobile, 557

isosteric heat, 567-568, 570

kinetic measurements, 582-584



kinetics, 572, 574-575

mean stay time, 550-551, 615

mobile, 557

monolayer and multilayer, 616

multimolecular layer, 558

net rate, 574

nondissociative, 575, 578

physical, 551, 553, 555, 561-562, 567

precursor state, 579-580, 582

Adsorptiondesorption theory, 348-352

Adsorption isotherms, 349-351, 367, 551-567

chemisorption, 569-570dissociative Langmuir, 554-555, 571, 580

DubininRadushkevich, 617

equation, 617

Freundlich, 566-567

Gibbs, 563, 571

HillDeBoer equation, 565Langmuir, 552-554, 579, 617

multilayer adsorption, 617-618

observed behavior, 568-572

physical, 568

Temkin, 566, 571, 617

Adsorption lifetime, 20Adsorptive equilibrium, 559

Alcohol lathing, 619-620

Analytical approximations, 538-541

Anode current, 322, 329

Appearance potential, 448, 450



Argon instability, 337-339

Argon shower, 330, 338

Argon treatment, 330

Atmosphere, standard, 5

Atomic beam, 27

Auger electron spectroscopy, 608-609, 612, 620

Avogadro's law, 4, 6

Avogadro's number, 6-8, 70

determination, 17-18

aAl system, constitutional diagram, 276

ack-diffusion coefficient, 221, 223, 230

acking pump, 248-249, 527-529

UHV/XHV, 646-647

ackscattering, 261

ackstreaming:

oil, 499, 536

roots blower, 520

ackstreaming factor, 670

a getters, 276-291

diffusion process, 282-284

endothermic, 277

evaporation conditions effect, 287-288

exothermic, 278flashing, 277-278

frittable, 290-291





a getters (Continued )

gas-doped, 289-290

gas-surface reactions, 288-289

high-yield, 290

interaction with gases, 278-280

low-argon, 291

sorption

characteristics, 279-284

distribution, 288

temperature-dependence, 284-286

thickness-dependence, 285-287

stages of gas sorption, 282-283

sticking probability, 281

structure, 282

total yield, 290

aH2 system, equilibrium isotherms, 284-285akeout, 338, 614, 619-621

ar, 5

ase pressure, 511

ayardAlpert ionization gauge, 417-419, 626, 634

calibration, 683

geometric variations, 419-421high-pressure limit, 426

ion current linearity, 435

modulated, 421-422, 630, 635

eam:

atomic, 27



molecular, 28

eer's law, 469

ent-beam gauge, 629-631

ernouilli's equation, 121

essel box gauge, 631-632

etatron oscillations, 72

lasius relation, 112

oltzmann constant, 3

oltzmann equation, 134-135

modified, 56

ombing test, 493

ourdon gauge, 382-384oyleMariotte law, 659

oyle's law, 3

rownian motion, 69

particle distribution, 17-18

runauerEmmettTeller model, 558-559, 561-562

alibration:

capacitance diaphragm gauges, 676-680

comparison method, 673-676

ionization gauges, 683-686

mass spectrometers, 686-689

spinning rotor gauges, 680-683test leaks, 689-692

alibration chamber, 665-666, 668-669

gas flow rate, 672

alibration leaks, 502

apacitance, parallel plate formula, 385



apacitance diaphragm gauges, 384-389

accuracy, 387-388

advantages and disadvantages, 388-389

calibration, 676-680

deflection of thin tensioned membrane, 386-387

sensitivity, 385-386

thermal transpiration, 388

apacitance manometer, see Capacitance diaphragm gauges

apacity, definition, 356

apillarity effects, 584-588

apillary condensation, 562

apillary leaks, 689apture coefficient, see Sticking coefficient

apture pumps, UHX/XHV, 643-646

apture vacuum pumps, 259

arbons, activated, 584

atalysts, 606

athode fall, 317, 319athodes, hot, 636-638

avitation, liquid ring pumps, 154, 156

avity ringdown spectroscopy, 470

eto getters, 297

haracteristic fragment ions, 449

harles' law, 4hemisorption, 263-265, 551, 553

kinetics, 575-582

dissociative, 579-580

equilibrium coverage, 579

fractional coverage, 578



homonuclear diatomic molecules, 575, 579-580

potential energy curve, 575-578

second-order, 581

sticking coefficient, 580, 582-584, 586

oxygen, 610-611

houmoff gauge, 426, 428

lausiusClapeyron equation, 351, 567

law pump, 162-164

oefficient of heat conductivity, 42

oefficient of interdiffusion, 63-64, 65

oefficient of self-diffusion, 62

oefficient of slip, 38-39oefficient of thermal separation, 58

oefficient of viscosity:

compared with heat conductivity, 42-43

definition, 29

at low pressures, 37-39

relation tomean free path, 30-32

molecular diameter, 31-32

unit, 30

variation with temperature, 32-33

old-cathode discharge, 318, 326

old-cathode gauges, 427-435calibration, 430, 433

inverted-magnetron gauge, 429-434

magnetron gauge, 431, 433





Penning discharge, 434

theory of crossed field discharge, 431

ollision, molecular, see Molecular collisions

ollision cross section, mutual, 8

ollision frequency, 33

ollision rate, 9

omparison method, calibration, 673-676

ompressible flow, 116-121

adiabatic flow, 117

approximation for flow through aperture, 121

choked flow, 116-117

choked pressure ratio, 116

relationship between

entry and exit velocity, 118

throughput and entry velocity, 118

speed of choked aperture, 119temperature changes, 120

through aperture or short duct, 119-121

time to vent chamber, 120-121

ompression ratio, 496, 521-522

ondensation coefficient, 22

ondensation rate, 22, 532ondensations, 525

onductance, 83-84

baffles and cold traps, 197-198

correction, 670

limited value in continuum flow, 107



molecular flow, 85-86

aperture, 86

end effect, 88

long ducts, 87

short ducts, 87-88

tubes, 88-90

transitional flow, 130-131

onductivity, permeation, 517-518

onnections, graphic symbols, 705-706

onstant pressure technique, 662

onstant temperature Pirani gauge, 406-410

ontinuity equation, 522ontinuous expansion, 659, 665-670

ontinuum flow, 81-82, 105-128

assumption of incompressibility, 108

choked pressure ratio, 124-126

compressible, 105, 116-121

entrance correction model, 122-124flow obstruction corrections, 121-122

friction factor, 128

kinetic energy model, 124-126

long duct criteria, 126-128

turbulent, 112-116

viscous flow, 108-109orrection factor, 669

osine law, 19-20

oulomb scattering, charged particles, 72

ounterflow helium leak detectors, 496-499

overage:



adlayer, 560

equilibrium, 579-580

fractional, 553, 578

rossover, 494-496, 529

ryo-condensation pumps, 347-348

UHV/XHV, 645

ryopumps, 347-364

adsorptiondesorption theory, 348-352

boiling pool, 359

capacity, 355-357

configuration, 359-363

convection heat loads, 361cryotrapping, 352-353

impulsive heatload, 362

open-loop, 359

partial regeneration, 364-365

pumping rate, 349

pumping speeds, 353-355refrigeration technology, 357-359

regeneration, 363-364

sorption roughing pumps, 364-368

UHV/XHV, 645

ultimate pressure, 353-355

ryopump sets, 535-537ryo-sorption, hydrogen by charcoal, 351-352

ryo-sorption pumps, 347-348

limiting pressure, 645

UHV/XHV, 645-646

ryosurfaces:



predicting performance, 542

pump combinations, 534-535

pumping speed, 531-534

ryotrapping, 352-353

ycloidal mass spectrometer, 465-466

D

DarcyWeisbach equation, 112

e Broglie wavelength, 73

Delay times, 587-588

Desorption, 261, 263-265

adsorbed gases, 614-615

electron-stimulated, 419

kinetics, effect on permeation, 600-605

net rate, 574

over barriers, 584-585

processes, 547-548

Desorption frequency, 548, 550, 572, 575

Diaphragm pump, 169-170, 499

Diffusion, 261, 265-267

activation energy, 592

Fick's second law, 266

finite slab, 598-599

Fisk's first law, 265-266

gases in Ba film, 282-284outgassing control, 513

rates, 590-591

semi-infinite slab, 596-598, 618, 621

thermal, see Thermal diffusion







Diffusion coefficient, 221-222, 265-266

determination, 65

temperature dependence, 65

Diffusionejector pumps, 183-185

Diffusion of gases, kinetic theory, 62-69

Diffusion pumps, 176-183

backstreaming, 194-195

baffle design, 197-198

boiler design, 182

cold cap, 182-183

cold traps, 231

compression ratio, 181, 190

cooling water flow, 200

design, 181-183

development, 176-181

dispersion characteristics, 228-229entrance chamber design and speed, 191-192

fluid vapor pressure, 192-194

fractionating oil, 179-180, 192

heater input, 200

jet deflection, 220

jet flow pattern, 209, 211multistage oil, 181

nozzle design and speed, 190-191

oils, vapor-pressure data, 200-201

pump fluid, properties, 207

pumping action theory, 202



speed dependence on design, 182

speed equation, 202-204

speed factor, 191

speed measurement, 186

UHX/XHV, 642-643

ultimate pressure, 193, 221

use in manometers, 378

vapor velocity at nozzle exit, 208

Diffusion pump sets, 528-531

Diffusion rate, Brownian particles, 70

Diffusivity, 591

apparent, 604Dispersion forces, 347, 551

Displacement, 261

Distillation rate, variation with pressure, 25

Dry helium leak detector, 499-500

Dry vacuum pumps, 159-170

claw pump, 162-164multistage piston pumps, 167, 169

roots pump, 159-162

screw pump, 164-165

scroll pump, 165-168

two-stage diaphragm pumps, 169-170

Dynamic method, 665

ffusion law factor, 191

ffusion rate, small orifice, 24

lastic scattering, electron, 72

lectrical matrix, correspondence with vacuum matrix, 544



lectrolytic abrasive polishing, 619

lectron:

