Solid-state sintering

A necessary condition for densification to occur is that the grain boundary energy 7gb be less than twice the solid/vapor surface energy This implies that the equilibrium dihedral angle 0 shown in Fig. 10.3 and defined as 

Similarly, it can be shown that the total surface energy of the 10 pm spheres is w6 J. The change in enthalpy associated with the coarsening is 

Mass conservation requires that o = 4/37rr or a 0.4 pm, where a is the length of the side of the cubes. The total grain boundary area (neglecting free surface) is 

Thus the energy of the system after sintering is 1.28 x 72 92.16 J. which is less than the original of 120 J. The difference between the two is the driving force for 

In contradistinction, if a powder compact coarsens, no shrinkage is expected in a dilatometric experiment. In that case, the coarsening kinetics are best followed by measuring the average particle size as a function of time via optical or scanning electron microscopy. 

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Figure C2.11.7. An illustration of tlie equilibrium dihedral angle, 0, fonned by tlie balance of interfacial energies at a pore-grain boundary intersection during solid-state sintering.

Liquid-phase sintering is significantly more complex tlian solid-state sintering in tliat tliere are more phases, interfaces, and material transport mechanisms to consider. In general, densification will occur as long as it is... 

There is a qualitative distinction between these two types of mass transfer. In the case of vapour phase transport, matter is subtracted from the exposed faces of the particles via dre gas phase at a rate determined by the vapour pressure of the solid, and deposited in the necks. In solid state sintering atoms are removed from the surface and the interior of the particles via the various diffusion vacancy-exchange mechanisms, and the centre-to-cenU e distance of two particles undergoing sintering decreases with time. 

Figure 19.2 shows, at a microscopic level, what is going on. Atoms diffuse from the grain boundary which must form at each neck (since the particles which meet there have different orientations), and deposit in the pore, tending to fill it up. The atoms move by grain boundary diffusion (helped a little by lattice diffusion, which tends to be slower). The reduction in surface area drives the process, and the rate of diffusion controls its rate. This immediately tells us the two most important things we need to know about solid state sintering ... 

A pellet is pressed of an intimate mixture of finely divided reactants and reaction induced either by arc melting and high-T annealing or by solid-state sintering in an electrical or high-frequency furnace. Isolating the borides from reactive container components can be a problem. The use of boron nitride liners has proved effective. In some cases the protective liner is made of sintered boride containing the same elements as the boride in preparation. 

Three stages of solid-state sintering are recognized, although there is not a clear distinction between them, and they overlap to some extent. 

W.S. Coblenz, J.M. Dynys, R.M. Cannon, and R.L. Coble. Initial stage solid-state sintering models A critical analysis and assessment. In G. C. Kuczynski, editor, Proceedings of the Fifth International Conference on Sintering and Related Phenomena, pages 141-157, New York, 1980. Plenum Press. 

G.C. Kuczynski. Theory of solid state sintering. In W. Leszynski, editor, Powder Metallurgy, pages 11-30, New York, 1961. Interscience Publishers. 

The driving force for densification is the reduction in surface energy as the free surfaces of particles disappear and how this is accomplished defines the terms firing , solid state sintering and liquid phase sintering. 

Typical microstructures developed by solid state sintering, liquid phase sintering and firing a porcelain are shown in Fig. 5.20. 

For sintering to proceed, two conditions must be met. First, there must be a means or mechanism for materials transport that will allow material to flow to fill pores and create bonds between particles. Second, there must exist a source of energy to drive or activate that materials transport. There are several different forms of sintering, each with its own combination of conditions, as shown in Table 7.6. We examine solid-state sintering in depth as one of the most general methods, but similar principles can be seen to apply to all sintering methods. 

Solid state sintering was discussed previously in this chapter. The sintering kinetics depend upon the rate determining step, which can be either viscous flow, grain boundary diffusion, or lattice diffusion. These sintering kinetics are summarized in Tables 16.4 and 16.6 for the initial and intermediate stage and Section 16.3.2.3 for the final stage. 

The solid state sintering of Si3N4 is complicated by evaporation at temperatures higher than 1850°C... 

Gas-solid reactive sintering can also be used in the oxidation of most metals or, more important, mixtures of metals. After oxidation, solid state sintering takes place. With mixtures of metals, a mixed oxide is produced which can be sintered by either solid state or liquid phase sintering. One example of alloy oxidation to produce a ceramic is in the synthesis of the superconductor YBa2Cu3Q. ... 

As with cold pressing, HIP resolves the problems of density variation inside the ceramic, which is prevalent in hot pressed ceramics. When solid state sintering is performed before hot isostatic pressing, the combined process is called sinter-HIP or post-HIP. 

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