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1.POWDER METALLURGY
1.1. POWDER FABRICATION
1.1.1 MECHANICAL FABRICATION TECHNIQUE
There are four mechanisms for reducing a material into powder mechanical
combinations: impact, attrition, shear and compression. Impaction involves the rapid.
Instantaneous delivery of a blow to a material, causing cracks and resulting in size
reduction. Attritioning applies to the reduction in particle size by a rubbing motion.Shear is a cleavage type of fracture associated with operations like crushing. Powders
formed by shearing are coarse and not often found in powder metallurgy unless the
material is extremely hard. Finally, comminution can be by compressive forces: it the
material is sufficiently brittle it will not deform. But break into a coarse powder. The
formation of metal powders by mechanical techniques generally relies on various
combinations of these four basic mechanisms. The following subdivisions demonstrate
how these fundamental comminution techniques are manifested with respect to metal
powders.
1.1.1.1 Machining
Coarse powder with irregular shape results from the shear associated with the
machining of wrought metal. Because of the large amount of machining scrap
produced in metalworking operations, machining chips are an abundant source of
powder. This scrap can be further reduced in size by grinding. Machining is not a first
choice approach to powder fabrication, and by itself proves inefficient and slow.
1.1.1.2. Milling
Milling by mechanical impaction using hard balls is a classic approach to
fabricating powders from brittle materials. A jar mill such as diagramed in Figure1.1.1
uses a ceramic lined cylindrical jar filled with balls and the material to be milled. As
the jar rolls on its side, the balls continuously impact on the material, crushing it into
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powder. Milling is not useful for most metals because of their ductility, cold welding
and low process efficiency. Brittle materials are more responsive.
Figure1.1.1 A view of the action in a jar mill.
The jar is rotated on its side and the impact of
the falling balls leads to grinding of the
material into a powder.
1.1.2. ELECTROLYTIC FABRICATION TECHNIQUES
A powder can be precipitated at the cathode of an electrolytic cell under certain
operating conditions. Common examples of metals formed into high purity powders by
such an approach include titanium, palladium, copper, iron, and beryllium. The anode
and cathode reactions corresponding to copper and iron are shown in this Figure1.1.2.
The cathode deposit is removed and cleaned by washing and drying. Subsequently the
cathode cake is ground into fine powder and drying. Subsequently the cathode
cake is ground into fine powder and annealed to remove any strain hardening.
Figure1.1.2 The formation of metal powder
from an electrolytic cell. Material is dissolved
at the anode and deposited at the cattode
(examples of reactions are shown for copper
and iron)
1.1.3. CHEMICAL FABRICATION TECHNIQUES
Almost all metals can be fabricated into powder by a chemical technique.
Typically the particle size and shape can be adjusted over a wide range by control of
the reaction variables. There are several variants to the chemical synthesis approach;
powders can be formed by gas-solid, liquid, or vapor phase reactions.
1.1.31. Decomposition Of A Solid By A Gas
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The classic form of metal powder fabrication is oxide reduction. The process
starts with a purified oxide such as magnetically separated iron oxide (magnetite).
Such oxides are easily milled into fine powders. Oxide reduction is achieved by
thermo chemical reactions involving reducing gases such as carbon monoxide or
hydrogen.
Feo(s) + H2(g) Fe(s) + H2O(g)
Thus, for FeO reduction by hydrogen, as long as the moisture is removed from
the reaction, the reaction can go to completion.
1.1.3.2. Thermal Decomposition
Powder particles can be fabricated by the combination of vapor decomposition
and condensation.
1.1.3.2. Precipitation from a liquid
A dissolved metal salt such as a nitrate, chloride or sulfate can be treated to
produce either a metallic precipitate or a metal containing precipitate. Precipitates
involving metallic salts are an easy means of producing powder. A soluble salt is
dissolved in water and precipitated by a second compound.
The precipitation techniques are well suited to forming composite powders. In
this case, one phase is used to nucleate the precipitation reaction. Example nuclei are
thoria, Titania, and tungsten carbide.
The precipitated powders have some characteristics in common. Generally, the
crystallite size is quite small and agglomeration is a natural tendency. The powder
purity is usually over 99.5 % with the dominant impurities coming from the reaction
bath. The particle shape is irregular or cubic, or in some instances sponge-like.
Consequently, the flow properties are poor and the packing densities are low.
1.1.4. ATOMIZATION FABRICATION TECHNIQUES
In the last twenty years, P/M has turned to several advanced powder fabrication
techniques, which fall under the general heading of atomization. Prior to the
development of atomization, powder chemistry and shape characteristics could not be
fully controlled. The flexibility of the approach coupled to its applicability to several
alloys and easy process control, make it an attractive alternative. A main feature of
atomization is the general reliance on fusion-based technology.
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1.1.4.1.Gas Atomization
The use of air, nitrogen, helium or argon as a fluid for breaking up a molten
metal stream provides a versatile powder fabrication technique. The liquid metal
stream is disintegrated by rapid gas expansion out of a nozzle. The approach has
proven ideal for super alloys and other highly alloyed materials. The designs may vary
with respect to the metal feed mechanism and the sophistication of the melting and
collection chambers: however the main idea is to deliver energy (from a rapidly
expanding gas) to the metal stream to form droplets.
. Figure1.1.3 shows a schematic diagram of vertical inert gas atomizer. The
melt must be superheated over the melting ( liquids ) temperature.
Figure 1.1.3. A vertical gas atomizer. The mainfeatures are a vacuum induction furnace, gas
expansion nozzle, gas recirculation/supplysystem free-flight chamber and powder
collection chamber
Because of the volume of gas used in atomization, it is important to exhaust the
gas to avoid a backpressure. It is necessary to incorporate a cyclone separator.
Gas atomization can be performed totally under inert conditions. Thereby
maintaining the integrity of high alloy feedstock. The particle shape is spherical with a
fairly wide size distribution. The list includes gas type, residual atmosphere, melt
temperature and viscosity as it enters the nozzle, alloy type, metal federate, gas
pressure, gas federate and velocity, nozzle geometry, and gas temperature.
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The atomization physics can be described by the drawing shown as
Figure1.1.4. The expanding gas around the molten metal stream causes disturbances in
the melt surface, giving a cone shape after exit from the nozzle. From the top of the
cone, expansion causes the metal stream to form into a thin sheet. The sheet is unstable
because of a high surface area to volume ratio. The liquid continues to respond to the
shear and acceleration forces, giving first ligaments and subsequently finer spherical
particles. The size reduction is limited by the melt viscosity and temperature, and by
the response to the acceleration forces. The effect of superheating the melt above the
liquids is to decrease its viscosity and to prolong the post-atomization solidification
time. The particle shape sequence with distance from the nozzle is cylinder-cone-
sheet-ligament-sphere. Depending on the amount of superheat and other variables, any
one of these shapes may be produced.
Figure 1.1.5 The formation of a metal powder
by gas atomization involves the break-up the
liquid stream by rapidly expanding gas. The
stream first form into a thin sheet, and
subsequently forms ligaments, ellipsoids, and
spheres.
Shorter distances between the gas exit and melt stream favor better energy
transfer, aiding the formation of finer powders. The gas velocity on exit from theatomizer is the dominant factor in determining the resulting particle size. In terms of
metal characteristics a low- density metal favors coarser particle sizes because of more
rapid acceleration out of the expansion zone.
D1 = 3
2/1
3
VW
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Where m is the melt density and is the surface energy.
There is obvious interest in linking the mean particle size to the atomizationconditions. A Droplet formation during atomization is enhanced by a large difference
between the gases and melt velocities. This occurs with high gas pressures and gas
flow rates, giving an empirical form as follows
D =57.022.0
m
m
m
U
V
C
Where C is a nozzle geometry constant, and Um is the melt viscosity. A
particle size dependence on the inverse of the gas velocity has proven applicable to the
atomization of several metals, including tin, iron, led, steel and copper.
1.1.4.2. Water Atomization
Water atomization is the most common technique for producing elemental and
alloy powders from metals, which melt below approximately l600C. In Figure 1.1.5.
an example of water atomizer geometry is shown. The water can be directed by a
single jet, multiple jets or an annular ring. The process is similar to gas atomization,
except for the rapid quenching and differing fluid properties. High- pressure water jets
are directed against the melt stream, forcing disintegration and rapid solidification.
