Unit 5 ultra low temperature cryo refrigerators

Cryogenics [email protected]

1 | P a g e

UNIT – 5

ULTRA LOW TEMPERATURE CRYO –

REFRIGERATORS

Magneto Caloric Refrigerator:

An apparatus that utilizes the principle of adiabatic demagnetization to

continuously maintain a constant low temperature is known as a

magnetic refrigerator (see Fig). This is possible through the use of

superconducting thermal "valves." These are strips of metal, such as

lead, which are superconducting below a "transition" temperature in the

absence of a magnetic field and have normal electrical resistance in the

presence of a magnetic field. In the superconductive state, thermal

conductivity is reduced. Thus, a superconductor can be used as a thermal

switch by turning a magnetic field on (switch "closed") or off (switch

"open").


2 | P a g e

Magnetic refrigerator


3 | P a g e

Thermodynamic cycle for the magnetic refrigerator

The process that occurs in a magnetic refrigerator is shown in Fig.:

1. With the system at a steady-state temperature (Tl at approximately

1 K), the working salt is brought into thermal contact with the liquid

helium bath by opening the upper thermlll valve and closing the lower

thermal valve.

As the magnetic field is applied for process step 1-2, the entropy of the

salt is decreased isothermally.

2. After applying the magnetic field, both thermal valves are closed and

the magnetic field around the working salt is adiabatically reduced in

process step 2-3 to an intermediate value. This causes the salt to cool to

a temperature of T3 •


4 | P a g e

3. With the upper thermal valve closed and the lower thermal valve

opened, the magnetic field is further reduced in process step 3--4 while

heat isabsorbed isothermally from the space to be cooled by the reservoir

salt and by the working salto

4. In process step 4--1, both thermal valves are closed and the working

salt is adiabatically remagnetized to its starting condition.

The refrigeration effect for this proeess is

= m (

where m is the mass of the working salt. The amount of energy rejected

as heat from the working salt is

= m (

The net work for the cycle is then

= | | | | m (

Therefore, the coefficient of performance for an ideal magnetic

refrigerator is

COP =

=

which is the same as that for a Carnot refrigerator.

Dilution refrigerator:

In 1951, H. London made the suggestion to use a solution of the rarer

isotope in the more common isotope

to obtain low

temperatures. In any dilute solution, the solute molecules can be

considered to behave like a gas whose pressure and volume correspond

to the osmotic pressure and volume of the solution. Dilution of the

solution by adding more solvent causes an "expansion" of the solute

"gas" and cooling should result. A practical dilution cycle was first

developed in 1962.


5 | P a g e

The density of is less than that of

. Therefore, at temperatures

below 0.87 K, solutions of and

exist in two liquid phases with

the rich phase residing above the

phase. The migration of

atoms across the liquid-liquid interface is similar to evaporation in that

the atoms exert no drag force on the

atoms. Since the osmotic

pressure of the dilute phase extrapolates to about 0.0023 MPa at 0 K

instead of 0 MPa, it suggests that, near absolute zero, a stable solution of

these isotopes should contain about 6.4 % 3He. During the phase

transition of into the

solution at constant temperature, the

entropy increases and heat is absorbed by the 3He to increase its

enthalpy. This is the driving force behind the dilution cycle.

In a continuously operating dilution cycle (see Fig.), helium gas

composed of essentially pure is compressed with the aid of a

vacuum pump, cooled, and sent through a heat exchanger followed by

heat exchange in two helium baths, the first at 4.2 K and the second near


6 | P a g e

1 K. A throttling device in the line provides the necessary temperature

adjustment to permit the mixture to supply the necessary energy to

operate the still. After further cooling in another heat exchanger, the

mixture is admitted to the mixing chamber. Two liquid phases appear as

the temperature is further decreased with the less dense -rich mixture

on the top. Since this is a continuous process, diffuses into the

phase in the mixing chamber and must be replenished in order to

maintain equilibrium. The lower part of the mixing chamber contains

in the superfluid form (He II), through which

easily diffuses.

This expansion of the into the more dense

phase provides the

refrigeration effect. The mixture is returned through the heat

exchanger to the still where the is evaporated from the mixture.

This vapor is warmed and returned to the vacuum pump where

recompression of the completes the cycle. This compressed

replaces the originally dissolved in the

phase. Temperatures

down to about 15 mK have been achieved for hundreds of hours using

this method.

