SOLID STATE SINTERING

Dr. Palanki Balakrishna

Principal, Bhoj Reddy Engg College for Women, Hyderabad bpalanki@rediffmail.com

August 17, 2009

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CONTENTS 1 Introduction

2 Solid State Sintering

3 Fundamentals of sintering

3.1 Surface forces 3.2 Driving force for sintering 3.3 Geometry of sintering 3.4 Stages in sintering 3.4.1 First stage 3.4.2 Intermediate stage 3.4.3 Final stage 3.5 Material transport in sintering 3.6 Density and shrinkage 3.7 Role of grain boundaries

3.7.1 Types of solid-solid interfaces 3.7.2 Pores on grain boundary 3.7.3 Boundary pinning 3.7.4 Rules of grain growth 3.8 Firing schedule

4 Multicomponent systems

4.1 Sintering of mixtures 4.2 Kirkendall effect

5 Additive effects in sintering

5.1 Preservation of the ideal powder characteristics 5.2 Provision of high diffusivity paths 5.3 Enhancement of lattice diffusion 5.4 Prevention of exaggerated grain growth

6 Effect of pre-sintering processes

7 Defects in sintering

7.1 Origin of defects 7.2 Hourglassing 7.3 Lamination 7.4 End-capping 7.5 Low density 7.6 Bloating 7.7 Radial and circumferential cracks 7.8 Coring

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List of figures Fig. 1 Powder particles of increasing specific surface area by way of decreasing particle diameter. Fig. 2 Three particles of the same diameter but with increasing surface areas. Surface roughness and porosity increase the surface area. Fig. 3 Effect of process parameter (calcination temperature) on development of particle morphology. (a) High temperature calcination yielded coarse particles (b) low temperature calcination yielded fine particles Fig. 4 Structural and topographical features of a solid with areas between which a driving force for transfer of matter exists Fig. 5 Sintering shown in two dimensions Fig. 6 Truncated Octahedron (Tetracaidecahedron). This is the lowest energy configuration for the grains in a solid Fig. 7 Experimentally observed frequency distribution of the number of edges per face in various systems. These mostly lie between 4 (in the case of square) and 6 (in the case of hexagon) Fig. 8 Stages of sintering shown in three dimensions (a) The particles are in contact (b) Necks have formed between contacting spheres (c) Necks have grown and pores form a continuous channel along three-grain edges Fig. 9 (a) Variation of permeability with relative density (b) Variation of open porosity and closed porosity with relative density. Note that beyond 95% density, there is no open porosity and permeability is zero. Fig. 10 Compared to a tensile test bar, the stress distribution at a weld neck is loaded in reverse by the pull of surface tension acting upon its necked region Fig. 11 Diffusion paths at a sintering neck: a slice of material is removed from the grain boundary by (1) lattice or (2) grain boundary diffusion and is distributed on the pore surface, mainly by (3) surface diffusion Fig. 12 Shrinkage of UO2 pellets sintered in a heating microscope Fig. 13 Shrinkage of 5 mil copper wire compacts, sintered in hydrogen at 100, 1050 & 1075C. Original void volume 9% Fig. 14 Schematic drawing of polycrystalline specimen. The sign of curvature of the boundaries changes as the number of sides increases from less than six to more than six, and the radius of curvature is less, the more the number of sides differs from six. Arrows indicate the directions in which boundaries migrate. Fig. 15 (a) Pore shape distorted from spherical by moving boundary (b) Pore agglomeration during grain growth Fig. 16 Comparison of the linear shrinkage as a function of time during sintering at 1000C and 1100C of compacts of tungsten powder (0.5 m size) without and with the addition of 0.5wt.% nickel Fig. 17 Schematic model of enhanced sintering Fig. 18 Phase diagram for an ideal additive Fig. 19 Schematic representation of the effects of powder size distribution on the sintered microstructure. For example, in (a-1), with a narrow size distribution and control of the grain boundary-pore interaction, dense sintered bodies with the grain size slightly larger than the particle size are possible. Fig. 20 (a) flaw less compact before and after sintering (b) Flaws existing in green compact get enlarged in sintering Fig. 21 Conditions leading to lamination (a) Compact within a die on punch withdrawal with radial stress balancing die reaction. (b) ejected portion after stress relief and radial expansion Fig. 22 Conditions leading to end-capping (a) axial expansion within die of a perfectly elastic compact on punch withdrawal (a) die wall friction is zero (b) die wall friction significant