Consequently, the powder shape is more irregular than with gas as the fluid. Also the
powder surface texture is rough, with some oxidation. Because of the rapid heat
extraction, shape control requires superheats far above the liquids. Because of the high
cooling rate, the water -atomized particle takes less time to solidify. Chemical
segregation within an alloy particle tends to be quite limited.
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Figure 1.1.5. The water atomization process, where
multiple water jets disintegrate a molten metal
stream
Mathematical models for particle size from water atomization have similarities to
those for gas atomization. A high pressure, or high water velocity, causes a decrease in
the mean particle size. In a simle form the relation can be expressed as follows.
D = ( )aVC
sin.
Obviously, the water velocity is a major factor in controlling particle size.
1.1.4.3. Centrifugal Atomization
The desire to control particle size and the difficulties in fabricating powders from
reactive metals have led to the development of centrifugal atomization. The centrifugal
force throws off the molten metal as fine spray which solidifies into a powder. The
rotating electrode concept is shown in Figure1.1.6.
Figure 1.1.6 Centrifugal atomization by the rotatingelectrodes process is shown in this diagram. A
rapidly rotating spindle is melted by an arc using a
tungsten cathode. The powder is formed by the meltthrown from the anode, and can be solidified in
either a vacuum or inert gas environment
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.
The mean particle size is increased by higher melt rates, slower rotations, andsmaller anodes.
D =43.0
64.0
2.0
mWd
M
Where M is the melt rate, d is the anode diameter, W is the angular velocity, is the
surface tension of the melt and m is the density.
Typically, the melt rate is on the order of 10 -7 m /s the rotation velocity between
1000 and 50.000 rpm and the anode diameter between 2 and 5 cm
1.1.4.4. Other Atomization Approaches
The melt explosion (vacuum chamber ) technique in Figure1.1.8. uses a
hydrogen saturated liquid metal and rapid desaturation in vacuum to form a fine
powder spray. The melt is pressurized with 1 to 3 Mpa of hydrogen. A siphon tube
then exhausts the saturated melt into a large vacuum chamber. Both the high velocity
and hydrogen desaturation cause the melt to literally explode into the vacuum
chamber.
Figure 1.1.8 The melt explosion technique for
forming spherical powders. Molten metal ispressurized with hydrogen and exhausted via a
siphon tube into a low pressure chamber. The rapidpressure change and hydrogen desaturation from
the melt cause the liquid stream to explode into afountain of droplets. The droplets solidify duringfree-flight are collected at the bottom of the chamber
1.2 POWDER CHARACTERIZATION
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This chapter is designed to introduce the techniques and measures available for
describing powders. The influence of the powder characteristics on processing and
properties will be demonstrated in subsequent chapters.
1.2.1 POWDER SAMPLING
Atypical production lot may be several tons in size; a sample of this lot will
probably be on the order of a kilogram. Many of the modern analytical instruments
require sample sizes of a gram or less for particle size analysis. Assuming a spherical
shape, the particle population in one gram depends on the size and material density
( theoretical density).
1.2.2. PARTICLE SIZE
The size of a particle depends on the measurement technique, specific
parameter being measured, and particle shape. Particle size analysis can be achieved
by several techniques, which usually do not give equivalent determinations due to
differences in the measured parameters. The basis for analysis can be any of the
obvious geometric values, such as surface area, projected area, maximum dimension,
minimum cross sectional area, or volume. Particle size is probably one of the most
important powder characteristics to the powder metallurgist. Size data are most useful
when presented within the context of the measurement basis and the assumed particle
shape. A particle size analysis should convey information on the particle size
distribution, particle shape, and state the basis for measuring particle size. The desire is
to use a particle dimension most characteristic of the powder.
1.2.3. MEASUREMENT TECHNIQUES
1.2.3.l. Microscopy
The procedure is covered in American Society for Testing Materials
specification E20 (ASTM E20). Although the technique is reasonably accurate, the
tedium of sizing statistically significant quantities of particles has led to use of
automatic image analyzers. The image for analysis is generated by optical, scanning
electron or transmission electron microscopes. The instrument choice depends on the
particle size. By microscopic counting of diameter, length, height or area, a frequency
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distribution can be generated. Counting two or more small particles as a large particle
will cause a skewing of the distribution towards the coarse sizes.
1.2.3.2 Screening
The most common technique for rapidly analyzing particle size is based on
screening. A square grid of evenly spaced wires creates a mesh. Mesh sizes can not go
to very small opening sizes; thus, the screening technique is usually applied only to
particles larger than 38 m. There are electroformed meshes available down to 5 m,
but agglomeration and particle adhesion to the mesh generally make the electroformed
screens of little practical use. A listing of mesh sizes and opening sizes for the U. S.
Standard series of screens appears in Table l.2.3 (ASTM E11).
TABLE 1.2.1 Standard Sieve Sizes (U. S. Standard. ASTM E119 )
Mesh
SizeOpening in m
Permissible Variation
+,- m
Maximum Individual Opening
in m18 1000 40 1135
20 850 35 970
25 710 30 81530 600 25 695
35 500 20 585
40 425 19 502
45 355 16 425
50 300 14 363
60 250 12 306
70 212 10 263
80 180 9 227
100 150 8 192
120 125 7 163
140 106 6 141
170 90 5 122
200 75 5 103
230 63 4 89
270 53 4 76
325 45 3 66
400 38 3 57
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The powder is loaded onto the top screen and the screen stack is vibrated for a
period of 20 to 30 minutes. For particle size analysis, a sample size of 200 g is usually
sufficient when using 20 cm diameter screens. After vibration, the amount of powder
in each size interval is weighed and the interval percent calculated for each size
fraction (ASTM B214)
1.2.3.3. Sedimentation
Particle size analysis by sedimentation is most applicable to the finer particle
sizes. Particles settling in a fluid (liquid or gas), reach a terminal velocity dependent on
both the particle size and the fluid viscosity. On this basis, particle size can be
estimated from the settling velocity. Depending on the particle density and shape,
sedimentation techniques are most applicable to particles in the 0.05 to 60 m range.
Assuming a spherical particle shape, settling at the terminal velocity in a
viscous medium is represented by a balance of forces. The buovancy and viscous drag
forces act to retard particle settling as diagramed in Figure. Alternatively the
gravitational force, at the terminal velocity the forces are balanced. The settling force
equals mass times acceleration.
FG = gD m
6
3
Where D is the particle diameter, g is the acceleration (gravity) and m is the
particle density. The buoyancy force is determined by the volume of fluid displaced by
the particle,
FB = gD t
6
3
Finally, the viscous drag force Fv is given as.
FV = DVU3
U is the fluid viscosity. For a sedimentation experiment, the velocity is
calculated from the height and time. Combining equations gives.
V =( )
( )UgDtm
182
For the terminal velocity, which is known as Stokes law. It is experimentally
most convenient to work with a known settling height H while measuring the time for
settling.
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D = ( )( )
2/1
18
tmgtHU
Figure 1.2.1 The force balance leading to a constant settling velocity for a spherical particle in a
viscous fluid.
The technique of particle size analysis by sedimentation uses a predetermined
settling height and places a dispersed powder at the top of a tube. Measurements of the
amount of powder setting at the bottom of the tube (weight or volume) versus settling
time then allows calculation of the particle size distribution. Obviously, the fastest
settling particles are the largest while the smallest can take considerable time to settle.
Automatic instrumentation for performing sedimentation based analyses use light
blocking, x-ray attenuation, weight or settled cake height to determine the size
distribution.
Internal porosity in the powder decreases the mass, thereby causing slower
particle settling.
There are mathematical limits to Stokes law. The derivation assumes that
viscosity controls settling. Accordingly, at Reynolds numbers R in the range of 0.2 to
l.2 the assumption of viscosity controlled settling break down. At high settling
velocities the sedimentation model is invalid if the calculated Reynolds number is
large, where gives the Reynolds number in terms of the settling parameters. Finally,
the fluid and powder can not react chemically. In spite of these several difficulties,
sedimentation techniques are in use for several powder systems such as the refractory
metals.