The refrigeration effect for the dilution refrigerator can be determined by

an energy balance around the mixing chamber

= )

where is the molar flow rate of

in the refrigerator, is the

molar enthalpy of the in the more dense phase leaving the mixing

chamber, and is the molar enthalpy of the in the less dense

phase entering the mixing chamber. Below temperatures of 40 mK the

enthalpies in units of J/mol can be approximated by

where and are the temperatures of the streams leaving and

entering the mixing chamber, respectively. Typical refrigeration effects

are on the order of 2-10μW.

The simplest dilution refrigerator may be operated as a single cycle. The

-

mixture is condensed into the mixing chamber, precooled, and

then circulated. Temperatures of 4-5 mK have been obtained with such a

device since heat is not added continuously with the liquid feed.


7 | P a g e

Pomeranchuk Cooling:

Satoh's Pomeranchuk cooling machine

A method for achieving temperatures around 2 mK by using the

properties of solid was originally proposed in 1950 by

Pomeranchuk and subsequently developed in 1969 by Wheatley. Pure

liquid will not solidify at 0 K unless a pressure of about 3.5 MPa is

applied to the liquid. The melting curve has a minimum at 0.3 K for

which the required pressure is close to 3 MPa. Below 0.3 K, the solid

has a high er molar entropy than the liquid. In fact, at 20 mK the molar

entropy of the liquid is only 1/7 that of the solid.

This implies that a substantial cooling effect could be gained by

adiabatic solidification under compression at these low temperatures.


8 | P a g e

However, for this process to work, the compression has to be performed

without frictional heating.

This frictional effect is so significant that at 8 mK, a 1 % conversion of

mechanical work into heat reduces the available refrigerating capacity to

zero.

A schematic of a Pomeranchuk cooling machine proposed by Satoh is

shown in Fig. A major problem in the operation of such cooling devices

on a large scale is the method of precooling . In Satoh's device, two

Leiden dilution refrigerators (LDR) use to precool the

. After

cooling the liquid below 300 mK the liquid is sealed into the

compressor cell and the bellows are used to mechanically and

adiabatically compress the cell.

Once the liquid is compressed up to the solid line, a "Pomeranchuk cell"

will form with liquid isolated from the surroundings by a solid shell. The

cooling effect can be realized by compressing this cell until it becomes

solid.

For the most efficient cooling effect, a limit must be set on the solid

content in the cell to avoid friction caused by crushing. The performance

of this cooling machine, however, is rather poor since a cooling effect is

produced that is about 1 % of the work input to the process.

Nevertheless, Pomeranchuk cooling provides a greater cooling effect

than that obtained from -

dilution systems. Its major

disadvantage is that it operates on a batch basis and requires

considerable time to precool the working fluid to low enough

temperatures.

Measurement Systems for low temperatures:

Accurate measurement of Thermophysical properties is very essential

for controlling the process parameters and efficient performance of the

individual pieces of equipment of the cryogenic process plants.

Measurement of temperature, pressure or vaccum level, liquid level, and

flow rate, is often needed for production, storage and transportation of

cryogenic fluids.

Temperature measurement at low temperatures:


9 | P a g e

Temperature is one property, which cannot be measured directly by

compairing it with a ‘standard’ as in the case of length, mass and time. It

is determined indirectly by measuring another temperature-dependent

property, such as

1. Length of thread of a liquid (e.g. mercury or alcohol) in a glass

capillary,

2. Electrical resistance of a metallic wire.

3. Pressure of a gas of known volume.

4. Pressure of a boiling liquid.

5. E.m.f generated between two dissimilar metals.

6. Speed of sound in gas.

7. Refractive index.

8. Magnetic susceptibility of a paramagnetic salt.

9. Thermal expansion of two different metals, etc.

For each such type, the values of the property at an interval of two fixed

temperatures, such as freezing point and boiling point of water must be

known in order to define the temperature scale. The smallest unit in the

scale is defined by dividing the difference in these two fixed points by a

fixed number, say 100, to obtain the value of a degree. However,

different devices may not show agreement at intermediate temperatures,

though they may show satisfactory agreement at the fixed temperatures,

as most properties do not vary linearly with temperature. The selection

of temperature measurement devices or thermometers often depends on

the range of operation of the device.

In some cases, there is no alternative but to select only one device

because of nonexistence of any choice. When more choices are

available, then the selection of the device is made based on the accuracy,

reproducibility, stability, simplicity, heat conduction, heat capacity,

sensitivity, cost and convenience. Sensitivity of measurement is the most

important criterion, which includes the other primary factors for

selection and needs a systematic analysis. The optimum choice,

however, depends on the requirement of the specific application and

available instrumentation.