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1 Introduction In the course of manufacture, some times problems arise in meeting quality requirements of the product. Experiments are usually carried out to determine the cause of a problem and to arrive at a solution. All theory is nothing but generalizations formed out of experiences of several engineers, who have taken the trouble of documenting and publishing their knowledge. The science of sintering gives you the experience of others in a nut shell. A little theoretical knowledge greatly narrows down the extent of experimentation required in your shop floor. The savings in manufacturing cost are enormous ensuring survival in a competitive environment. One way to make a metallic component is to begin with melting, casting into an ingot, hot working or cold working and machining. What you get is a solid piece, consisting of crystals or grains. The grains are randomly oriented and each grain is enveloped by a surface called the grain boundary. The ideal shape of a grain is the tetracaidecahedron (a symmetrical shape that has eight hexagons and six squares as its faces). You have in the process, some loss due to scaling in hot working and material removal in machining. Instead of casting into an ingot, you may even cast the molten metal into the final shape. You have to remove the risers, sprues, flash etc which are not needed in the part and there may be some machining. Another way to make the same metal component is to begin with a metal powder, give a shape to the powder by compacting in a die and then heat it to some temperature, without melting it. Again you end up with a solid piece, consisting of grains with grain boundaries, the ideal shape of a grain being the tetracaidecahedron. In this process, you do not have to detach risers, sprues and flash and you have no machining losses. Since there is no melting, you are conserving a lot of energy. This process of heating a shaped powder compact at a temperature below its melting point is called sintering. The unfired compact is called the green body. It consists of several particles, weakly held together and with several vacant spaces in between. The density of the green shape is about 40 to 70% of the theoretical density of the metal or material. On heating, the vacant spaces disappear. There is an increase in density from the original 40-70% TD to the final density of almost TD. This has been achieved by the movement of atoms from one place to another. Since porosity has decreased, there has to be a shrinkage accompanying densification. There is no change in shape, though there is a change in size. Why sintering? In a globalised economy, you can survive only by cost reduction and quality improvement. This is most visible in the automotive sector. What was earlier made by conventional metallurgy is now made by powder metallurgy. For economy, you have to switch over to sintering. For quality improvement, you have to understand the basics of sintering which also gives you the ability for defect prevention. What are the forces at work in this remarkable phenomenon of densification in the solid state? Consider a liquid in a beaker. The liquid consists of atoms or molecules. Most of the atoms are in the bulk, while a few are on the surface. What are the forces acting on each atom? Each atom experiences a force of attraction by its neighbour. In the bulk, the forces cancel out, whereas at the surface, there is a net inward force. This net inward force tends to pull the liquid inwards. In other words, it tends to decrease the surface area. Nature has provided for a reduction in surface area or surface energy. The minimum surface area for a liquid is a sphere. A drop of mercury or a drop of water tends to assume the shape of a sphere, the minimum surface area configuration. When you bring two drops of mercury together, these two readily combine into one, again, minimizing the surface area. Reduction in surface area is spontaneous. On the other hand, if you wish to divide a masse into smaller pieces, work has to be done, as in ball milling. In crystalline solids too, atoms in the bulk experience no net forces, while those on the surface experience a net inward force. Just as drops of liquid easily join together, solid particles too can easily join together to form a unified mass. This is what is being achieved in sintering. Bring together a number of particles, and in appropriate conditions, they join together to become a single mass. While the joining becomes possible at room temperature for liquids, the solid particles require some heating, since the atoms become mobile only on heating. What is remarkable is that there is no melting involved. Sintering then is the process of heating a powder compact at a temperature below its melting point, usually 0.5 0.8 Tm, in order to enhance the strength and/or density. We say strength or density, since there is no densification in the making of porous filters. What is happening in sintering? We will first see the two dimensional picture. Consider circles in contact with each other. Each circle represents a powder particle. The group of circles represents a pressed powder compact, where the particles are in contact with each other, as opposed to loose particles. The configuration is characterized by two things. There are curved surfaces and there are voids. Voids are present as the

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surfaces in contact with each other are curved. The density is low due to the presence of voids. The presence of voids is indicative of existence of surface energy. If the voids can be eliminated, it means that you have reduced the surface energy. In sintering, the curved surfaces are becoming straight or flat and the voids are getting eliminated. The density also increases by elimination of the voids. This is our aim in sintering. If the circles are changed to hexagons, in other words, if the curved lines are replaced by flat ones, there are no voids left. This is precisely what happens in the sintering process. Curved surfaces flatten and voids tend to round, shrink and disappear. What are the requirements for sintering? We said that nature has provided for reduction in surface energy or surface area. So we must have a large amount of surface area to begin with. In other words, we must have fine particles. Fine particles have large surface areas. For example, in one ceramic powder, the surface area is of the order of 3 m2/g. Once you have fine particles, what else is required? We need temperature. The atomic mobility increases with temperature. Since atoms move by diffusion, temperature is an important parameter. Since diffusion is time dependent, time will be another important parameter. Which materials can be sintered? Metals, ceramics, composites can all be sintered. 2 Solid State Sintering The term sintering is used to describe the phenomena which occur when useful solid products are made from inorganic powders - either metallic or nonmetallic, of suitable particle size (a few microns or less in diameter). Sintering may be carried out in pure metals, alloys, compounds, mixtures or composites. Compaction provides the basic shape to the powder and sintering leads to inter-particle bonding and thereby improvement in properties. Sintering is the process of heating a powder compact to a temperature between 1/2 to 3/4 of the absolute melting point (with or without the application of external pressure) by which particles are formed into a coherent body, to achieve strength and density. At high temperatures, atoms of a solid take part in diffusional motion. Surface atoms are much more mobile than the atoms in the interior of a crystal. The diffusional movement of atoms enables crystals to reach their equilibrium shape when main-tained at high temperature. For a compacted powder, this shape is a solid piece of material. The formation of solid pieces from powder by a surface and volume diffusion process is called `sintering'. A green compact has 40 to 60 percent void space. During sintering, the particles join together, the piece shrinks, and much of the void volume which resulted from the initial misfit of the powder particles is eliminated. This can be achieved by solid state reactions or alternatively in the presence of a liquid phase. Sintering can be regarded as the coordinated shape change of all grains in a powder compact to allow them arrange themselves in a space filling manner. Sintering is the process through which small particles fuse or join together to form a monolithic, dense body in the absence of large scale melting. Solid state sintering frequently occurs at temperatures less than MP but high enough so that atomic motion in the solid state is significant. Particle boundaries disappear but grain boundaries are present after sintering. Prior to sintering, the compact is brittle and its strength, known as green strength, is low. Bonding and fusion of the individual particles occur during sintering. The nature and strength of the bond between the particles depend on the mechanisms of diffusion, plastic flow, and evaporation of volatile matter in the compact, recrystallization, grain growth and shrinkage. Sintering is the fundamental fabrication process in both powder metallurgy and ceramics, but there are important differences, which stem from the differences in the nature of the materials. Powder Metallurgists are most interested in the phenomenon of particle joining, since a compact of moderate strength can be plastically deformed and heat-treated to control the final product. Brittle ceramics cannot be treated in this way, and the porosity and grain size present at the end of the sintering operation are those that appear in the final product. As a result, ceramists have focused most attention on compact shrinkage, pore elimination and grain growth. The process variables in sintering are (a) sintering temperature (b) sintering time (c) sintering atmosphere. The material variables are (a) particle size and particle size distribution (b) particle shape (c) particle structure (d) particle composition and (e) green density. The success of sintering is frequently judged, in the case of metals, by mechanical properties, the reduction of area, the ultimate tensile strength and the density; or in the case of ceramics, by the porosity, cold crushing strength and permanent changes on re-heating. 3 Fundamentals of sintering 3.1 Surface forces