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1.2.3.4. Light Scattering
1.2.3.5. Electrical Conductivity
1.2.3..6. Light Blocking
1.2.3.7. X-Ray Techniques
1.2.4. PROBLEMS IN PARTICLE SIZE ANALYSIS
For sieves, this is generally above 38 m. optical microscopy is restricted to
particles above l m. In contrast, techniques such as sedimentation are only applicable
to a narrow size range because of limitations in the applicable physics.
1.2.5. PARTICLE SHAPE
The shape of a particle is a distributed parameter, which can influence packing,
flow, and compressibility of a powder. Particle shape provides information on the
powder fabrication route and helps explain many processing characterictics. Because
of the difficulty in quantifying particle shape, qualitative descriptors are used. Figure
1.2.2 gives a collection of particle shapes and shows the appropriate qualitative
descriptors.
The most straightforward such descriptor is the aspect ratio. The aspect ratio is
defined as the maximum particle dimension divided by the minimum particle
dimension. For a sphere, the aspect ratio is unity, while for a ligament type particle a
value near 3 to 5 is more likely. A flake particle can have an aspect ratio in excess of
ten and in some instances can be as high as 200.
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Figure 1.2.2 A collection of possible particle shapes and qualitative descriptors.
1.2.6. INTERPARTICLE FRICTION
Under the general heading of interparticle friction come two main concerns:
powder flow and packing. As the surface area increases, the amount of friction in a
powder mass increases. Consequently, the friction between particles increases, giving
less efficient flow and packing. These concerns are important in automatic die filling
during powder compaction, as well as packaging, transportation, blending and mixing
of powders.
The main feature of friction is a resistance to flow. Also, the density or
packing properties decrease because of poor flow past neighboring particles. Theapparent density of a powder is the density (mass/volume) when the powder is in the
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loose state without agitation. This is also known as the bulk density. The tap density is
the highest density that can be achieved by vibration of a powder without the
application of external pressure. The theoretical density corresponds to the handbook
density for a powder material; the density when there is no porosity present. The angle
of repose is another friction index. It is the angle formed by pouring a powder into a
pile as shown in Figure 1.2.3, where the tangent of a equals the height divided by the
radius of the loose powder pile. Finally, the flow rate is a measure of the rate a powder
will feed under gravity through a small opening. Most fine powders will not flow
because of their high interparticle friction. Such powders are termed non-free flowing,
and present particularly difficult problems to engineers looking for high productivity in
forming operations.
Figure 1.2.3 The angle of repose is a measure
of the interparticle friction. It is determined
from the height and radius of the powder alter
passing through a funnel.
There are two common devices for measuring the apparent density. Examples
of both the Hall flowmeter and the Scott volumeter are given in Figure 1.2.4. The Hall
flowmeter is used for the coarser particles; both the flowrate and the apparent density
are measured by this device. Alternatively, the Scott device is applied to the fine
refractory powders which have higher interparticle friction. Both devices are covered
by ASTM specifications (ASTM B212 and B213 for the Hall and ASTM B329 for the
Scott).
The flow rate for a powder is usually expressed as the time for 50 g of powder
to flow through the Hall flowmeter , Smal flow times indicate free flowing powders
while long times are an indicator of high interparticle friction. The apparent density
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and flow times are easily obtained with the Hall flowmeter by combining a precision
volume cup with the funnel. In this case the apparent density is the weigh of powder
divided by the cup volume.
Another simple test for interparticle friction is the tap density. Powder is
Vibrated in a cylindrical volume for l000 cycles at 284 cycles per minute using a 3.2
mm throw from an eccentric cam (ASTM B527). Usually the initial powder volume is
250 ml. The tap density is the weight divided by the final volume. Both the tap and
apparent densities can be expressed as fractions of theoretical density.
Figure 1.2.4 The basic compenents of the Hall flowmeter and Scott volumeter for measuring the flow
and packing of powders.
1.2.7. CHEMICAL CHARACTERIZATION
The elemental powders are relatively high-purity materials where chemical
analysis focuses on the impurity concentration. The prealloyed
Powders constitute micro-castings with multiple elements in a predetermined
ratio. For the prealloyed powders, attention is given to the alloy composition
as well as the impurity concentrations.
Beyond the bulk chemical information, there is often a need to know the
surface condition of the powder. Hence, there is concern with oxides, adsorbed organic
films and the presence of surface coatings like silica.
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Beyond such tests, metallography can be applied to assess the inclusion
concentration. Also, for gas atomized powders, metallographic examination will show
the presence of internal gas pockets. In a few instances, techniques such as Auger
electron spectroscopy have been applied to characterize the surface chemistry. Most
recently, transmission electron microscopy has been applied to thinned particles to
determine the micro segregations and phases.
Bulk chemical characterization of a powder can be obtained from emission
spectroscopy, colorimetry, x-ray fluorescence and neutron activation analysis.
The prealloyed powders should be checked to verify adherence to chemical
tolerances. These powders tend to have higher oxide surface concentrations. In the
cases involving premixed powder blends (such as copper and tin to form bronze during
sintering), the blend chemistry should be checked and blend uniformity should be
assured by reblending and deagglomeration.
1.3. PRECOMPACTION POWDER HANDLING
This part discuses the powder handling steps before compaction, including
blending, mixing, classification and lubrication. The characteristics of common
lubricants are discussed as they affect powder properties.
1.3.1. PRECOMPACTION
It is necessary to tailor specific properties into a powder for easier compaction
and sintering. Examples of operations that occur in the pre-compaction stage include
classification, blending, mixing, agglomeration, de-agglomeration, and lubrication.
Classification is used to obtain a specific size fraction from a powder..
1.3.2. MIXING and BLENDING APPROACHES
Blending and mixing both combine powders into a homogeneous mass.
Blending refers to the combination of different sized powders of the same chemistry,
while mixing implies different powder chemistries. In spite of the recognized necessity
of such precompaction steps, the processes are poorly understood. These operations
can be a source of problems in fabricating components. Some simple rules reduce the
likelihood of problems:
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1. Do not use a powder after transport without reblending.
2. Do not vibrate a powder.
3. Do not feed a powder through a free-fall where fine and coarse sizes can
segregate due to different settling rates.
The mechanisms of powder mixing are diffusion, convection and shear. These
three types of mixing are illustrated in Figure 1.3.1 as diffusional mixing in a rotating
drum, convective mixing in a screw mixer, and shear mixing in a blade mixer. A
diffusional mix occurs by the motion of individual particles into the powder lot. An
inclined plane of the powder bed breaks down at the outer edge, allowing flow over the
surface.
Figure 1.3.1 The three modes of powder mixing are diffusion, convection and shear. These processes
are given schematically, although in powder mixing all three contribute to the homogenization sequence
1.3.2.2. Powder Lubrication
Interparticle friction reduces the powder flow and packing properties. A more
fundamental problem is the friction between the die wall and the powder duringpressing. As the compaction pressure is increased, ejection of the powder mass from
the die becomes more difficult. Consequently, lubricants are used to minimize die wear
ease ejection from the die body.
There are two means of lubricating a pressing; die wall and powder lubrication.
Die wall lubrication is preferred in theory, but is not easy to incorporate into automatic
compaction equipment. The lubricants are usually mixed with the metal powder as a
final step before pressing. For metal powders, stearates based on Al. Zn. Li. Mg. Or
Ca are in common use. The stearate is added to the metal powder as a fine (typically
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atomized) spherical form. A mean size of 30 m is common. Concentrations of the
lubricant range up to 2.0 wt.%.
1.4. COMPACTION
Pressure is used to form powders into engineered shapes with close
dimensional control. This compaction process involves both rearrangement and
deformation of the particles, leading to the development of inter-particle bonds.
1.4.1 PHENOMENOLOGY of COMPACTION
An external pressure is needed to both shape the powder and promote higher
packing densities. The schematic of powder compaction shown in Figure 1.4.1
provides a basis for defining the stages of compaction. The initial transition with
pressurization is from a loose array of particles to a closer packing. Subsequently, the
point contacts deform as the pressure increases. Finally, the particles undergo
extensive plastic deformation. At the beginning of a compaction cycle, the powder hasa density approximately equal to the apparent density. Voids exist between the
particles, and even with vibration, the highest obtainable density is only the tap
density. For a loose powder there is an excess of void space, no strength and a low
coordination number (number of touching neighbor particles). As pressure is applied,
the first response is rearrangement of the particles, giving a higher packing
coordination. The initial pressurization is therefore analogous to vibrating the powder,
because the density increases by powder restacking. Large pores caused by particle
bridging are initially filled by rearrangement. The rearrangement portion of
compaction is aided by hard particle surfaces (such as with oxides).
