Sintering of Single Metai Compacts

As discussed above, important changes in the dimensions of compacts occur when green compacts are heated to the sintering temperature. In many sintering operations, green compacts shrink and may even reach the density of corresponding wrought materials. Even when compacts shrink only minimally or not at all, changes in interior geometry

Temperature, °F 600 1400 2000

Temperature, °F 600 1400 2000

occur. In pressed compacts, the approach of the surfaces of the individual powder particles toward each other to distances on the order of metal lattice dimensions is quite limited.

One of the important occurrences in the early stages of sintering is the increase in the contact strength between particles. This may occur without significant changes in the overall density of the compact. Another change within the green compact that does not necessarily involve large density change is the rounding and spheroidization of the pore structure, which is best observed by metallography. Changes in mechanical properties during sintering are, of course, a direct consequence of these geometrical changes.

During compacting, powder particles are subjected to strain hardening that increases with higher pressure. At low temperatures, sintering causes annealing, during which strain hardening is relieved, primarily through recrystallization. A small portion of the geometrical changes that occur in compacts during sintering results from recrystallization. However, the fact that a well-developed sintered microstructure is formed only at temperatures above the recrystallization temperature range indicates that the major driving force for sintering is the reduction in surface energy, not cold work.

The principal driving forces are capillary forces due to the surface and interfacial tensions, also called specific surface and specific interfacial free energies, of the free surfaces and the interfaces between grains (Ref 1). These forces cause stresses that are related to the curvature of the surfaces and interfaces. Stresses due to surface and interfacial tension forces tend to decrease the surface and the interfacial areas and are the principal driving forces in sintering.

In single-phase systems, the existing interfaces are the free surfaces between the solid and gas phase and the interfaces between grains with different orientations. The simplest case would be a single-phase, monocrystalline system, for which the relationship between surface tension (specific surface free energy) and stress is given by the Laplace equation:

tj=7

where <Jis the stress, 7is the surface tension, and rx and r2 are the radii of curvature of the surfaces. Under convex surfaces for which the curvature is negative, the surface stress is tensile (ff < 0). For concave surfaces with positive curvature, the surface stress is compressive. Experimental methods for readily determining the surface tension of metals and alloys at sintering temperatures are available (Ref 2). The stress defined by the Laplace equation causes a gradient in chemical potential between surfaces with different radii of curvature:

where His the atomic volume.

Single-phase metal powders shrink rather than expand during sintering, except for soft metal powders compacted at high pressures. Gases entrapped in these compacts may expand when heated during sintering. Stress caused by gas pressure, which increases with increasing temperature, counteracts surface tension stresses that cause shrinkage.

In this discussion of the driving forces that cause sintering--or, more specifically, material transport during sintering--compacts are assumed to be sintered without the application of external pressure. If external pressure is applied, the capillary forces are of secondary importance compared to external forces, particularly in metallic systems.

Several possible mechanisms have been identified that cause material transport under the influence of a chemical potential gradient. In single-phase systems, the chemical potential gradient is due to the stress gradient between surfaces and interfaces.

One of the early mechanisms postulated is evaporation and condensation. Atoms evaporate from surfaces that have a higher vapor pressure and are transported through the gas phase to highly curved convex surfaces that have a lower vapor pressure, where they condense. Because most metals do not have high vapor pressures at temperatures near their melting points, evaporation and condensation contribute nominally to material transport in the most common metallic systems.

Diffusional flow is the most important mechanism of material transport (Ref 3). It is based on the concept that a certain concentration of vacancies exists in the crystal lattice of a metal. This concentration is a function of temperature and may reach values on the order of one vacancy for every 10,000 occupied lattice positions at temperatures near the melting point of the metal. Vacancy concentration also is a function of the chemical potential or stress to which the surface of the metal is subjected. Consequently, a gradient of vacancies exists between a highly curved convex surface, which has a higher vacancy concentration, and an adjacent flat surface, which has a lower vacancy concentration.

Studies of diffusional flow have concentrated on the first or initial stage of sintering, where the small necks between particles become larger. This causes rounding of the pores and some decrease in total pore volume. However, the original particles are distinguishable. The studies were based on theoretical analysis and on experiments on models, such as those in which a sphere is sintered to a flat surface (Ref 4) or in which two spheres are sintered together (Ref 5).

Figure 10(a) schematically illustrates a cross section of a two-sphere model. The radius, P. is formed at the end of the neck between the two particles in Fig. 10(a). Figure 10(b) shows the geometry near this radius in more detail. Assuming that the two particles are single crystals, with different orientations, a grain boundary is formed at the neck. The difference in curvature at the neck with /■'and the adjacent flat surface causes a difference in stress and chemical potential between the two points, which in turn produces a gradient in the concentration of vacancies between the highly curved neck surface, which has a high vacancy concentration, and the adjacent flat surface, which has a lower concentration.

Fig. 10 (a) Schematic cross section through two spheres sintering together. Radius, P, is at the end of the neck. (b) Types of material transport when two single crystal spheres with a grain boundary at the interface sinter together. Path a, volume diffusion from the flat surface to the neck. Path b, surface diffusion from the flat surface to the neck. Path c, grain-boundary diffusion from the grain boundary to the neck. Path d, volume diffusion from the grain boundary to the neck

The difference in vacancy concentration under surfaces with different radii of curvature can be expressed mathematically (Ref 3). This difference causes a flux of vacancies away from the highly curved surface to the flat surface, which is equivalent to a diffusional flow of atoms in the opposite direction.

There are two types of diffusional flow possible under the influence of vacancy concentration differences between flat and highly curved surfaces. They are volume diffusion, indicated schematically by path a in Fig. 10(b), and surface diffusion, indicated by path b. As shown in Fig. 10(b), these two types of diffusional flow cause rounding and spheroidization of irregular pores in a compact. However, they do not explain shrinkage, which would be represented by a decrease in the distance between the centers of the two spherical particles.

To explain shrinkage, flow of atoms from the grain boundary to the neck must be considered. This is indicated by path c, which represents grain-boundary diffusion, and path d, which represents volume diffusion from the interior of the grain boundary to the neck. When atoms flow from the grain boundary to the neck, vacancies flow in the opposite direction and are thus eliminated at the grain boundaries. This causes the centers of the two particles to approach each other, and shrinkage occurs. The rates of the diffusional mechanisms (volume diffusion, surface diffusion, and grain-boundary diffusion) vary significantly, and the geometries that govern transport also vary and are quite complex even for simple model systems, such as sintering a sphere to a sphere. Nevertheless, the calculated rates of pore rounding and shrinkage in model systems, based on known values of specific surface and interface free energy, and the various types of diffusivities closely approximate those observed experimentally (Ref 6).

Rates of material transport during the initial stage of sintering can be calculated for model systems such as the two-sphere model discussed above. The presence of neighboring particles has constraining effects on neck growth and shrinkage (Ref

Mathematical models have been constructed not only for the initial stage of sintering, but also for the intermediate and final stages. During the intermediate stage of sintering, the original particles are less distinguishable, because the pore channels between particles are pinched off and become closed. Grain boundaries between the original particles migrate due to grain growth. The pores form a more or less connected continuous network throughout the compact. They become isolated in the third or final stages of sintering. Models for the intermediate and final stages of sintering are complex (Ref

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