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A drop of a liquid tends to assume a spherical shape in order to minimize its surface energy. The energy results from unsaturated chemical bonds at the surface and it therefore exists as a surface property in crystalline solids as well as in liquids. It is a tendency of nature that processes take place that lower surface energy. When drops of a liquid are brought together, the drops lose their individual surfaces and acquire a common surface enveloping them all. Similarly when solid particles are brought together contacting each other, under appropriate conditions, the particles can lose their individual surfaces and become a single solid by sintering. 3.2 Driving force for sintering The driving force for sintering is the excess surface energy of a compact of powder particles, and all sintering phenomena bring about a reduction in the total interfacial energy. The powder particles change their shape by rounding off sharp corners or developing facets at low energy orientations consistent with the constraints placed by contacts with adjacent particles. Sintering is motivated by capillary forces (climb of liquids in capillary tubes) or surface tension forces (spheroidization of water droplets) which try to reduce the total surface and consequently the energy of the system. These forces actuate mass flows which tend to enlarge contact areas between adjacent particles and decrease the pore volume. The mass of powder contains extra energy which can be released when the powder compact is converted into a solid body. Fig. 1 shows particles of decreasing size and increasing specific surface area. Fig. 2 shows three particles of the same diameter but with increasing surface area. Particle size reduction is usually much more effective to achieve densification than particle surface roughening or introducing porosity in the particle. Process parameters in powder production determine the particle size achieved. For example, Fig. 3 shows the effect of calcination temperature on the size of the particles obtained. High surface energies in the powder particles are achieved by suitably choosing the process parameters. The difference in rates of spheroidization of water droplets and that of densification of metal or ceramic powder compact is due to the difference in viscosities. Even close to melting point, solid metals have viscosity orders of magnitude higher than that of liquid water. If one considers pores rather than droplets, this stress is supported by the material surrounding the pores. The effect is equivalent to that of an external hydrostatic pressure, and the stress will operate in a direction to make the pores shrink by whatever mechanism of matter transport may operate. Fig. 4 shows the structural and topographical features of a solid with areas between which a driving force for transfer of matter exists. 3.3 Geometry of sintering Sintering can be regarded as the coordinated shape change of all grains in a powder compact to allow them arrange themselves in a space-filling manner. This implies that the grain centres move towards each other, thereby reducing the size of the compact and eliminating the pores. In two dimensions, initially circular grains (with voids in between) would become hexagons (without voids in between) to give full packing, as shown in Fig. 5. In three dimensions, spheres would transform into tetrakaidecahedra. Both final arrangements give a space filling packing with minimum possible specific interface area in their respective dimension. The reduction of surface and interface area is the driving force for the process. In a crystalline material, atoms can only be removed and added at interfaces (with the exception of dislocation climb). The grain centre approach is achieved by removing atoms from the grain boundaries and adding them at the pore surfaces, transported by thermally activated diffusion. In contrast, in amorphous materials, the grain shape change can be brought about by viscous flow. In materials with glide systems with sufficiently low shear stress (most metals, and possibly MgO), it can occur by dislocation glide. A multiphase body consists of a series of cells or grains which meet in stable configurations, three to an edge and four to a point. These three-grain edges and four-grain corners are the fundamental units of structures and their shapes are determined by the equilibrium between the various surface energies involved. 3.4 Stages in sintering 3.4.1 First stage