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Figure 1.4.1 A simplified view of the stages of metal powder compaction. Initially, repacking occurs
with the elimination of particle bridges. With higher compaction pressures, particle deformation is the
dominant mode of densification.
. High pressures increase density by contact enlargement through plastic
deformation. The interparticle contact zones take on a flattened appearance. During
deformation, cold welding at the interparticle contacts contributes to the development
of strength in the compact. The strength after pressing, but before sintering, is termed
the green strength.
At low pressures, plastic flow is localized to particle contacts. As the pressure
increases, homogeneous plastic flow occurs throughout the compact. With sufficient
pressurization, the entire particle becomes work (strain) hardened as the amount of
porosity decreases.
1.4.2. CONVENTIONAL COMPACTION
Conventional powder compaction is performed in hard tooling of the type
shown in Figure 1.4.2.
When pressure is transmitted from both the bottom and top punches, the
process is termed double action pressing. Alternatively, when pressure is transmitted
from only one punch, the process is termed single action pressing.
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Figure 1.4.2 A conventional punch and die set
for powder compaction; the punches provide
compression and the die gives lateral support
to the powder.
A general system of part classification exists for declaring the shape
complexity. As the number of part levels and the complexity of the pressing directions
increase, the part classification also increases as noted in table 1.4.1.
There are several modes of pressing and accordingly there are several types of
presses, including hydraulic, mechanical, rotary, isostatic, and anvil.
TABLE 1.4.1 The Classifications of P/M Patrs
Class Part Levels Pressing Directions
1 One One
2 One Two
3 Two Two
4 Sveral Two
1.4.3. THEORETICAL BASIS
The main problem in powder compaction is the die wall friction with the
powder. This friction causes the applied pressure to decrease with depth in the powder
bed. There are many important intrinsic characteristics of a powder that affect the
pressure-density-strength relations in a powder compact. These include the material
properties like hardness, work (strain) hardening rate, surface friction, and chemical
bonding between particles. Equally important are the extrinsic factors associated with
the powder size, shape, lubrication and the mode of compaction.
1.4.3.l. Fundamentals of Compaction
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Consider a cylindrical compact of diameter D and height H such as drawn in
Figure 1.4.4. Analyzing a thin section of height d H when theres is an external pressing
force, shows that the pressure on top of the element P and that transmitted through the
element bottom Pb will differ by the normal force acting against friction.
Mathematically, the balance of forces can be expressed as follows:
( ) nb uFPPAF + 0
Figure 1.4.4 The balance of forces during die
compaction, where the difference in the
applied and transmitted pressures results from
the frictional force at the die wall. A small
element from the compact serves as the basis
for calculating the pressure distribution.
Where Fn is the normal force, u is the coofficient of friction between the
powder and the die wall, and A is the cross sectional area. The normal force can be
given in terms of the applied pressure with a proportionality constant z. the factor z
represents the ratio of the radial stress to the axial stress, thus
Fn =zPDdH
The friction force Ff is calculated directly from the normal force and the
coefficient of friction as,
Fr= zPDdHu
Combining terms gives the pressure difference between the top and bottom of
the powder element d P as,
dP = P-Pb = -Ft/a = -4uzPdh / D
Integration of the pressure term with respect to compact height shows that the
pressure at any position x below the punch is given by the following expression:
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[ ]D
uzxP
Px 4exp
This equation is applicable to a single action pressing. It shows that the
pressure decreases with depth in the powder bed. Examples of plots of this expression
are given in Figure. Note the effect of an increase in the term uz H/D; attention will be
given to the significance of this term in part 3 of this section. The wall friction
contributes to a decreased pressure with depth. Hence, for homogeneous compaction,
small height to diameter ratios are desirable.
For a single ended pressing, the average compaction stress is estimated as,
( )DuzHP 21
and for a double ended pressing the average stress is approximately.
DuzHP 1
The average stress is dependent on both the geometry (H/D), the interparticle
friction (z), and the die wall friction (U). High average streses are attained in short
compacts, with large diameters and lubricated die walls. The most important parameter
is the height to diameter ratio of the compact.
1.4.3.2. Particle Bonding in the Green State
A high initial packing density aids the formation of interparticle bonds.
Additionally, a clean powder surface aids bond strength. When the compaction force is
sufficiently high, shear forces will act to discrupt surface films.
1.4.3.3. Goals in Compaction
The predominant goal in powder compaction is to achieve compact propertieswith minimal wall friction. Thus, efforts are made to decrease the axial to radial forces
to minimize die wear and improve pressing efficiency. The height to diameter ratio is
important to uniform compact properties. Generally, when the height to diameter ratio
exceeds five, die compaction is unsuccessful. A low compact height allows for
successful single action pressing: however, double action pressing is the predominant
approach.
The ratio zu H/D is a sensitive gauge of the pressing operation. Powder
lubrication raises z while lowering u. First, the die wall friction u depends on the
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amount of lubricant, the more lubricant, the lower the friction. Second, the die wall
friction decreases as the pressure increases. Third, the pressure ratio z increases with
approximately the square root of the applied pressure.
In die pressed powder compacts, density gradients result from the pressure
gradients. For a copper powder, the density gradients with both single and double
action pressing are shown in figure. In both compacts, the height to diameter ratio is
unity, the coefficient of friction is 0.3 and the pressure ratio is 0.5.In the single action
pressing, the lowest density occurs at the compact bottom. Alternatively, the double
action pressing has the lowest density in the very center of the compact.
The other important factor is the height to diameter ratio. As this ratio is
increased, density gradients in a compact will increase and the overall compact density
will decrease. For a single action pressing of copper using a constant compaction
pressure of 700 M Pa. Plots of the approximate pressure distribution in the compacts
are given for height to diameter ratios of 0.42, 0.79 and l.66. An increase in the height
to diameter ratio results in greater density gradients and a lower bulk density.
1.5 SINTERING
Sintering is the process whereby particles bond together at temperatures typically
below the melting point by atomic transport events. A characteristic feature of
sintering is that the rate is very sensitive to temperature. The driving force for sintering
is a reduction in the system free energy, manifested by decreased surface curvatures
and an elimination of surface area.
1.5.1. SINTERING THEORY
1.5.1.l. Characteristic Stages
Consider two spherical particles in contact such as shown in Figure 1.5.1. As the
bond between the particles grows, the microstructure changes as shown in Figure
1.5.2. The initial stage of sintering is defined as occurring while the neck size ratio
X/R is less than 0.3 for uncompacted powders.
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Figure 1.5.2 The development of the interparticle bond during sintering, starting with a point contact.
The pore volume shrinks and the pores become smoother. As pore spheroidization occurs, the pores are
replaced by grain boundaries.
During initial stage sintering shows that it is the curvature gradient at the neck
which guides the mass flow.
In the intermediate stage, the pore structure is much smoother. The pores have
an interconnected, cylindrical structure. At this point attention shifts from the
interparticle neck growth to the grain-pore structure. The predominant development of
compact properties occurs in the intermediate stage. The driving force is the interfacial
energy, including both the surface and grain boundary energy. It is common for grain
growth to occur in the latter portion of the intermediate stage. As a consequence, either
pore motion or pore isolation can occur.
With shrinkage of the pore structure, the cylinders become unstable at
approximately 8% porosity. At this point, the cylindrical pores collapse into spherical
pores which are not effective in slowing grain growth. In many cases, the
microstructure exhibits pores separated from the grain boundaries. The isolation of the
pores at grain interiors results in a drastic decrease in the densification rate. In the final
stage, the kinetics are very slow. The driving force is strictly the elimination of the
pore-solid interfacial area. The presence of a gas in the pore will limit the amount of
final stage densification.