10 | P a g e

The fundamental thermodynamic temperature scale is defined in terms

of the properties of the ideal gas, i.e., the working substance of a Carnot

engine and the two temperatures between which it is operating,

according to the second law of thermodynamics. This concept relates to

the efficiency of a Carnot engine, which depends on these two

temperatures only and is independent of the working substance.

Accordingly, the fundamental thermodynamic scale represents the

absolute scale or Kelvin scale. The numerical value of the unknown

temperature in this scale is conceptually obtained in terms of one fixed-

point temperature, say, the triple point of water, i.e., 273.16K, and the

ratio of the heat rejected to the heat absorbed by a Carnot engine

operating between these two temperatures. However, this scale is not

practically possible.

A practical and reproducible temperature scale is, however, accepted to

be one that closely approaches the absolute temperature scale, like the

one first introduced in 1927 as the International Temperature Scale (ITS-

27). This included six fixed points out of which only one, namely, the

normal boiling boiling point of oxygen is in the range of cryogenic

temperatures. In 1968, the International Practical Temperature Scale

(ITPS-68) extended the range of temperature scale to the triple point of

hydrogen (13.81K) and the values of the primary fixed points were

revised as those listed in table below.

Fixed Point Condition Temperature (K)

Gold point Normal melting point 1337.58

Silver point Normal melting point 1235.08

Zinc point Normal melting point 692.73

Steam point (water) Normal boiling point 373.15

Triple point (water) Standard triple point 273.16

Oxygen point Normal boiling point 90.188

Triple point (oxygen) Standard triple point 54.361

Neon point Normal boiling point 27.102

Hydrogen Normal boiling point 20.28

Hydrogen (at 25 torr) LP boiling point 17.042


11 | P a g e

Triplepoint(hydrogen) Standard triple point 13.81

The standard measuring instrument selected for more accurate

measurements between the triple point of hydrogen and the freezing

point of antimony (903.89 K) was a platinum resistance thermometer,

though a platinum resistance thermometer is more sensitive for

measurement of cryogenic temperatures.

Resistance Thermometers:

Metallic Resistance Thermometers:

Since the resistivity of pure metals varies with change in temperature,

metals have been used as simple and reliable temperature-measuring

devices. Many elements or compounds, however, are not suitable for use

in low-temperature resistance thermometry because they lack one or

more of the desirable properties of an ideal resistance thermometer.

These properties include the following:

1. A resistivity that varies linearly with temperature to simplify

interpolation.

2. High sensitivity.

3. High stability of resistance so that its calibration is retaiined over long

periods of time and is not affected by thermal cycling.

4. Capability of being mechanically worked.

Although a number of metals such as lead, nickel, copper or indium are

more or less suitable for resistance thermometry, platinum has come to

occupy a predominant position, partly because of its excellent

characteristics, such as chemical inertness and ease of fabrication, and

partly because of custom. Certain desirable features such as ready

availability in high purity and the existence of a large body of

knowledge about its behavior have come into being as its use grew and

have tended to perpetuate that use. Its sensitivity down to 20K and its

stability are excellent. Its principal disadvantages are (1) low resistivity,

(2) insensitive low about 10 K, and (3) a variation in the form of the

resistance– temperature relation from specimen to specimen below about


12 | P a g e

30 K. for platinum, the dependence of resistance on temperature is

expressed by the following relationship:

Where is the resistance at T°C, is the resistance at the ice point

273.16 K, and A, B, C are constants determined by calibration of the

device for three out of the remaining fixed points. Typical values of the

constants for a 25-ohm platinum resistance thermometer are: A = 3.946×

° ; B = -1.108 × ° ; and C = 3.33 × ° .

The sensitivity of a resistance thermometer is defined as (1/R)(dR/dT). It

is desirable that the temperature coefficient (dR/dT) of a metal be

significantly high to make it sensitive as an element to be used for a

resistance thermometer over the entire range of temperature. Also, the

purer is the metal, lower is its resistance, R, and so more is its sensitivity

with temperature. For example, a 25-ohm (at room temperature)

platinum resistance thermometer will have a resistance of less than 0.2

ohm at 20K, whereas its temperature coefficient at 20K is one-fifth of

that at room temperature. Accordingly, platinum resistance thermometer

has a higher sensitivity at 20K than at room temperature. However, the

instrument should be able to measure the very low resistance at the low

temperature with precision. Similarly, indium is also found to have good

sensitivity over the entire range from 4K to room temperature. Lead has

high temperature coefficient, but it becomes superconducting at 7.2K,

beyond which it cannot be used as a resistance thermometer.