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For a collection of particles of a single phase the dihedral angle will be usually high and therefore points of contact between particles will grow into necks if some mechanism is available to allow the equilibrium geometry to be reached. This stage of neck growth is known as the first stage of sintering. The first step to achieving full density is to maximize the contact points per grain (coordination number) by reordering the grains through translation and rotational movement. Secondly, as soon as the temperature is high enough to allow diffusion, the network of grain boundaries and pore surfaces has to reach a status of local force equilibrium. As a consequence, the grain contact areas have to widen until the equilibrium angle is reached. Together with the increase in coordination number, this leads to a change in curvature of the free grain surfaces from convex to concave. A coordination number of 12.5 - 14.5 is found in dense structures. The initial stage has ended when this final value is reached and no further arrangement of grains is possible. Irregular packing of mono-sized spheres can be viewed as a mixture of simple cubic and hexagonal close packing. The resulting relation between density and coordination number is plotted. From this the initial stage can be estimated as ending at 75% relative density. For coarse-grained materials with long diffusion paths, densification will stop at this stage. 3.4.2 Intermediate stage All the grains are now in contact with their nearest neighbours, so that the movement of grains as a whole has stopped. Shrinkage can only proceed by transfer of material from between the grains to the neck surface brought about by lattice or grain boundary diffusion. The pores form a continuous network consisting of cylindrical channels around the necks. The stage ends at around 93% relative density when the pore channels become too narrow to be stable and decompose into closed pores. After a time, and at a point where the porosity is about 15%, the grain boundary energy begins to be a significant contribution to the total energy of the system and the grain boundaries begin to rearrange themselves to minimize their total area. The geometry in this second stage of sintering thus becomes that of an assembly of polyhedral grains with pores along the three-grain edges, and the tendency to minimize the grain-boundary area results in grain growth. This arrangement of the grain boundaries is very similar to that of the soap films in froth, and it can be shown that the average cell or grain possesses 13.4 faces, 22.8 vertices, and 34.2 edges. This equilibrium shape of a grain in a solid, called tetracaidecahedron (which is actually a truncated octahedron) is shown in Fig. 6. Fig. 7 shows experimentally observed frequency distribution of the number of edges per face in various systems. These mostly lie between 4 (in the case of square) and 6 (in the case of hexagon). 3.4.3 Final stage The pores continue to shrink as sintering proceeds and in the third stage of sintering they become unstable as approximate cylinders along the three-grain edges and pinch off to become isolated pores at four-grain corners. This stage commences at about 5% total porosity and may continue until all porosity is eliminated. In the final stage, the pores are now closed and situated mainly at four-grain junctions. Major grain growth can now occur. If the pores contain gases, which are insoluble in the solid, then on shrinking the internal gas pressure will rise and eventually stop shrinkage. The different stages of sintering are illustrated in 3 dimensions in Fig. 8. Necks forming between particles substitute grain boundary area for surface area, always with a net reduction in total interfacial energy. The resulting network of porosity often is reduced in volume; it often coarsens and eventually loses connectivity as the branches pinch off, giving first blind pores and finally isolated pores. Models have been proposed for each stage of the sintering process: (a) two-sphere initial stage model (b) tubular pore intermediate stage model and (c) isolated void on grain boundary model. A combined stage model has also been derived. The basic phenomena during sintering are (a) shrinkage, (b) pore elimination, (c) grain growth and (d) pore growth. While compacted powder is permeable, the permeability is lost on sintering, as shown in Fig. 9a. The decrease in porosity is shown in Fig. 9b. 3.5 Material transport in sintering Compared to a tensile test bar, the stress distribution at a weld neck is loaded in reverse by the pull of surface tension acting upon its necked region, as shown in Fig. 10. Early in the sintering process, when the radii of curvature of the free surfaces of the pores are very small and the stresses due to surface-tension forces are high, material transport by dislocation motion should predominate in analogy to the dislocation

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motion mechanism of creep at high stresses. At small particle sizes the pressure difference due to surface curvature is of the order of the shear strengths normally observed. When the necks between particles grow and the pores spherodize, the radii of curvature of the free surfaces increase, the stresses decrease and material transport by diffusional flow should take over, again in analogy to the diffusional creep at low stresses (Nabarro Herring Creep). The vacancy source is the surface at the periphery of the neck between sphere and flat, which has a very small radius of curvature and is under high tensile stress due to surface tension forces. Vacancy sinks are either the flat or nearly flat surfaces adjacent to the neck or the grain boundary between sphere and plane. Vacancy diffusion takes place under the influence of a gradient of stress which is also a gradient of chemical potential. Diffusion paths in a sintering neck are shown in Fig. 11. 3.6 Density and shrinkage The shrinkage obtained in a compact of uranium dioxide as a function of sintering temperature in a heating microscope is shown in Fig. 12. Once the powder characteristics are fixed, the sintered density of a compact depends on the green density and the sintering conditions (Temperature, time and furnace atmosphere). As the magnitude of these parameters is increased, sintered density increases. The increase in density is accompanied by shrinkage. However, it may be desirable to produce a part of high density without allowing much increase in density (and consequent shrinkage) during sintering for the following reasons:

1. For structural parts, a higher sintered density is desirable, as it leads to better mechanical properties.

2. For better dimensional accuracy, it is preferable to minimize the increase in density during sintering. This can be achieved by using a powder of high compressibility. Such a powder gives a high green density and allows moderate sintering temperature. Another important benefit of such powder is that larger parts can be produced with a specific press tonnage. Sintering mostly involves densification but not always. For example, loose powder or lightly pressed powder is used in some types of filters where open porosity is required to be obtained in addition to formation of bonds between particles. During sintering, some pores initially undergo a growth because of the non-uniform densification of fine aggregates and the priority elimination of the intra-aggregate pores. There is a critical ratio of pore size to mean particle size for pore shrinkage. Smaller pores may shrink and be eliminated during sintering; larger pores shrink at nearly the same rate as the compact and are not eliminated during sintering. For a compact with some pores larger than the critical ratio, the mean pore size may increase during sintering because of the priority shrinkage and disappearance of the small pores. At the initial and early intermediate sintering stages, compacts with a higher green density have a higher sintered density and lower shrinkage. From the perspective of shrinkage during sintering, porosity in a green body can be considered to occur in two classes: the first class of porosity contains pores smaller than the critical ratio and the second class all pores larger than the critical ratio. The final shrinkage is proportional to the porosity of the first class; this porosity does not affect the final sintered density much. The final sintered density is inversely proportional to the porosity of the second class but this porosity does not affect sintering shrinkage much. When the green density difference is caused by the porosity of the second class, the final sintered density is proportional to the green density. To achieve high densities, an optimum combination of intra-aggregate (intercrystalline) and inter-aggregate porosity and pore size must be achieved in the compacted material. The degree to which this is achieved will depend in turn on the achievement, in the powder, of the optimum combinations of crystal size, inter crystalline porosity and collapsibility of the aggregates under the compaction pressures used. In order to get the highest final sintered density, it is important to eliminate pores larger than the critical ratio when processing the green body. 3.7 Role of grain boundaries 3.7.1 Types of solid-solid interfaces