1.5.1.2.Transport Mechanisms
The transport mechanisms are the ways in which mass flow occurs in responseto the driving forces. There are two classes of transport mechanisms surface transport
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and bulk transport. Surface transport, as shown in Figure 1.5.2 involves neck growth
without a change in particle spacing (without densification).these paths are shown in
Figure 1.5.2. In contrast to surface transport, bulk transport controlled sintering results
in net dimensional changes. The mass originate at the particle interior with deposition
at the neck region, as shown in Figure 1.5.2. The bulk transport mechanisms include
volume diffusion, grain boundary diffusion, plastic flow, and viscous flow (for the
amorphous solids)
Figure 1.5.3 The two classes of sintering
mechanisms as applied to sphere-sphere
sintering. Surface transport mechanisms
provide for neck growth by moving mass from
surface sources (E C= evaporation-
condensation, SD = surface diffusion, VD =
volume diffusion). Bulk transport processes
provide for neck growth using internal mass
sources (PF = plastic flow, GB = grain
boundary diffusion. VD = volume diffusion).Only bulk transport mechanisms give
shrinkage.
1.5.1.3.Initial Stage Sintering
A point contact between particles leads to the growth of a neck at a rate which
depends on the mechanism of mass transport. The sintering rate depends on the rate of
material arriving from the various transport paths. Although viscous flow is a possible
transport mechanism, for crystalline materials it is not applicable.
The model for neck growth during initial stage sintering represents the
contribution of several investigators as noted by Thummler and Thomma, and Exner.
Assuming monosized spheres initially in point contact, the neck growth by a single
mechanism can be represented by a generalized equation,
( ) mn
R
BtR
X
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Where X is the neck radius, R is the particle radius, t is the isothermal sintering time,
and B is a collection of material and geometric constants.
It is important to consider the distributed nature of powders when discussing
the particle size effect. The models for sintering assume a homogeneous geometry.
However, in real powder systems there is a distribution in particle size, number of
contacts per particle, and contact flattening due to compaction.
1.5.1.4. Intermediate Stage Sintering
The intermediate stage is the most important in determining the properties of
the sintered compact. This sccond stage is characterized by densification coupled to
grain growth. The pore structure becomes smooth but remains interconnected until the
final stage. In many instances, dimensional change is not acceptable during sintering.
For such cases, short sintering times are typically combined with lower sintering
temperatures and high compaction pressures to minimize densification. Alternatively,
with the refractory metals, emphasis is on achieving densification. Consequently, the
intermediate stage is viewed quite differently. For this discussion, the focus will be on
the physics of intermediate stage sintering without a distinction between the possible
merits and demerits of the observed densification
1.5.1.5.Final Stage Sintering
Final stage sintering is a slow process wherein isolated, spherical pores shrink
by a bulk diffusion mechanism. The isolation of a pore in the final stage of sintering is
illustrated in Figure 1.5.3. For the pore sitting on a grain boundary, a small dihedralangle causes a large pinning force. Spherical pores are expected after grain boundary
breakaway. After boundary breakaway, the pore must diffuse vacancies to distant grain
boundaries to continue shrinking, which is a slow process. Also, with prolonged
heating, pore coarsening will cause the mean pore size to increase while the number of
pores will decrease. Differences in the pore curvature will lead to growth of the larger
pores at the expense of the smaller, less stable pores.
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Figure 1.5.3 The sequence of steps leading to pore isolation and spheroidization in the final stage of
sintering; a) pore on the grain boundary exhibiting an equilibrium dihedral angle, b)and c)correspond
to grain growth with pore drag, and d)represents pore isolation because of boundary breakaway.
1.5.2 ENHANCED SINTERING
There are four common approaches to sintering enhancement in metal
powders: hot pressing, phase stabilization (or mixed phase sintering). Activated
sintering, and liquid phase sintering.
1.5.2.l. Hot Pressing
Uniaxial hot pressing resembles die compaction with both an upper and lower
punch. The rate of densification due to an external stress can be estimated in terms of a
surface energy enhanced driving force. The action of an external stress is to promote
grain and particle sliding by diffusional processes, to generate excess vacancies, and to
cause pore collapse. The overt effect is a more rapid densification. More extensive
discussion of hot pressing is given in the next chapter on full density processing.
1.5.2.2. Phase Stabilization
The volume diffusivity of a material is determined by several factors including
the temperature, crystal structure and the defect configuration. For a material like iron,
the volume diffusivity at 9l0C is 330 times higher in the body- centered cubic (BCC)
phase, ferrite, than the face-centered cubic (FCC) phase, austenite. Stabilization of the
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BCC phase provides an avenue to more rapid sintering of iron. Elements like
molybdenum, phosphorus and silicon stabilize ferrite above the polymorphic
transformation temperature.
1.5.2.3.Activated Sintering
The term activated sintering refers to any of several techniques which lower the
activation energy for sintering. The term implies enhanced densification or improved
properties in the sintered product. Activated sintering allows for a lower sintering
temperature, shorter sintering time, or better properties. Several techniques have been
invented to achieve this goal, ranging from chemical additions to the powder, to the
application of external electrical fields. In this respect, mixed phase sintering
treatments can be categorized as activated sintering.
In activated sintering, the amount of activator and the particle size are very
important parameters. First, the activator must be either a metal or compound which
fores a low melting temperature phase during sintering. Secondly, the activator must
have a large solubility for the base metal, while the base metal shown have a low
solubility for the activator. The operation of the activator is to slay segregated to the
interparticle interfaces during sintering. Such a segregated layer provides a high
diffusivity path for rapid sintering. The lower melting point ensures a lower activation
energy for diffusion, while the solubility ensures that the activator is not dissolved into
the base metal during sintering.
Chemical additions are the most successful means of activating sintering.
1.5.2.4. Liquid Phase Sintering
In two phase systems involving mixed powders, liquid formation is possible
because of differing melting ranges for the two or more components. In such a system,
the liquid may provide for rapid transport and therefore rapid sintering if certain
criteria are met. The liquid must form a film surrounding the solid phase, thus wetting
is the first requirement. Secondly, the liquid must have a solubility for the solid. The
formation of a liquid film has the benefit of a surface tension force acting to aid
densification and pore elimination. In this sense, the liquid phase acts like a low
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pressure external stress. Common systems involving liquid phase formation during
sintering include Cu- Co, W-Cu, W-Ni-Fe, W-Ag, Cu-Sn, Fe-Cu, WC-Co, and Cu-P.
The combination of wetting, liquid flow and particle rearrangement all
contribute to a rapid change in volume of the compact. With continued heating in the
presence of a liquid phase, the solid phase begins dissolving into the liquid. If the solid
has a high solubility in the liquid, then it is possible for the liquid composition to
recross a solidus boundary and solidify.
1.5.3. SINTERING ATMOSPHERES
Due to their porous structure, pressed powder components react more readly
with the surrounding atmosphere than fully dense materials. For this reason the
sintering atmosphere is very important. The protective atmospheres used are mainly
gases, in specials cases vacuum. The choice of gas must taken into account possible
reaction between the gas. These reactions depend on temperature and pressure and are
numerous. Because gases used in commercial production often contain trace gases
such as H2, H2O, CO, CO2 or N2. Additional gases may be envolved during
aannealing due to interactions with the sintering components.
1.5.3.1.Pure gases
Hydrogen (H2) is the most common of the commercially pure gases. Although
pure dry hydrogen is a relativly expensesive protective gas, it is widely used as a
sintering atmosphere because it provides the most effective reducing atmosphere.
Because of the high damger of explosion resulting from air ingress, special safety
precautions must be taken. Hydrogen-air mixture4s are explosive in the range of 4 to
74% H2; their minimum ignition temperature is 574C.
1.5.3.2.Dissociated (cracked) ammonia
Sintering plants often use dissociated ammonia ewhen a furnace gas is required
which will have a reducing effect. Dissociated ammonia has a high hydrogen content is
free from CO, CO2 and water, and does not contain any other oxygen or sulhur
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compounds. Its use is suitable for many materials including those, which contain
alloying components, which oxidise readly (Cr-Ni steels). Due to its high H 2 content
the gas is decarburising and is therefore not suitable for sintering steels containing C.