charge, 7

secondary, 326-327

lectron cloud, 324-326

drift velocity, 324

space charge, 324

lectron emitters, 607

lectron-stimulated desorption, 419, 630

lectrostatic ion pumps, 318

leyRideal mechanism, 607, 612

nergetic neutrals, 337theory, 330

nergy:

activation, 550

dissociation, 576

kinetic, 3

translationalconservation, 10

distribution formula, 14

mean, 20

nergy loss:

due to thermal conduction, 44

fractional, 71nskog's formula, 222

nthalpy of vaporization, 561

ntrance correction model, 122-124

quation of state, ideal gas, 4

quilibrium pressure, 267-269



rror function, 597, 599

vaporation rate, 22-25

metals, gas pressure effect, 67-69

xpansion by molecular beam, 659

xpansion ratio, 662, 664

xpansion technique, 662

disadvantage, 663-664

xtractor gauge, 422, 629-630

xtreme high vacuum:

capture pumps, 643-646

definition, 625

gas-phase parameters, 627hardware, 652

kinetic pumps, 642-643

leak detection, 647-648

measurement limits, 628-642

comparison of gauges, 641-642

gauges with long electron paths, 639-640hot cathode effects, 636-638

residual currents, 629-636

outgassing, 648-651

pump comparison, 646-647

pumping speed, 628

anno line, 224

araday constant, 6

araday cup ion detection, 454

ick's first law, 590-592, 600







ick's second law, 591, 595-596, 598-599, 618

isk's first law, 265-266

isk's second law, 266

low, of gases, see Gas flow

lowmeter, 694-695

lux:

diffusive, 590-591

steady-state permeation, 602

orce, unit, 4

orce constants, in repulsive force relation, 59

orepumps, pumping speed, 519-520

orepump sets, 519-524

ore-vacuum pumps, 519-520

owlerNordheim equation, 327

ranckCondon principle, 448

ree-molecule conductivity, 46-50ree path, mean, see Mean free path

riction factor, 112-114, 128

G

Gain factor, secondary electron multiplier, 456

Gas:

active, interaction with getters, 275

dissolved, permeation, 616

effusion, 22

getterable, sputter-ion pumps, 335-336

interaction with Ba film, 278-280

noncondensable permanent, 534



permeation, 516-518

properties, 83

purge, 500, 536-537

tracer, leak detection, 493

see also Kinetic theory of gases

Gas ballasting, 144-147

Gas chromatograph, 587-588

Gas constant, 6

Gas density, 3

Gas desorption, 484

Gas discharge vacuum pumps, 317-319

Gas factor, 82-83

Gas flow, 81-137

conductance, 83-84

continuity assumption, 84

desorption, 502

equation, 543

free molecular, 81

leak, 482

permeation, 484, 488

pressure reduction, 474-475

regimes versus Knudsen number and pressure, 82

throughput, 83, 667

total, 494

transitional, 82, 128-137

see also Continuum flow; Molecular flow

Gas load, 547

high-vacuum systems, 513-519

process, 518-519



time-dependence, 514-515

Gas-phase parameters, 627

Gas pressure, 18-22

Gas-surface interactions, 547-548

types, 261-262

van der Waals interactions, 555

see also Adsorption

Gas volume, striking unit area per unit time, 21

Gay-Lussac's law, 4

Getter, bulk, 596

Getter effect, 321, 329

Gettering, 262

sputter-ion pumps, 329-330

Gettering capacity, 262

Gettering rate, 262, 298

terminal, 270

Gettering speed, 264

Getter-ion pumps, UHX/XHV, 643-645

Getter materials, 269-310

activation, 273-274

applications, 313-315

basic concepts, 262-263

characteristics, 269

evaporable, 271-272


see also Ba getters; Ti sublimation getter pumps

interaction with residual gases, 275

nonevaporable, 271-272, 297-310

activation, 303-304, 308-309




binary Zr and Ti alloys, 298-301

Ceto getters, 297

compressed and sintered structures, 310-313

configurations, 310-313

diffusion rate, temperature dependence, 300, 302

gettering rates, 298

gettering speeds, 301-302

multicomponent alloys, 310

sorption characteristics, 311, 313

surface analyses, 304

ternary allows, 305-309

ZrAl alloy, 299-304

ZrCo alloys, 305

ZrFe alloys, 305

ZrNi alloys, 305

ZrTi alloys, 305

ZrV alloys, 305

ZrVFe alloy, 306-309

reactivation, 274

sorption speed and capacity, 269-271

types, 271-275

Getter pumps, evaporable and nonevaporable, UHV/XHV, 645

Getters, 262

GiffordMcMahon cycle, 348

GiffordMcMahon refrigerator, 357-358

Glow discharge, 620





Gravimetric technique, 662

Grazing incident, 337, 339

Gyromagnetic radius, 318

H

Halogen sensor, 485

Heat capacity, 41

Heat conductivity, see Thermal conductivity

Heat flow, between concentric cylinders, 360

Heat load, 532

Heat of adsorption, 621

Heat of solution, 590, 592

Helium leakage rates, standards, 503

Helium leak detector, 486-487, 494

counterflow, 496-499

detection limits, 498

direct-flow, 494-496

dry, 499-500

mass spectrometer, 494

measurement range, 502

oil-free, 499-500

recalibration, 502

sensitivity, 495-497

vacuum components, 487-490

vacuum systems, 490-492

Helmer gauge, 423-424

Henry's law, 552-553, 563, 565, 568, 574-575

High-pressure ionization gauges, 426-428



High-vacuum pump sets, 524-537

cryopump sets, 535-537

with cryosurfaces, 531-535

design, 525

diffusion pump, 528-531


turbomolecular, 526-528

ultimate pressure, 525

High vacuum region, 9

High-vacuum systems, 507-546

calculation methods, 537-546

analytical approximations, 538-541

numerical methods, 541-546

equivalent electrical circuit, 544-545

fore-vacuum pumps, 519-520

outgassing, 513-516

roots combinations, 520-524

see also High-vacuum pump sets

HillDeBoer equation, 565

Ho coefficient, 191

Hot-cathode gauge equation, 414-419

Hot-cathode gauges, comparison, 641-642

Hydraulic diameter, 106

Hydrocarbons, interaction with getters, 275

Hydrogen:

atomic, 607-608

flux, Arrhenius plot, 602-603

sputter-ion pumps, 336-337

Hydrogenmetal systems, pressurecompositiontemperature curves, 268



Hydrogen permeation constant, 594-595

deal gas law, 2-6

differentiation, 689

three-dimensional, 564mpedance, 83

nfrared absorption measurement, partial pressure, 469-470

nlet system, 668

nteractions, adsorbateadsorbate, 567, 568

nteratomic spacing, 556

nverted-magnetron ionization gauge, 429-434, 639-640

on burial, 330-331

on detection, 454-456

Faraday cup, 454

microchannel plate detector, 456-457

secondary electron multiplier, 454-456

onization gauges, 414-441

accuracy, 435-438

BayardAlpert gauge, 417-419, 626, 634

calibration, 683

geometric variations, 419-421

high-pressure limit, 426

ion current linearity, 435

modulated, 421-422, 630, 635

bent-beam, 629-631

Bessel box, 631-632

buried collector gauges, 420


cold-cathode gauges, 427-435



controllers, 439-441

degas mode, 685

electron-stimulated desorption, 419

equation, 415-416

extractor gauge, 422, 629-630

factors influencing calibration, 437-438

gauge constant ratios for gases, 438-440

generalized, 415

Helmer gauge, 423-424

high-pressure, 426-428

hot-cathode gauge equation, 414-419

long electron path length gauges, 424-425, 639-640

outgassing rates, 672

as reference standards, 688

reverse x-ray effect, 419

secondary electron production, 685

secondary standard hot-cathode gauges, 425-426

as secondary standards, 684-685

sensitivity, 684

stability of calibration, 436

types, 414

x-ray effect, 417

onization potential, 448, 450





onization process, electron-impact, 448-451

on motion, 323-324

ons, drift velocity, 464

on sources, 447-453

closed, 452-453

electron-impact ionization process, 448-451

open, 449, 451-452

sentropic flow, 119

solation devices, graphic symbols, 704

ump frequency, 590-591

K

Katharometer, 44, 65

Kelvin equation, 585

Kinetic energy model, 124-126

Kinetic pumps, 642-643

Kinetics, quasi-first-order, 605

Kinetic theory of gases, 1-73

Avogadro's number, 6-8

derivation of pressure relation, 2

fundamental postulates, 1

ideal gas law, 2-6

molecular collisions, 8013

Kinetic vacuum pumps, 173-254

diffusion-ejector pumps, 183-185

diffusion pumps, 176-183

see also Vapor-jet pumps



Knudsen cell, 20

Knudsen correction factor, 669

Knudsen equation, 130-131, 133

Knudsen number, 9, 51, 54, 81-82

flow regimes versus, 82


afferty gauge, 640

afferty magnetron gauge, 424-425

angmuir equation, 562

angmuirHinshelwood mechanism, 607, 612

angmuir isotherm equation, 332

angmuir model, 552-554

angmuir's film theory of heat conduction, 52-53

eakage rate, 490, 689-690

conversion, 503-504

measurement, helium leak detectors, 486-487

minimum detectable, 500

measured, uncertainties, 692

normalized, 484, 488

quantitative measurements, 493, 502-504

standards, 502-503

uncertainty, 502

units, 482-484

conversion factors, 483

eak detection, 481-505

future developments, 504-505

gross leaks, 485

partial pressure measurements, 486



special methods, 493

total pressure measurements, 484-486

tracer gases, 493

UHV/XHV, 647-648

eak detector:

calibration, 503

inlet pumping speed, 501

intrinsic partial pressure sensitivity, 500

partial-flow arrangement, 490-491

partial flow connection, 491-492

pumpdown time, 488, 501

quadrupole mass spectrometer, 492

total gas flow, 491

vacuum components, 487-490


see also Mass spectrometer, leak detectors

eak gas flow, 482

eak localization, 488

eaks:

calibration, 502

flow conditions, 504

temperature dependence, 503

test, calibration, 689-692

types, 482


ennard-Jones potential, 556

'Hôpital's Rule, 208

ight, velocity, 7

iquid, density, molecular diameter from, 40



iquid manometers, 378-379, 659

iquid nitrogen trap, 494-496

iquid ring pumps, 151-158

accessories, 158

cavitation and protection against cavitation, 154, 156

drives, 157-158

materials of construction, 157

mechanism, 151-152

operating liquid, 154

conveyance, 156-157

operating ranges, 154-155

sealing, 157

single-stage, 152-153

two-stage, 153-154

types of operation, 156

MF mode, see Penning discharge

ong electron path length gauges, 424-425

oschmidt number, 7

M

Mach angle, 218

Magnetic focusing, charged particles, 72

Magnetic ionization gauges, 639-640

Magnetic sector mass spectrometer, 460-463

resolving power, 462-463

Magnetron gauge, 424-425, 431, 433

Magnetron ionization, 639

Manometer, liquid, 378-379

Masking, leaks, 488








application, 15, 18

MaxwellLoschmidt method, 65-67

Maxwell's distribution law, 210

Mbar, 5

McLeod gauge, 379-381

linear mode, 381

quadratic mode, 380

sources of error, 381

Mean free path, 8, 26-28, 586-587

electrons, 41

experimental determination, 27

homogeneous maxwellian gas, 9molecular collisions within unidirectional beam, 72

relation to coefficient of viscosity, 30-31

StefanMaxwell formula, 63

temperature effect, 32

values, 34

at very low pressures, 21Mean stay time, adsorption, 615

Membrane, thin tensioned, deflection, 386-387

Mercury vapor, mean free path and molecular diameter, 34

Mercury vapor pumps, 177-178

Metals:

classification by adsorption properties, 574evaporation rate, gas pressure effect, 67-69

Microchannel plate detector, 456-457

Molar flow rate, 6

Molar volume, 4

Molecular beam expansion, 670-673





long ducts, 87

short ducts, 87-88

tubes, 88-90

time constant in unsteady flow, 103

unsteady flow cases, 102-105

Molecular flux, incident, 21

Molecular impingement rate, 548

Molecular mass, determination, 22

Molecular velocity, 12-13, 16-17

Molecules:

free paths, 26-28

masses, velocities, and rates of incidence, 16number per monolayer, 36, 41

number per unit volume, 7

random motions, 69-71

Molthan angular distribution function, 212

Momentum, linear, conservation, 10

Multistage claw pumps, 162-164Mutual diffusion coefficient, 63

N

Newton, 5

Noble gases:

interaction with getters, 275

sputter-ion pumps, 337-338Nondestructive testing, 504





Numerical methods, 541-546

dedicated software, 541-542

network approach, 542-546

O

Ohm's law, 543

Oil backstreaming, 499, 536

Oil contamination, 499

Oil-free helium leak detector, 499-500

Oil-sealed vacuum pumps, 143-149

accessories, 149

design, 143-144

gas ballast, 144-147

oil suckback, 148

power requirements and system protection, 148-149

pump oil, 147-148

Omegatron, 466-467

Optical measurements, partial pressures, 467-470

Orbitron pump, 645

Orifice flow method, 665

Oscillating quartz crystal viscosity gauge, 402-403

Outgassing, 513-516, 614-621

bakeout, 620-621

desorption of adsorbed gases, 614-615

dissolved gases, 616

flow rate, 538

in situ surface treatments, 620

mitigation, 619



pumpdown curves, 616-618

rate, 596-598, 672

rate reduction, UHV/XHV, 648-651

surface treatments during construction, 619-620

UHV/XHV, 648-651

artial-flow factor, 490

artial pressure analysis, 447-477

calibration of analyzers, 475-477

computer control, data acquisition, and presentation, 470-471

infrared absorption measurement, 469-470

ion detection, 454-456

ion sources, 447-453

laser multiphoton ionization, 468-469

optical measurement, 467-470

residual gas analysis, 471-474

vacuum process analysis, 474-475

see also Mass analysis

artial pressure analyzers, calibration, 687

artial pressure gauge, 486

article beams, scattering, 71-73

article distribution, at levels in gravitational field, 18

artition functions, 550

ascal, 5

enning discharge, 318-329, 650

configuration, 343

discharge modes, 320

electron cloud, 324-326

electron transit and collision parameters, 434



ion motion, 323-324

pump sensitivity, 321-323

secondary electrons, 326-327

sputtering, 329

transition from HMF to HP mode, 327-328

transition from LMF to HMF mode, 328-329

enning gauge, 427-429

ermeability, 484, 593-595

ermeability constant, 594-595

ermeation, 516-518, 615

dissolved gases, 616

effect of desorption kinetics, 600-605

kinetics, 591

steady-state, 592-595

surface contaminants, 604-605

transient, 595-600

ermeation conductivity, 517-518

ermeation gas flow, 484, 488

ermeation leaks, 689

hotoionization measurement, partial pressure, 468-469

hysiosorption, 551

hysisorption, 263-265

irani gauge, 406-410

comparison with thermocouple gauge, 412

irani leak detector, 410

iston gauges, 659-661

iston pressure balance gauge, 381-383

iston pump, 167, 169

lasma coating, anode, 330



lasma processing, 620

oisson's equation, 324, 327

olymer materials, outgassing, 514-515

ositive displacement pump, 141-170

dry vacuum pumps, 159-170

liquid ring pumps, 151-158

oil-sealed, 143

otential energy, 600-601

curve, 575-578

well, 549

otential well, 556-557, 576, 578, 589, 600

randtlMeyer formula, 214, 216

randtlMeyer ratio, 216-217

ressure:

allowable in synchrotron, 73

definition, 18, 657

effect on rates of evaporation of metals, 67-69

flow regimes versus, 82

kinetic theory relation, 2

limiting ratio, 53

measurement, 21

ranges, 658

time-dependence, 509

units, 5, 657

see also Partial pressure analysis





ressure gauges, total, 484

ressure units:

conversion factors, 377, 707

vacuum measurements, 377

rocess gas loads, vacuum systems, 518-519

rocess pressure, vacuum systems, 511-513

umpdown, UHV range without bakeout, 649

umpdown curve, 510, 513, 616-618

umpdown equations, 508-511

umpdown time, 538-539

ump fluid:

properties, 207

vapor pressure, 192-194

umping speed, see Volume throughput

umping system, 669-670

ump orifice, 669umps:

booster, 183-184

diffusion, 176-183

diffusion-ejector, 183-185

dry vacuum, 159-170

liquid ring, 151-158oil-sealed vacuum, 143-149

see also specific pumps

Q

Quadrupole mass spectrometer, 447, 456-460, 486, 631-632

closed ion source, 452-453



filter structures, 457-458

leak detection, 492

Mathieu equations, 459

operating line, 460

potential difference, 452

quadrupole potential, 457

resolving power, 459

Quadrupole potential, 457

Quartz helix Bourdon gauge, 383-384

R

Random motions, molecules, 69-71

Rate constants, 579, 581

Rayleigh line, 224

Reactivation, getter materials, 274

Readsorption, 616

Reference gauge, 673

Reference standard, 658, 676

Refrigeration, technology, 357-359

Refrigeration loss, 359

Refrigerator cryosurface combination, 533

Regeneration:

cryopumps, 363-364

partial, 364-365

Regenerative drag pumps, 251-254

Relaxation time, 21

Repulsive force constant, 60-61

Residual currents, 629-636

Residual gas analysis, 471-474

diagnosing leaks and contamination, 472



filament selection, 472

Residual gas analyzer, see Quadrupole mass spectrometer

Reverse x-ray effect, 419

Reynolds number, 105

in terms of throughput, 106


transition from viscous laminar to turbulent flow, 106

units conversions, 107

Roots blower, 520

efficiency, 521

predicting performance, 542


Roots combinations, 520-524

Roots pump, 159-162

Rutherford formula, scattering cross section, 72

aturation time, 335

cattering, particle beams, 71-73

crew pump, 164-165

croll pump, 167-169, 499

econdary electron multiplier detection, 454-456

econdary standard hot-cathode gauges, 425-426

emimetals, classification by adsorption properties, 574

ensitivity, 475-477

eparation of gases, by thermal diffusion, 60

ieverts' equation, 303, 307

ieverts' law, 267-268

ieverts' plots, H2, 299-300

I system, pressure units, 377



lip theory, 129

niffing device, 492

niffing technique, 505

olid, density, molecular diameter from, 40

olubility, 267-268

equilibrium, 590

orption:

Ba film properties, 279-284

processes, 547-548

titanium sublimation getter pumps, 292-295

orption capacity, 269-271

orption roughing pumps, 364-368

orption speed, 269-271

ound, velocity, relation with molecular velocities, 16-17

pecific heat:

molar, ratio, 17

molecular, 42-43

ratio, 42-43

pectrometer, linear response, 475

peed factor, 191





pinning rotor gauge, 391-402

accommodation coefficient, calibration, 397-398

advantages and disadvantages, 401-402


commercial, 394-397

fluctuations due to timing errors, 396

gassurface interaction assumptions, 391-392

head, 394-395

residual drag changes, 398-400

secondary or transfer standard, 399-401

stability, 397-400

theory, 391-394

puttering, 329

puttering pattern, 323, 337

puttering rate, 339

putter-ion pumps, 317argon instability, 337-339

bakeout, 338

''built-in", 334, 341

diode-type pump, 338-339

discharge current as function of nitrogen pressure, 322

distributed, 332gas discharge vacuum pumps, 317-319

getterable gases, 335-336

gettering, 329-330

hydrogen, 336-337

ion burial, 330-331



life, 329

magnetron-type, 345-346

magnet system, 345-346

memory effect, 343-344

modes, 320-321

noble gases, 337-338

Penning discharge, 318-329

starting pressure, 342-343

trapped electron density, 333

triode-type, 331, 340-341

types, 338-342

UHX/XHV, 643-644ultimate pressure, 343-344

putter yield, 329-330

tandard

primary, 658-673

definition, 658

secondarydefinition, 676

see also Reference standard

tandard atmosphere, 5

tatic expansion, 659, 661-665

uncertainties, 665-666

tay time, adsorption, 588tefanMaxwell formula, mean free path, 63

ticking coefficient, 22, 264, 334, 349

chemisorption, 580, 582-584, 586

ticking probability, 264, 281

urface chemical reactions, 606-614



classes, 606

cleanoff, 609

continuous expansion method, 665-670

EleyRideal mechanism, 607, 612

LangmuirHinshelwood mechanism, 607, 612

liquid manometers, 659

molecular beam expansion, 670-673

piston gauges, 659-661

standard, primary, 658

static expansion, 661-665

structure-sensitive or structure-insensitive, 606-607

water cycle, 612-614urface coverage, 264

urface defects, 566

urface diffusion, 587

urface heterogeneity, 566-568

urface lifetime, 578, 581, 615

mass spectrometric molecular beam techniques, 582-583mean, 550, 587

urface machining processes, 619-620

urface reactions, 261

titanium sublimation getter pumps, 295

urface roughness, 619

urface tension, 563utherland constant, 32-33

antalum, evaporation rate and vapor pressure, 23

emperature:

absolute, 3, 6



definition, 2

discontinuity, 50

two-dimensional critical, 565

hermal conductivity, 41-44

compared with coefficients of viscosity, 42-43

at low pressures, 44-53

free-molecule, 46-50

temperature discontinuity, 50-53

molecular, values, 48

variation with pressure, 45-46

hermal conductivity gauges, 403-414

ambient temperature compensation, 411applications, 413-414

calibration, 406-408, 410-411

comparison of Pirani and thermocouple gauges, 412

constant temperature Pirani gauge, 406-410

convection enhanced, 410-411

energy loss mechanisms, 403-404energy transfer by radiation, 405

integrated transducers, 412-413

lowest useful pressure, 408-409

precautions for use, 414

stability, 408-409, 412

theory, 404-406





hermal conductivity gauges (Continued )