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There are two basic types of solid-solid interface (i) the interphase boundary, corresponding to the liquid-liquid interphase boundary, where there is a change of crystal structure, crystal orientation and chemical composition across the boundary (ii) the grain boundary in a polycrystalline single-phase material. Here the composition and crystal structure is the same on each side of the boundary, which marks a change in orientation of the lattice of the crystals (grains). 3.7.2 Pores on grain boundary In order to shrink the volume of the system, all vacancies have to be eliminated either by diffusing them out of the system or destroying them in internal sinks. The first alternative does not seem to be feasible because of the relatively large distances involved and the slowness of the diffusion process in the condensed phase. The second possibility requires the existence of effective vacancy sinks inside the crystals. Grain boundaries are the effective sinks of vacancies. When a spool of copper wires was sintered, it was observed that tubular pores shrank uniformly as long as they were connected by a network of grain boundaries. When by prolonged annealing, the grain boundaries were virtually eliminated, the shrinkage ceased. Voids spheroidize and decrease in volume as sintering proceeds. Grain boundaries remain attached to voids until spheroidization is complete. During this process shrinkage occurs. Once spheroidization is over, grain growth starts. Grain boundaries get detached and eliminated. Shrinkage stops when the voids are no longer connected to grain boundaries. Fig. 13 gives shrinkage as a function of time and temperature in copper wire compacts. A high shrinkage indicates a high degree of densification. Higher sintering temperatures may not necessarily lead to higher densities. This is due to the separation of pores from grain boundaries. Pores move under the pull of a grain boundary. Movement can occur by diffusion on the surface of the pore, or by transport of vapour across the pore. The mobility increases with decreasing pore size. If the mobility of the pores is great enough to permit them to keep up with the boundary, they will remain there as grain growth occurs and will eventually be eliminated through shrinkage. If the pores, in response to the forces exerted upon them by the grain boundaries, can achieve a velocity equal to that achieved by the boundaries acting in response to all the forces exerted upon them, then exaggerated grain growth will not occur, pores will remain on boundaries, and it will be possible to sinter to theoretical density. 3.7.3 Boundary pinning Second phase inclusions especially when they are finely dispersed and insoluble in the bulk material (e.g., oxides in metals) have a drastic effect on the sintering process, because they are much more efficient than the pores to pin down the grain boundaries. Grain growth is thus strongly hampered. Forcing sintering by raising the temperature leads to discontinuous grain growth. 3.7.4 Rules of grain growth 1. Grain growth occurs by grain boundary migration and not by the coalescence of neighbouring grains as do water droplets. 2. Grain boundary migration is discontinuous or jerky and its direction may suddenly change. 3. One grain may grow into a neighbouring grain on one side while it is being consumed from another side. 4. The rate of consumption of a grain frequently becomes more rapid as the grain is about to disappear. 5. A curved grain boundary usually migrates towards its centre of curvature. 6. When grain boundaries in a single phase meet at angles other than 120 degrees, the grain included by the more acute angle will be consumed so that the angles approach 120 degrees. Conditions of grain growth are shown in Fig. 14. Pore shape distorted from spherical by moving boundary is shown in Fig. 15a. Pore growth caused by grain growth is shown in Fig. 15b. 3.8 Firing schedule The three surface energy reduction processes that take place during sintering are particle coarsening, densification, and grain growth. By conserving surface energy in the first process, namely particle coarsening, it is made available in the second, namely densification. In many cases, particle coarsening,

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densification and grain growth processes operate at different temperature regimes in increasing order of temperature. Since a high densification rate without grain growth usually occurs at an intermediate temperature, a firing schedule can be designed to prolong the dwell time in the densification regime at intermediate temperatures. In Rate Controlled Sintering, particle coarsening is avoided by heating rapidly to an intermediate temperature, and grain growth is prevented by a limited exposure to high temperatures. 4 Multicomponent systems 4.1 Sintering of mixtures The parameters which control the kinetics of homogenization are particle size, sintering time and sintering temperature. Particle size is important because homogenization is related directly to the square of the diffusion distance. Powder particle size determines this distance and plays an important role. If the compacts are made of a mixture of two powders, the particle size of the minor constituent is more important in determining diffusion distances, since this minor constituent will be dispersed in a more or less continuous matrix of the major constituent. As near as possible ideal statistical distribution of the constituents contributes to more rapid homogenization, which means that the constituents should be well blended. A high compacted density will produce better contact between particles, which must diffuse into each other and will accelerate the rate of homogenization. Temperature affects rates of homogenization because of the temperature dependence of the diffusivity between the constituents of the powder mixture. At a temperature of 1100C, the diffusivity of carbon into austenite is of the order of 7 x 10-9 m/sec. On the other hand, when homogeneous iron-nickel or iron-manganese alloys are to be produced from mixtures of elemental iron with nickel or manganese powders, either very fine powders or long sintering times and high sintering temperatures are necessary. At 1100C the diffusivity of iron into nickel is of the order of 8 x 10-14 m/sec, about 105 times lower than that of carbon into austenite at the same temperature. If a completely homogenized alloy steel composition from powders is desired, a pre-alloyed powder, containing the metallic alloying elements but no carbon, may be mixed with graphite powder, compacted and sintered. The compressibility of the alloy powder - graphite powder mixture will, however, be lower than that of an elemental powder mixture. In the sintering of a mixture, it is necessary that the minor constituent particles B dispersed in the major constituent A are small enough, so that no stable void is left on the dissolution of B in A. For example, in the sintering of UO2-Gd2O3, the size of the minor constituent Gd2O3 should not exceed about 5 m, so that the voids left on dissolution of Gd2O3 are unstable and shrink to closure. The pore closing sintering pressure p is given by p = 2 / r, where r is the pore radius and is the surface energy. On the other hand, if the particle size is 50 m, the voids left are too large to close and the sintering pressure is too small. Gases trapped inside the closed voids can even cause bloating of the compact in the sintering process. 4.2 Kirkendall effect The mechanism of interdiffusion between two metals is generally based on the interchange of atoms with vacancies in the lattice. During interdiffusion between the two constituents, one will diffuse faster than the other. This phenomenon is called the Kirkendall effect. An artificial compact was produced by winding alter-nate layers of 125 m diameter copper and nickel wires upon a copper core and sintering 3 hours at 995C in vacuum. The more rapid diffusion of copper into nickel than of nickel into copper causes porosity to appear in copper wires. At higher temperatures (1070C), the nickel wires grow and copper wires gradually disappear. Because of the Kirkendall effect, porosity will appear during the dezincification of alpha brass. As zinc diffuses out, the slower moving copper atoms are unable to diffuse back rapidly enough to prevent the formation of pores by the precipitation of the vacancies left by the removal of zinc. The driving force for the dezincification process is many times the surface tension driving force for sintering, so that lattice vacancy fluxes may be tremendously different than they would be in a pure metal or ceramic. While the diffusion coefficients for the different ions in oxides may also be tremendously different from one another, the requirement of electrical neutrality prevents the formation of voids with only surface tension as the driving force. Thus, in compounds, changes in composition as a result of different diffusion rates of ions of opposite charge will not occur as they do in a solid solution alloy.