1.5.3.3.Protective gases produced by burning hydrocarbons
1.5.3.4.Vacuum
Various developments in vacuum technology have widened the use of vacuum
in sintering. these developments include the development of high performance pumps
and other additional equipment as well as the availability of furnaces capable of
continues operation. Vacuum has the advantages that metals are protected from
oxidation (a high vacuum of 10-2 Pa, for instance yields a dew point of about -90C)
And no impurities enter the furnace zone during sintering. Furthermore, evaporation
from the surfaces of the parts causes a certain self purification of the sintering stocks
vacuum deoxidation is used to remove oxides, which is adhere to most mass produced
sintering materials after pressing. . However it is a slow process which is a
disadvantages of this processing method for this reason vacuum (high vacuum) tends
to be used as a sintering atmosphere only when the materials to be sintered have a very
high sintering reactivity especially with oxygen, moisture and the hydrogen.
1.5.4. SINTERING FURNACES
The sintering furnace provides the time- temperature control to the sintering
cycle. Additionally, it contains the atmosphere, provides for removal of the lubricants
and binders, and controls the heat treatment. The furnace performs these various
functions in either batch or continuous mode. A batch furnace is loaded with thematerial to be sintered and then is raised to temperature. A continuous furnace
provides for the compact treatment by controlling the position in a preheated furnace.
Figure 1.5.4 shows the type of time-temperature cycle needed in commercial sintering
treatments. The difference between furnace types depends on control of either the
furnace temperature or compact position versus time.
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Figure 1.5.10 The sequence of operations occurring in a sintering furnace. The lower diagram shows
the time-temperature profile typical to metal powder sintering.
In continuous furnaces, parts are moved through a multiple zone furnace by a
conveyor, such as a belt, pusher or other mechanical device. Usually, the conveyor
proves to be a major limitation in the furnace operating temperature. Several different
heating elements are available for generating the temperature. Elements which require
a reducing atmosphere are kept under hydrogen while at temperature. Otherwise, the
furnace heating elements can be located external to the atmosphere, with radiant
heating through a furnace muffle.
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2.PARTICLE PACKING CHARACTERISTICS
2.1. STRUCTURES IN ONE AND TWO DIMENSIONS
There are two very different types of packing structures, random and ordered.
A random packing is constructed by a sequence of events that are not correlated with
one another. The result of such a random assembly procedure is a structures without
long-range repetition. Random structures have a lower packing density than attainable
with the high packing density ordered structures. An ordered structure occurs when
objects are placed systematically into periodic positions, as are the bricks in a wall or
atoms in a crystal structure.
The spherical particle shape has received greatest attention in three-
dimensional packing. This is because only one size parameter, the diameter, is needed
to specify the dimension of spheres. Other than regular polyhedral shapes, (for
example, a cube), most other shapes require multiple parameters to specify their size
and shape.
The analogous packing problem in one dimension is termed parking and is
analyzed in terms of segments placed on a line. For an ordered structure, the parking
density of line segments will equal 100%, because of perfect end-to-end alignment of
the segments. This is similar to a string of pearls without any gaps. Without a random
placement of segments the coverage is less than complete. In three dimensions the
problem is termed packing, while in one and two dimensions the problem can also be
referred to as parking and covering, respectively.
2.1.1. PACKING OF MONOSIZED SEGMENTS IN ONE DIMENSION
In the ordered structure, the assembly of the packing is systematic, and the
fractional packing density is 1,00. As illustrated in figure 2.1.12 The coordination
number is two with one contact at each end. Conceptually the first segment is placed at
one end of the string, the second is placed just in contact with the first, and the processis repeated to fill the string. Each added segment creates one new contact, which is
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shared by two segments, giving a net coordination increase of two contacts per
segments. Total coverage occurs with this end-to-end ordered structure.
figure 2.1.1 one dimensional packing of segments along a line a) ordered packing packing with full
coverage b) random packing with incomplete coverage
2.1.2. PACKING OF MONOSIZED SEGMENTS IN TWO DIMENSION
2.1.2.1 Ordered Packing
Because of the shape, the packing structure is not totally covering for the
underlying structure. Indeed, significant overlap of the disks is required to attain total
coverage, with in an estimated excess in disk area of 21% over the covered area
necessary to produce a complete covering. For this reason, adisk (or sphere in three
dimension) is termed a low packing efficiency.
There are three ordered packing of disks that can be repeated to fill space, as
shown in figure2.1.2.these are the best characterized by the number of contact points
for each disk, which is the coordination number Nc, and the fraction density . The
fraction density is the density expressed as a fraction of the theoretical density for the
material. The lowest density structure has a coordination number of three and the
highest density structure has a coordination number of six. The packing density
increases with the coordination number. There is no repetive unit with five-fold
symmetry. However a statistical model of two-dimensional packing gives an estimated
density of 0.78 for the five-fold geometry.
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Figure 2.1.2. a sketch of the ordered structures of disks packed in two dimensions with
coordination numbers of three, four, and six
The six-fold geometry is termed closed-packed. Packing disks on every other
lattice site in a square grid, where the occupied sites are those having either both
coordinates odd and both even, can construct it. This structure gives the theoretical
maximum packing density for disks. This planar structure is the same as that which
makes up the most dense ordered packing in three dimensions. The actual minimum
unit for creating this geometry is cluster of three disks. This is the unit cell in two-dimensional space that is space filling.
2.1.2.2. Random Packing
The random packing density of disks in two-dimension is largely dependent on the
procedure used in two assembling the packing. Indeed, two random conditions are
possible, loose and dense. Most studies use some force in maintaining contact between
the disks, giving a maximum packing density for the random structure, the dense
random packing. This can be unidirectional force, such as gravity, or a central
attraction force. Random packing without such a force will allow low density regions
with zero or one contact per disk, the random loose packing. Alternatively, packing
formed with a force will have at least two contacts per disks and a correspondingly
higher density. Vibration has a slight influence on the packing density, but this
influence is less than observed in three-dimensional packings. With small packing
cluster, cluster size also effect. Generally at least 1000 disks are needed to ensure
behavior representative of true random packing without disruption from container.
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The actual packing density for a random mixture can vary over a considerable
range, yet the transition between random and ordered packing occurs when the
fractional density exceeds 0.82.
The coordination number in a random packing is variable from point to point.
Some regions with a coordination of six will exist while other regions will have values
as low as two. The structure is better characterized as regions of order separated by
random or defective regions. Consequently, a random packing with a density over
approximately 0,82 can be treated as a mixture of random and ordered regions.
2.1.3. PACKING OF MIXED SEGMENTS IN ONE DIMENSION
The random placement is important in packing problems, since random events
are more typical in natural process. Although randomly placed segments produce a
packing density below that for an order structure, if two segments sizes are used to
randomly pack a line, then it is possible that the smaller segments can preferentially
fill the voids left in packing of larger segments. For a bimodal one-dimensional
packing density depends on the size ratio between the segments and the compositional
ratio. The size ratio denoted by DL/DS, which is the ratio of the large to small sizes.
The composition is given in terms of the fraction of small segments X S and the packing
density ig given as .f the segments are very different in size then the smaller
segment will increase the packing efficiency by filling many of voids between the
larger segments. However, the additional factor of composition becomes important: if
there are too few of the small segments then there is little packing benefit.
Alternatively if there are too many of the small segments, then the packing density is
controlled by their inherent void space.
It is possible that a distribution in segment sizes would be beneficial in
attaining a high packing density from randomly placed segments. The character of the
optimal distribution presents a difficult problem. In computer simulations of random
one-dimensional packings, it has been determined that wide variations in the
distribution width are indeed beneficial. The packing density increases as the
normalized coefficient of variation increases. The coefficient of variation for a
distribution is defined as the standard deviation divided by the mean size. Goldman et
al. examined several types of distribution and found that the packing density not only
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increased with large coefficient of variation, but a high population of large segments
was most favorable. For a given packing density the small segments break up the line
length more rapidly than the large segments. That is the small segments preempt space
disproportionately to their packing contribution.