The metal element for the resistance thermometer needs to be free from

any mechanical strain, as it increases the resistance. It is thus necessary

to mount the metallic wire on a support ensuring that mechanical and

thermal strains are eliminated. One method of mounting designed,

involves winding the metallic wire in the form of a helix and then

winding the helix around a notched mica support, as shown in fig. The

sensing element is annealed in order to remove any mechanical strains

and is then inserted in a platinum tube. The tube is filled with helium gas

at 30 – 40 torr at room temperature prior to sealing. Several variations in


13 | P a g e

encapsulation and shielding are available for commercial applications

with time constants in the range of 1.3 to 1.6 seconds.

Platinum resistance thermometers. ( Capsule, strain–free)

Thermocouples:

Thermocouples are temperature measuring devices commonly used for

measurement of cryogenic as well as for above-ambient temperatures.

Thermocouples are simple, easy to install, inexpensive and temperature-

sensitive having low heat capacity. It is used as a secondary standard at

cryogenic temperature regions till as low as 12K. A thermocouple

consists of two dissimilar wires connected to each other at one end

where the temperature needs to be measured. The temperature difference

between the joined and unjoined ends (at reference temperature)

generates a difference in electrical potential (e.m.f) which may be quite

small and requires a sensitive instrument such as a galvanometer,

potentiometer, standard cell, low temperature bath for reference point.

For example, for measurement of low temperature, copper-constantan

thermocouple is very common and it generates 40Mv per degree at room


14 | P a g e

temperature whereas 17μV at 90K (liquid oxygen temperature), 5μV at

20 K (liquid hydrogen temperature) and almost zero at absolute zero.

Only limitation in measuring a very low temperature using a

thermocouple is that the reference point should be at the boiling point of

liquid nitrogen or liquid hydrogen at a known pressure. Otherwise, an

e.m.f., of the order of 5mV, should be measured with an accuracy of

1μV in order to get an accuracy of 0.1K, in case an ice bath is used to

provide a reference temperature.

Thermocouple types as defined by the ASTM are discussed below.

Type E Thermocouples. The ASTM designation type E indicates a

thermocouple

pair consisting of a Ni-Cr alloy and a Cu-Ni alloy. This type of

thermocouple has the highest Seebeck coefficient, S, of the three ASTM

standard thermocouple types commonly used at low temperatures, types

E, K, and T. Also, both elements of this thermocouple have low thermal

conductivity, reasonable homogeneity, and corrosion resistance in moist

atmospheres. This type is the best thermocouple to use for temperatures

down to

about 40 K.

Type K Thermocouples. The ASTM designation type K indicates a

thermocouple pair consisting of a Ni-Cr alloy and a Ni-Al alloy. The

sensitivity is only about half that of the type E combination at 20 K

(4.1μV /K compared with 8.5μV/K). The negative element is a bit more

homogeneous than the EN element. Both materials have low thermal

conductivity and are corrosion resistant in moist atmospheres. Type K

thermocouples are recommended by the ASTM for continuous use at

temperatures within the range 3-1533 K in inert atmospheres.

Type T Thermocouples. The ASTM designation for type T indicates a

thermocouple pair consisting of Cu and Cu-Ni alloy. Type T is one of

the older, more popular combinations, and is the only one of the

standardized types for which limits of error below 273.15 K have been


15 | P a g e

established. Type T thermocouples are recommended by the ASTM for

use in the temperature range from 89 to 644 K in vacuum or in

oxidizing, reducing, or inert atmospheres.

Gold-Iron Alloy Thermocouples. The increasing use of liquid

hydrogen and liquid helium has created a demand for specialized

thermometry below 25 K. Ordinary thermocouple combinations are only

marginally acceptable because of their low sensitivity in this range.

Dilute alloys of noble metals and transition metals, however, have

relatively high temperature sensitivity below 25 K; Au-2.1 at. % Co is

perhaps the best known of this type. Unfortunately, this alloy is a

supersaturated solid solution. Powell et al. found that the thermoelectric

power decreases with time when stored at room temperature. This

gradual change is probably due to diffusion of cobalt atoms to grain

boundaries. Dilute alloys of iron in gold are metallurgically stable and

have extremely useful thermoelectric properties at very low

temperatures. A differential thermocouple made with Au---0.02, 0.03, or

0.07 at. % Fe as the negative element and copper, "normal" silver (Ag-

O.37 at. % Au), or KP as the positive element provides a usable

sensitivity, even below 4 K.