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5 Additive effects in sintering 5.1 Preservation of the ideal powder characteristics Significant particle coarsening prior to densification has been observed during sintering. Certain dopants can prevent particle coarsening and thus preserve the ideal particle characteristics for densification. Boron is essential to densification of silicon carbide, because it impedes surface diffusion in silicon carbide and thus, inhibits particle coarsening in the powder compact at temperatures below 1500C. Since the rate of particle coarsening increases rapidly with decrease in particle size, dopants are required to suppress particle coarsening only when the particles are very small. 5.2 Provision of high diffusivity paths For certain metals, the addition of a small amount of an alloying element (doping) may cause the rate of densification to increase as much as 100 times compared with undoped compacts. It has been observed for the refractory metals tungsten, molybdenum, hafnium, tantalum, niobium and rhenium. The best activators are palladium and nickel. Fig 16 shows shrinkages in compacts of tungsten powder with a particle size of 0.5 microns pressed at 97 MPa and sintered at 1000 C and 1100 C without and with the addition of 0.5% nickel. Grain boundary self-diffusion in tungsten is greatly enhanced by the presence of nickel in grain boundaries. Enhanced sintering involves the addition of an alloy additive to the base material to increase the sintering rate by providing a short circuit mass transport path for rapid diffusion. This short circuit path is generally through a segregated second phase at the interparticle boundaries. Rapid diffusion of the base atoms through this layer results in enhanced sintering, leading to densification of the compact. The segregated phase may exist either as a solid or a liquid, hence the term `enhanced sintering' embraces both liquid phase and activated sintering. The real effect of the additive is assessed by its influence on diffusivity. Faster diffusion of the base metal in the segregated phase is the primary mechanism of enhanced sintering. Hence, the alloy or intermetallic layer formed at the interparticle boundaries should offer minimal resistance to the diffusing base metal atoms. In addition, the stabilization of a crystallographically more open structure for the base material would enhance its self-diffusivity. A liquid phase permits faster atomic diffusion than a solid phase, resulting in faster sintering rates. Thus, the theories of enhanced sintering identify the following main criteria for selection of an appropriate sintering enhancer: (i) high solubility of the base in the second phase (ii) segregation of the additive at the interparticle boundaries (iii) easy diffusion of the base material through the segregated phase. Schematic model for enhanced sintering is given in Fig. 17. Phase diagram for ideal additive is given in Fig. 18. 5.3 Enhancement of lattice diffusion Solid state sintering involves movement of atoms which is in turn dependent on concentration of structural imperfections such as vacancies and interstitials the concentrations of which are determined by temperature, atmosphere and additives. The presence of structural imperfections enhances diffusion of atoms. The lower concentrations at lower temperatures can be made up by using additives or by controlling the atmosphere. In other words, the effects of atmosphere and /or additives may be used to lower sintering temperature. For example ThO2 (melting point 3090C) can be sintered at only 1150C using Nb2O5 as additive.