2.1.4. PACKING OF MIXED DISKS IN TWO DIMENSION
It is possible to improve the packing or covering of disks by placing small
disks in the voids between large disks. Both ordered and random structures are
possible. The size ratio of disks determines the packing coordination at the highest
density
For the most efficient packing improvement as the gain in density per disk, the
added disk should just touch the three neighboring disks. Using the generalized
geometry shown in figure2.1.4.1The three existing disks have radiuses of R1 R2 and
R3. The radius of the disks that just touches these disks is noted as R4 and can be
calculated as follows:
1 / R4=(1 / R1) + (1 / R2) + (1 / R3)+2[(1/ R1R2) + (1/ R1R3) +(1/ R2R3)]1/2
If the three large disks are equal in size, this equation predicts R4 will have a
radius of 1/6.464 or 0.1547 of the large disk radius. The procedure for filling with
smaller disks can be continued with still smaller disks fitted into each of the voids
remaining after the first level of filling. Accordingly, the number of disks increases by
a factor of three as each new size class added.
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A general case is that of the disks sizes packed into the voids of an existing
structures where the disks sizes are very different. In this case more than one disks is
allowed to fit into each void. If each disks size has associated with it a fractional
density , then by filling the voids with smaller disks the packing density of the
mixture mix is improved to give,
mix =1 (1- )k
Where K is the number of levels of sizes. This says that the voids existing after
positioning the first level of diks, equal to 1 are filled to increase the packing
density by an additional amount . For an ordered bimodal mixture with an infinite
ratio of large to small disks sizes, the peak packing density will converge to 0.9913 at
the optimal composition. This differs from the efficient bimodal case where the large
to small size ratio is 6.464, which gives a maximum packing density of 0.9503. The
fractional density approaches unity as the number of size levels increase. How ever in
practice putting the small disks into the proper sites presents a mechanical problem
that limits the actual coverage.
The structure of binary disks mixtures has important implications with respect
to amorphous materials and random packing of particles. Consequently several studies
have been conducted to view thee two- dimensional structures using disks or spheres
with a size ratio close to unity. The two-dimensional factors are the size ratio and
composition of the mixture. The fractional packing density of a random assembly is
increased by mixing large and small disks. The degree of improvement depends on the
size ratio: if the sizes of the disks in a mixtures are not very different, then the packing
density shows little improvement over the random case.
In a mixture of large and small, three structures can form, depending on the
density. A random packing exists at low densities. At high densities, the structure is
ordered or at least exhibits regions of order surrounded by regions of disorder.
Depending on the composition and size ratio, segregation by size can also be seen,
especially when themixtures is vibrated. At intermediate densities with small size
ratios the structure is termed hexatic since there are local regions of order.
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2.2. FACTORS AFFECTING PARTICLE PACKINGSGenerally the density of a material has no significant influence on its fractional
packing density. Particles of an equal size and shape will pack to the same
fractional density in spite of differing theoretical densities. However, several
other factors do cause differences in fractional packing densities. The factors are
particle size, particle shape, agitation, particle size distribution, surface texture,
agglomeration, container size, segregation, bridging, surface-active agents, internal
powder structure, and cohesion.
2.2.1.STABLE POSITION
For gravitational stability a particle must have contact with at least three other
particles. Figure 2.2.1 illustrates the addition of a new particle to an existing
layer of particles. The initial point contact is unstable in comparison with the
lower energy double contact. In turn, a lower height and energy can be achieved
by further rolling the sphere into the valley between the three stationary
spheres. Within a powder mass, an individual particle requires at least four contacts
within a powder mass to ensure stability. These four contacts cannot lie on a
single equator or single hemisphere of the particle
Figure 2.2.1: an added particle attains a stable position by first impacting on one existing particle,rolling to contact two particles and finally rolling into a valley between existing particle
As the packing density of a powder decreases, conceptually it reaches a point
where the compact is no longer stable. Under perfect conditions stability might
persist at very low packing densities. However, a random structure becomes
unstable if there are fewer than 4.75 average contacts per particle. Based on
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various correlations between packing density and coordination number, a fractional
density of 0.35 for monosized spheres corresponds to approximately 3.5 to 5.0
contacts per sphere. This range agrees with the mean value of 4.75 contacts per sphere
mentioned above. Packed particles with fewer contacts will be unstable
PARTICLE SIZE
For packings composed of large particles, the particles size is not important
to the density. However, when the mean particle size is below approximately 100
m there is more interparticle friction, and particle bridging is more likely to occur.
The decreasing packing density with smaller particles is due to an increase in the
surface area, a lower particle mass, and a greater significance of the short-range,
weak forces such as electrostatic fields, moisture, and surface adsorption. Since
interparticle cohesion increases with a smaller particle size, there is more
agglomeration and inhibited packing. The smaller particles give a lower
packing density. The packing densities can be very low for particle sizes
significantly below 1 m.
2.2.3.PARTICLE SHAPE AND SURFACE TEXTURE
Another form of interparticle friction arises from irregularities on the particle
surface. The greater the surface roughness or the more irregular the particle shape,
then the lower the packing density. The data for the particle shape effect on
packing density are scattered, yet some general patterns are apparent. Figure 2.3.1
provides a schematic of the general particle shape and surface roughness
effects on the fractional packing density. On the left, the packing density is shown
as a function of the relative sphericity, which is defined as the surface area of a
sphere of equivalent volume divided by the actual surface area of the particle. The
closer the particle shape is to being spherical, the larger the relative sphericity.
On this basis both particle shape and surface texture are included in the relative
sphericity. The right half of this figure shows the effect of the relative surface
roughness. The relative roughness is a measure of the texture on the powder
surface for an otherwise spherical shape. In this regard, the effect of surface
roughness is similar to the particle shape effect. This is due to bridging of the
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particles. The use of vibration or lubricants can help attain a high packing density,
but problems may arise with agglomeration or size segregation. Water or various
oils can reduce the interparticle friction; however, treatments that increase the
surface stickiness of a powder will degrade the packing density.
Figure
2.3.1 schematic plots of the effects of particle shape and surface texture on the dense random fractionalpacking density. The highest density is associated with smooth spherical particles.
For powders of the same size but different shapes, the packing density
will decrease as the shape departs from equiaxed (spherical). This is easily seen in
the packing of fibers compared to spheres. The length to diameter ratio provides a
measure of the departure from an equiaxed shape. As the shape becomes more
fibrous, with a larger ratio of length to diameter, the packing density is reduced. In
powder mixing, an irregular particle shape will interfere with mixing, but will also
help maintain a homogeneous mixture by interfering with demixing. Density can
be improved by mixing different sizes of particles. This packing benefit is
independent of shape, but the starting densities are lower with irregular particle
shapes. However, with certain shapes under vibration, a high packing density
may be achieved by orienting the irregular particles. Such a high packing
density occurs most typically with equiaxed particles.
2.2.4. AGGLOMERATIONSmall particles cause difficulty in attaining a high packing density
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because of agglomeration due to cohesion. The attractive forces between
particles become larger as the surface area increases and the
particle mass decreases. In addition, small particles have a greater
tendency for vapor condensation at the particle contacts. Agglomeration
can be induced in a powder by inhomogeneously distributing a wetting
liquid. Most commonly, a condensed vapor will form pendular bonds
between particles. These bonds strengthen the particle cluster, but
inhibit dense packing. This is a particular problem with submicron-sized
powders exposed to humid air.
Agglomeration makes mixing more difficult. An alternative is to create
conditions that give rise to repulsive forces between particles by using thin coatings
of polar molecules. Surface repulsive forces contribute to high packing densities by
reducing the interparticle friction found with powders possessing cohesive forces.
Particles agglomerate into clusters of high coordination number separated by high
porosity regions, as sketched in Figure 2.2.3. Although this is an idealized situation,
many examples of agglomeration are evident in submicron powders.
Agglomeration occurs mostly with smaller particles, because of a high
surface area and the action of one of the weak forces. The common weak forces
are van der Waals attraction, electrostatic charges, chemical bonding, capillary
liquid forces or magnetic force. The van der Waals force is signi ficant for
parti cles below 0.05 m in size, Agglomeration can also occur during mixing
due to cold welding at the particle contacts.
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Figure 2.4.1 A sketch showing the large pores associated with the interagglomerate in an agglomeratedspherical powder the overall packing density is reduced by agglomeration.