thermistor Pirani gauges, 412-413

upper pressure limit, 410-411

hermal creep, 55

hermal diffusion, 57-62

hermal radiation, 532

hermal transpiration, 53-57, 354

capacitance diaphragm gauges, 388

effect in

mass spectrometer inlet, 57

variable capacitance diaphragm transducers, 57

effect on vacuum microbalances, 54

variation with Knudsen number, 43-55

hermal transpiration effect, 678, 684

hermistor Pirani gauges, 412-413

hermocouple gauge, comparison with Pirani gauge, 412hermomolecular flow, 53-57

hrottle valve, 495-496

hroughput, 83

units, 6

vapor-jet pumps, 198-202

ime constant, 500-501diffusion time, 501

electrical, 501

gas transport, 501

vacuum, 511-512

ime-of-flight analyzer mass spectrometer, 464-465



itanium sublimation getter pumps, 291-297

displacement phenomena, 295

peeling, 295

sorption

characteristics, 292

dependence on thickness, 293-295

temperature-dependence, 292-294

surface reactions, 295

types, 295-297

orr, 5

otal pressure measurements, 484-486

ownsend avalanche, 326racer gas, 486

leak detection, 493

rejection levels, 503-504

ransducers, 376

integrated, 412-413

ransitional flow, 128-137conductance, 130-131, 133

Knudsen equation, 130-131, 133

Knudsen number, 128-129

leakage through small hole, 131

long duct criterion, 134-135

long ducts, 129-134Reynolds number, 128-129

simple approximation, 133

slip theory, 129

through apertures and short ducts, 135-137

ransmission probability, 86



component combinations, 96-105

addition theorem, 100

entrance correction, 99

Oatley method, 98-99

overall conductance, 101

pump connected to chamber, 99-100

pump connected to chamber via second chamber, 102

pump connected to chamber via tubes or components, 102

series arrangement of different diameter tubes, 100-102

cross sections intermediate between rectangular and elliptical, 93

cylindrical annulus, 93-95

elliptical cross section, 92-93other shapes, 94, 96-98

rectangular cross section, 90-92

triangular section, 94

tubes, 88-90

rochoidal mass analyzer, 465-466

ubes, graphic symbols, 705-706ungsten, evaporation rate and vapor pressure, 23, 68

urbomolecular pumps, 238-247

backing pumps, 248-249

baking, 244

balancing and vibration, 243

bearing lubricant, 242in combination with other pumps, 245

combined with molecular drag pumps, 247-248

cooling, 244

design, 241-243

drive systems, 243



magnetic rotor suspension, 242

operation in magnetic fields, 244-245

performance data of commercial pumps, 245-247

pumping corrosive gases, 245

pumping speed, 240-241, 246-247

pumping toxic or radioactive gases, 245

rotor and stator geometry, 241-242

rotor materials, 243

rotor suspension, 242

theoretical considerations and performance data, 239-241

UHX/XHV, 643

venting, 243-244urbomolecular pump sets, 526-528

urbulent flow, 112-116

entrance correction model, 123-124

entry length, 116

friction factor, 112, 114

kinetic energy, model, 125-126shape factor, 112





U

Ultimate pressure, 511

Ultrahigh vacuum:

capture pumps, 643-646

definition, 625

gas-phase parameters, 627

hardware, 652

history, 625-626

kinetic pumps, 642-643

leak detection, 647-648

measurement limits, 628-642

comparison of gauges, 641-642

gauges with long electron paths, 639-640

hot cathode effects, 636-638

residual currents, 629-636

outgassing, 648-651

pump comparison, 646-647

pumping speed, 628

Ultrahigh-vacuum molecular beam scattering system, 582-583

Universal gas constant, 6

V

Vacuum chambers, graphic symbols, 704

Vacuum components:

graphic symbols, 701-707

helium leak detection, 487-490

Vacuum degassing, 619

Vacuum gauge constant, 684



Vacuum gauges, 375-376

Bourdon gauge, 382-384


capacitance diaphragm gauges, 384-389

direct gauges, 375

graphic symbols, 707

indirect gauges, 375

liquid manometers, 378-379

McLeod gauge, 379-381

piston pressure balance gauge, 381-383

stability, 680

thermal conductivity gauges, 403-414

see also Ionization gauges; Viscosity gauges

Vacuum matrix, correspondence with electrical matrix, 544

Vacuum measurements, pressure units, 377

Vacuum pumps, graphic symbols, 701-703

Vacuum systems:

calculations, 507-513

helium leak detection, 490-492

leaks, 516-517

process gas loads, 518-519

process pressure, 511-513

pumpdown equations, 508-511

with two chambers, 543

see also High-vacuum systems

Vacuum time constant, 511-512

Valve modes of operation, graphic symbols, 705

an der Waals equation, 39-40

an der Waals forces, 347, 551



Vapor-jet pumps, 185-202

back-diffusion of gases from fore-vacuum, 221-223

baffles and traps, 195-198

boiler pressure dependence, 199

breakdown, 187-188

DeLaval nozzle, 225

equation of continuity for gas flow, 186

flow pattern, 205-221

deflection from nonexpanding verticle nozzle, 219

forepressure below limiting value, 209

Gaede's alpha formula, 214

Mach angle, 218

maximum discharge rate, 206-207

Molthan angular distribution function, 212

specific heat ratio, 207

Documents

Foundations of Vacuum Science and Technology