An additive that generates point defects that would speed up the slower moving species by providing a high diffusivity path activates the sintering process. Additives that speed up the faster moving species are of no consequence to sintering. However an additive may assist in sintering by another mechanism, namely grain boundary pinning. 5.4 Prevention of exaggerated grain growth In the final stage of sintering, exaggerated grains separated from pores commonly appear in some regions of the microstructure when the processing is not carefully controlled. The tendency for exaggerated grains is higher when powder aggregates are dense, extremely coarse particles are present and the pore distribution is inhomogeneous. A high sintered density with minimal grain growth occurs when the material contains fine particles packed densely and when an additive called a grain growth inhibitor is dispersed and homogeneously distributed. Boundary pinning in the denser regions of inhomogeneous materials (even

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when the total density of the material is still representative of a relatively early stage in the sintering process) acts as an important way of preventing abnormal gain growth and restoring structural homogeneity. The role of the additive becomes that of reducing the consequences of micro structural inhomogeneity. The grain boundary mobility in undoped alumina is about 100 times faster than in magnesia doped alumina. When the concentration of the dopant is in excess of the solubility limit, second phase forms in the specimen. The second phase particle can significantly inhibit the grain boundary mobility and prevent exaggerated grain growth. 6 Effect of pre-sintering processes Sintering is closely interlinked with characteristics of the starting powder (particle size distribution, particle morphology, flowability and packing efficiency) and the shaping process of the green body. It is necessary to bring the particles together by compaction, to achieve unimodal sintering. The essence of green body formation is the manipulation of powder particles into a well-packed, homogenous moulding which is free from cracks and other flaws prior to sintering. The powder compact should have homogeneous density which means extremely small pores that are not clustered together. The microstructure of the green body is a decisive factor for the sintering process. The microstructure depends on powder morphology and forming method as well. Anisotropic shaped particles tend to orient themselves in many forming processes such as extrusion, injection moulding, pressing, slip casting and this may lead to anisotropic shrinkage, warping and cracking. An ideal microstructure for the green body is one with a homogeneous distribution of extremely fine pores and small particles. The effect of particle size distribution of the starting powder on the green and sintered microstructure are shown in Fig. 19. Equi-sized powder particles result in homogeneous green microstructure as shown in Fig. 17a. When the heating rate is normal, homogenous sintered microstructure is obtained. At faster heating rates and on overheating, grain growth occurs and porosity is trapped within the grains. Wide particle size distribution results in wide grain size distribution as in Fig. 19b. Fig. 19c shows bimodal particle size distribution leading to bimodal grain size distribution. Mono sized or narrow size particle size distribution is desirable with respect to uniform green and sintered microstructure. However, mono sized powders do not flow readily through powder transfer systems such as feed screws, bunkers and conveyors. While spherical powders flow most readily, many powders are not produced in spherical form for reasons of economy. For the same shape of the powder particle, wide particle size distribution powders flow more easily than do narrow size distribution powders which suffer from bridging and caking. It is also not economical to produce narrow size distribution powders. The powder manufacturing process parameters are carefully controlled at various stages to yield powders of wide size distribution but soft in nature. These powders transform to monosize distribution after final compaction and lead to desired sintered microstructure. Unreliable green bodies lead to unreliable fired products. The distribution of large flaws in the green body remains unchanged throughout sintering, unless further flaws are introduced by grain growth for example. A compact of high green strength can withstand internal stresses generated on relief of compaction pressure as well as ejection stresses. Green strength is also important for handling of powder compacts. A tensile strength of 5 MPa is sufficient for powder metal bodies. Most ceramic green bodies are weaker than this, 1 or 2 MPa being typical. Admixed lubricants and binders in the powder greatly enhance the green strength leading to defect-free compacts. 7 Defects in sintering 7.1 Origin of defects Most defects observed in the sintered body have their origins in the green state. A defect that formed in the green state is likely to get exaggerated on sintering, as indicated in Fig. 20. Many defects in ceramic parts are generated in the forming process, before firing. However, in several cases, it is not clear exactly in which stage of the process of ceramics production the defects arise. Indeed, cracks and other heterogeneities are very hard to identify in green ceramic bodies using conventional techniques, mainly due to difficulties in preparing samples suitable for observation. In the case of low pressure injection molding (LPIM), this problem is often critical, because of the high binder fraction (about 50% in volume) present in the green ceramic parts.

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7.2 Hourglassing In compacts where the L/D ratio is on the higher side, the compaction pressure is not fully manifest in the lower region in single punch compaction and in the central region in double compaction. The pressure being less, the green density will be lower in these regions. However, all regions sinter to the same final density, leading to greater shrinkage in the lower green density regions. Thus hourglassing (larger diameter at the ends and smaller diameter at the center) appear on sintering. 7.3 Lamination When the powder in the compacting die is subjected to axial pressure, the pressure gets transmitted to the die wall and reaction from the die wall radially compresses the powder. Under high pressure, the die bore increases in diameter. After the compact is ejected, the die returns to its original diameter. The ejected compact is slightly larger than the die bore. Defects can occur during ejection, since the portion already ejected tends to expand while the portion below is restrained from expanding by the die wall, as shown in Fig. 21. If the green strength of the compact is insufficient, circumferential cracks can appear in the compact, which dilate on sintering. This defect is called lamination. It can be avoided by providing a taper in the exit portion of the die bore to facilitate gradual stress relief in the compact under ejection. 7.4 Endcapping Endcapping is another defect that originates in green stage and is detected after sintering and finish grinding. As stated earlier, when the powder mass is subjected to compaction pressure, the die bore expands. The extent of expansion is dependent on the die material. After the compaction is over, the compact remains constrained within the die between the top and bottom punches. Once the detensioning, or withdrawal of compaction pressure begins, the compact tends to relax a bit. If there is no die wall friction at all, the compact slides along the die wall and increases its length as detensioning proceeds. However, in real dies there is significant friction, which restrains the circumferential portion of the compact from expanding. The central portion of the compact tends to expand axially, as shown in Fig. 22 and if the green strength is insufficient, a crack appears as end capping. The defect can be avoided by thoroughly polishing the die wall (to 0.1 micrometer or better), by lowering the compaction pressure, by using more rigid die material and by increasing the green strength of the compact by the use of an admixed lubricant or binder. 7.5 Low density The incidence of lower than specified density can be due to various reasons. For some reason, the compact may not have seen the necessary temperature or time needed for full densification. Low density may also be due to presence of cracks or voids in the green compact that are not able to close in the sintering process. The probability that a void closes is dependent on its size. The sintering pressure is given by p = 2 / r where r is the radius of the void. As the value of r is decreased, the sintering pressure that acts to close the void increases. Voids smaller than a critical size, say less than one m, readily close in the sintering process. Voids larger than about say, 30 m grow in size. The origin of the void may be a misfit or packing defect between the powder particles or particle clusters. The voids may also may be caused by dissolution of one constituent of the powder mixture in the other. A cause of residual porosity in sintered materials is the entrapment of insoluble gas in closed pores, which originated from the misfit of the original particles or aggregates of particles, close and no longer communicate with the free surface. These closed pores will contain the gas which was present in the furnace atmosphere when closure occurred. If a vacuum furnace is used, or if the furnace atmosphere is a gas that can readily diffuse through the substance being sintered, as hydrogen does through aluminium oxide, then subsequent pore shrinkage is not retarded. If the gas does not diffuse - as nitrogen does not through aluminium oxide, then pore shrinkage will be inhibited. As the pore shrinks past the size at the time of pore closure, the pressure inside the pore will ultimately reach the pressure that can be imposed by the surface tension of the material and the radius of the pore. When the surface tension of the substance is thus balanced by the internal pressure of the pore there is no longer any motivation for sintering. Continued heating will increase the pressure of the trapped gas and cause bloating or loss of density due to desintering. 7.6 Bloating This defect is some times encountered when powder mixtures are sintered. If constituent B is present as large particles mixed in constituent A, then in the course of sintering, B dissolves in A, leaving large voids that can not close. If gases from the furnace atmosphere are trapped in the voids by the time open porosity ceases, bloating can occur on prolonged heating, when the trapped gas pressure exceeds the void closure pressure. The remedial measure is to use B in smaller size or milling the powder mixture before compaction. Bloating may also be observed in single constituent powder compacts if there are large agglomerates causing packing problems during compaction. The open porosity disappears by the time the sintered density