Most typically, particles agglomerate due to adsorbed surface films,
especially during periods of agitation. Atmospheric vapors condense and establish
a surface concentration dependent on their partial pressure. Water is the most
typical vapor to condense on a powder. The amount of water adsorption depends on
the relative humidity and the surface curvature. Four cases of adsorption are
possible. First, at low vapor pressures the powder surface IB uniformly coated
with a thin layer of adsorbed vapor. Second, as the partial pressure increases, a
critical level is reached where the vapor condenses to form capillary bridges
localized at the particle contacts. These bridges are termed pendular bonds and are
shown schematically in Figure 2.4.2a.Third, as the vapor pressure increases, the
funicular state occurs. In the funicular state the pendular bonds merge, but the
pores are less than totally filled by liquid. In this state the pores are smooth and
surrounded by liquid. A connected path exists in the both the vapor and liquid
phases as shown in Figure 2.4.2.b, with the vapor phase existing as a cylindrical
shape. Finally, when the pore structure is saturated, the pores are filled with
liquid. This case is shown in Figure 2.4.2.c. For water vapor and spherical powders,
the-pendular bond state is anticipated at relative humidity levels between
approximately 65 and 80%.
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Figure 2.4.2 The states associated with agglomeration of powders due to wetting liquid: (a) pendular, (b) funicular, and (c)
saturated
A negative consequence of agglomeration is a decrease in, the packing
density. This is a particular problem with small particles. Clustering of particles,
especially those of similar size, is an unexplained characteristic of many structures. As
the particle size decreases and the number of particles in each agglomerate
increases, the agglomerates become stronger and exhibit a lower maximum packing
density. Besides decreasing packing density, agglomeration also creates problems
with mixing, settling from suspensions, compaction, and sintering, especially for
those systems with wide particle size distributions. The sensitivity to the particle size
distribution arises because the small particles are the primary cause of
agglomeration. In a wide particle size distribution, the smallest particles can exert a
strong effect on the larger particles. Alternatively, agglomeration can be selectively
used to minimize size segregation in powder handling.
2.2.5. SURFACE ACTIVE AGENTS
Small quantities of surface-active agents are often added to particles to alter
packing or mixing characteristics. Some common additives are polyvinyl alcohol,
stearic acid, sodium oleate, glycerine, and oleic acid. These additives reduce
interparticle friction by lubricating surfaces via short-range repulsive forces.
Generally, the flow and packing of particles are improved by the presence of' the
appropriate surface-active agent. The level of improvement is dependent on the
molecular size of the additive, its polar character, the layers of coverage, the particlesurface condition, the particle size, and the temperature. Polar molecular
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coatings with short-range interactions aid in keeping particles from agglomerating.
This is most important with the submicrometer particles that are dispersed in a
fluid for processing, such as in slip casting. The particle dispersion is
maintained by use of short range repulsive forces, possibly induced by surface
charges as measured by the zeta potential. The viscosity and surface energy of
the additive are not as important as the polarity and wetting ability. Agglomeration
is less of a problem with a narrow particle size distribution and larger particle sizes.
In contrast, sticky particle surfaces will have a high level of agglomeration, leading to
a lower particle packingdensity.
Intermediate chain-length polymeric molecules are used to lubricate powder
compaction, where they are used in high concentration. Alternatively, at low
concentrations small organic molecules are optimal because of their polar
character. Generally, a backbone chain length of approximately ten carbon
atoms is optimal as a surface additive for inorganic particles. Even so, for large
particles the relative packing benefit is low.
2.2.6. INTERNAL POWDER POROSITY
Many powders contain internal porosity, which is sometimes total ly
isolat ed from the powder surface. Shows sketches of cross-sectioned
particles with differing internal pore structures: a) fully dense, b) entrapped
pore, and c) open pore. Then closed porosity will not. Interact with a penetrating
f lu id . In contrast the sponge-like structure has vapor phase communication
from the external surface to the inner pores. Figure 2.6.1 contains two optical
photographs of cross-sect ioned and poli shed iron' powders.
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Figure.2.6.1 sketches of three forms of the particles with varying internal pore structures (a) dense (no
pores) (b) closed internal pore and (c) open internal pore.
The packing laws for particles ignore the internal porosity within the particles;
the focus is on the interparticle pores with the assumption of dense particles. If a
particle contains internal pores, then the intraparticle porosity will degrade the
packing density. Thus, in mixed particle size systems, the predicted mixture density
must be corrected for the internal porosity. Let s be the fractional solids content
for the powder, giving the fractional intraparticle porosity as 1 s Then, with f as
the predicted external fractional packing density (interparticle porosity is (1 e ),
the overall packing fractional density is,
= e. s
This equation says that the overall packing density is the product of the
fractional densities of the particles times the particle packing density. Generally in
this treatment, the focus will be on the interparticle porosity. However, when porous
particles are involved in the packing, the actual solids content will be reduced by
the intraparticle porosity. For very porous particles, this correction can be
substantial.
Beyond lowering packing density, internal porosity can influence several other
attributes. For example, the open pores will increase the measured specific surface
area. These are typically much smaller pores than the interparticle voids;
consequently adsorption and trapping of fluids will be favored in these
intraparticle pores. These will preferentially collect and retain wetting fluids. In a
sense, agglomerated particles represent one case of powders with internal pores.
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2.2.7 CONTAINER WALL
The container used to hold a powder will induce a local area of order at the
container wall in an otherwise random packing. The effect is more pronounced for
flat, smooth containers, giving local regions of oscillating high and low porosity in
the first few particle layers near the wall. Even in flexible containers there is
ordering near the wall. Besides packing density, the container wall influences
measurements because of the low-density regions near the wall. The packing
coordination is higher in the first few layers of particles near a container wall.
Figures 2.7.1 and 2.7.2 illustrate the magnitude of the container wall effect in terms
of the fractional packing density. Figure2.2.6plots the local packing density versus
distance from the wall in sphere diameters. This decaying oscillation in packing
density with distance has been confirmed in several studies. The wall effect persists
for several particle diameters into the packing. This same influence is evident at the
interface between a crystallized solid and its liquid; damped density oscillations can
be seen in the liquid bordering on the solidification interface. Figure 2.2.7 shows the
integral packing density versus distance for spheres packed in a cylinder. The inte-
gral density decreases from a low value at the wall to a constant value of
approximately 0.64 within the first two particle diameters.
Figure 2.7. 1 The loca l fr acti onal densit y ve rsus the dista nce from the container wall for monosizedspheres packed in a cylindrical container.
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Figure 2.7.2 The integral fractional packing-density for spheres in a cylindrical container.
There is less sensitivity of the integral density in comparison with the
local density shown in Figure 2.71.
Depending on the particle size, particle shape, and container shape, it takes
from one to ten particle diameters from the wall to establish truly random
packing. The effect is larger at higher packing fractions. In each case, as the
randomness increases, the packing density approaches an asymptotic value as the
ratio of container diameter to particle diameter increases. The
effect of the container wall on the packing density has been expressed in various
mathematical forms. For a given container, the container size influence on
density increases with the particle size and with the surface area of the
container. This same behavior can be seen when a close-packed structure
is separated. The resulting unfilled depressions on the surface of the
close-packed layer result in a slight density decrease. For spherical particles
the results by Ayer and Soppet fit the following equation:
f = 0.635 0.216 exp(-0,313 D c/D) (2.2)
Where D is the sphere diameter, D is the container diameter, and fis
the factional packing density. They found the overall packing den sity to be
within 1.5% of the calculated value.
For nonspherical powders there is inherently more randomness to the
packing; thus, the wall effect decays over a shorter distance from the container
wall. Equations for rough spheres and cylinders are analogous to those shown
above for hard, monosized spheres. Mixed particle sizes aid in minimizing the
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porosity variations at the container wall. Accordingly, as the width of the particle
size distribution increases, there is less influence from the container wall
Figure 2.7.3 Fractional packing density for random loose and random dense packingsof steel spheres, showing the extrapolated limiting densities with no container wall effects
2.2.8 SEGREGATION
Another concern in studying powder-packing characteristics is segregation in
mixed powders. This can lead to uneven packing densities and to distortion in
compaction and sintering. There are three causes of segregation: differences in
particle size, density, and shape. Of these three, size segregation is dominant. For
example, a pow
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