powder metallurgy-sayfa 85

8/2/2019 Powder Metallurgy-sayfa 85

1/84

1

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


2/84

2

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


3/84

3

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.


4/84

4

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.


5/84

5

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


6/84

6

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.


7/84

7

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


8/84

8

.

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


9/84

9

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


10/84

10

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


11/84

11

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.


12/84

12

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.


13/84

13

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.


14/84

14

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


15/84

15

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


16/84

16

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.


17/84

17

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:


18/84

18

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


19/84

19

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).


20/84

20

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.


21/84

21

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


22/84

22

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:


23/84

23

[ ]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


24/84

24

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.


25/84

25

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


26/84

26

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


27/84

27

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.


28/84

28

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


29/84

29

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


30/84

30

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


31/84

31

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.


32/84

32

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.


33/84

33

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


34/84

34

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.


35/84

35

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.


36/84

36

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


37/84

37

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.


38/84

38

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.


39/84

39

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


40/84

40

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


41/84

41

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


42/84

42

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.


43/84

43

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%.


44/84

44

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


45/84

45

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.


46/84

46

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.


47/84

47

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.


48/84

48

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


49/84

49

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

powder metallurgy-sayfa 85

Documents