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reaches 93% TD. The opening up or enlargement of voids under internal gas pressure is termed bloating or desintering. When there is no packing difficulty in compaction, there will be no bloating. When there is a packing problem leaving a large enough void, which persists at the time the compact stops communicating with the environment (93%TD), bloating occurs. Thus the problem is likely to be acute in high surface area agglomerated powders. 7.7 Radial and circumferential cracks Frequently cracks are not present in the green compact. However, these may appear in the course of sintering, The reason is believed to be differential sintering. By differential sintering, we mean different shrinkages at different locations in the same green body. The shrinkage is dependent on the initial green density. Low green density areas shrink more than the higher density areas. Large shrinkages in local areas may result in detachment of the area from its neighbourhood, leading to the formation of cracks. If, for some reason, the core of the green body is of a lower green density than the rim, the greater shrinkage of the core results in radial cracking. This can happen with very fine particles being compacted into large diameter shapes leading to a lower green density in the inner region. If the core happens to be of a higher green density, the shrinking skin meets with resistance from the core leading to radial cracks. 7.8 Coring Coring is the existence of two widely differing grain sizes in the core and rim of a sintered compact. It is some times seen in rapidly heated large diameter ceramic compacts made from extremely fine powders, where the skin, which sees the high temperature first gets sintered quickly. Due to poor thermal conductivity, there is a possibility of temperature gradient inwards. The inner region which sees the high temperature at a later stage cannot shrink inwards freely as it is restrained by the already sintered skin that has stopped shrinking. Trapped impurities in the inner region may act as grain growth facilitators. A fine grained rim surrounding a large grained interior gives the appearance of coring. On the other hand, certain additives inhibit grain growth. Loss of these inhibitors from the surface may cause abnormal grain growth in the rim, leading to a cored appearance. Such coring was noticed in magnesia doped alumina. Use of purer powders and slow heating rates are remedial measures against coring. Extremely fine powders may be re-calcined before compaction to avoid coring. Other defects may be caused by the use of incorrect temperature time profile, leading to incomplete binder burnout or too fast a heating or cooling rate or by reaction with components of the sintering furnace atmosphere. About the speaker Dr.Palanki Balakrishna, B.Tech (Honours): Indian Institute of Technology, Bombay 1969 M.Tech: Indian Institute of Technology, Bombay 1971 Ph.D: Indian Institute of Technology, Bombay 1994 Over 60 technical / research publications. Presented papers in Japan, Italy and Russia. Guest speaker at North Carolina State University, Florida State University, Wright State University, Florida International University in the US. Engineer of the Year, 1992 Award from the Institution of Engineers & Govt. of Andhra Pradesh. Best Metallurgist, 1995 Award from the Indian Institute of Metals and Govt. of India. Rashtriya Vidya Saraswati Puraskar 2009 from International Institute of Education and Management. Life Fellow of the AP Academy of Sciences.

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2 Solid State Sintering3 Fundamentals of sintering4 Multicomponent systems4.1 Sintering of mixtures5 Additive effects in sintering6 Effect of pre-sintering processes

7 Defects in sintering7.2 Hourglassing7.3 Lamination7.4 End-capping7.5 Low density7.6 Bloating7.7 Radial and circumferential cracks7.8 Coring2 Solid State Sintering3 Fundamentals of sintering4 Multicomponent systems4.1 Sintering of mixtures5 Additive effects in sintering6 Effect of pre-sintering processes

7 Defects in sintering7.2 Hourglassing7.3 Lamination7.4 Endcapping7.5 Low density7.6 Bloating7.7 Radial and circumferential cracks7.8 CoringAbout the speaker