Sintering at Pressures

Analytical sintering models are based on the idealized models for the three stages of sintering shown in Fig. 8.8. Because the vacancy concentration under the neck surface is not affected by the external stress, Eq. (5.134) is still valid, i.e., there is 

In the two-sphere model at the initial stage of sintering, / is usually assumed to be equal to the area of the sphere projected onto the punch of the hot pressing die divided by the cross-sectional area of the neck, i.e., j) = while in those at 

Using the parameters for K and j), the variations of ACv,p and ACv.b can be obtained [53]. For hot pressing, the difference in the concentration of vacancy between the neck surface and the grain boundary is given by AC = ACy.p — ACv,b therefore, for the initial stage, there is 

This equation indicates that, at the initial stage, AC for hot pressing is similar to that for normal sintering, but ysv + is used instead of ysv- Because and a are constant, hot pressing equations can be derived from the sintering equations by simply changing ysv into ysv + Pi aln. 

Creep equations can be appropriately modified as models of intermediate and final stages of sintering. For simplicity, the matter transport during creep of a dense solid is considered first. For a pure single crystal solid with cubic structure, which is a rod with a cross section of length L. Normal stresses pa nre applied to the rod on the sides, as shown in Fig. 5.23a. It is assumed that self-diffusion within the crystal 

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