Thermistors: Thermistors (TM) are essentially thermally sensitive resistors made up

of metal oxides. Frequently used materials are nickel, manganese, and

cobalt oxides. The temperature-resistance relationship for this type of

resistor has a negative slope much like the carbon or germanium

resistors. These resistors are becoming increasingly popular in

measurement and control circuits because they are small with short

response times, typically are of high resistance, which reduces the

overall effect of lead resistances, and have temperature-resistance

characteristics that are dependent on materials and procedures that allow

thermometers to be developed that are particularly sensitive over limited

ranges of temperature. Reproducibilities have been investigated

experimentally by Sachse and determined to be about ± 30 mK after


16 | P a g e

cycling between room temperature and liquid oxygen. After 1000

cyclings, the error was on the order of tenths of degrees.

Gas Thermometry: If the equation of state, i.e., the function relating pressure, volume, and

temperature, of a gas is known, the gas can be used to measure

temperature. If one of the variables is held constant and a second is

measured, the third can be calculated from the equation of state. In

thermometry, it has been found most advantageous to hold the volume

of a fixed amount of gas constant and measure the pressure. The

temperature of the gas is then determined. When properly corrected,

such a constant-volume gas temperature very closely approximates an

ideal gas thermometer, and is used to fix points on the absolute

temperature scale.

One of the simplest forms of the constant-volume gas thermometer

involves a bulb, which is at the low temperature to be measured. This

bulb is connected by a fine capillary to a Bourdon-type pressure gauge

maintained at room temperature. If the volume of the capillary is

assumed to be negligible, and if the gas can be assumed to be ideal over

the temperature range to be measured, then the temperature in the bulb is

given by the relation

T =

[ ] (1)

where is the volume of the gas-thermometer bulb, the volume of

the Bourdon pressure gauge, the temperature at ambient conditions,

and p the pressure measured in the gauge in consistent units. This simple

device can be quite accurate at low temperatures since most of the gas

will be in the gas-thermometer bulb. At higher temperatures, however, a

substantial amount of the gas will be in the Bourdon gauge, making the

thermometer rather insensitive to T. If the ratio of / is made

sufficiently large, such a device can have an accuracy of ±0.05 K at

temperatures below 30 K. In the same vein, Scott has noted that, if room

temperature is taken at 300 K and the ratio of / is equal to 20, a


17 | P a g e

straightline p-T relation through 20 and 77 K will deviate from Eq. (1)

by less than 0.2 K maximum over the 20-90 K temperature range.

Equation (1) may be considered the first step in obtaining an accurate

temperature with a gas thermometer, in that it corrects for the "nuisance

volume" or the volume of gas that is not at the temperature being

measured.

However, in order to obtain accurate results in gas thermometry, it is

also necessary to correct for the imperfection of the gas, the change in

volume of the bulk with changing temperature, variations in the amount

of gas adsorbed on the walls of the gas-thermometer bulb, and the

thermomolecular pressure gradient encountered at extremely low

pressures.

One engineering application of gas thermometers is achieved by

deliberately increasing the volume of gas maintained at ambient

temperature. This makes the gas thermometer nonlinear, increasing the

sensitivity at low temperatures, and compressing the scale at high

temperatures. At low temperatures, most of the gas in this arrangement

is at the measuring temperature and contributes to the measurement. At

higher temperatures, most of the gas is in the room temperature

reservoir, and does not contribute to the measurement. By using a

Bourdon gauge to show the pressure in this device, a simple gas

thermometer is achieved, which is useful for such purposes as

monitoring the cooldown of cryogenic apparatus. Accordingly, for

engineering applications, gas thermometry is recommended for

indicating the approximate temperature, or temperature trend. For

precision temperature measurements, the corrections are usually too

demanding for common use in the field.

Liquid level sensors:

Measurement of liquid level is important to know the amount of the

liquid remaining within the cryogenic storage vessel or dewar flask at

any instant of time. Liquid level measurement may pose problem, as it

has to be carried out under totally closed and insulated conditions. It can

be performed by a variety of methods, the simplest being the float and a


18 | P a g e

long stem with a pointer. The float may be used along with a mechanical

–electrical transducer for remote indication.

Engineering

Unit 5 ultra low temperature cryo refrigerators