Intermediate and Final Stage Sintering

Coble did not specifically adapt the intermediate and final stage sintering models to account for hot pressing, but as described below, he used a different approach based on a modification of creep equations. However, as we shall show later, if the differential equations for matter transport are formulated with the proper dependence of the chemical potential on surface curvature and applied... 

FIGURE 162 Densification of two log-nonnal alumina powders (dg = 1.3 and 0.8 fan) showing the initial, intermediate, and final stages of sintering. Sintering is under constant heating rate conditions tf 7.3°C/min. Data from Reed [1]. 

Since the introduction of a mathematical model for sintering by Kuczynski [12] numerous other models have been proposed. Reviews of these sintering kinetic models are given in references [13—19]. This description of sintering kinetics is organized into initial, intermediate, and final stage kinetic models. 

Diffusion models have been developed by Coble (1970) for initial, intermediate and final stages of pressure sintering including both the applied pressure and the surface energy as driving forces. The Mackenzie-Shuttleworth model is considered suitable for Newtonian viscous materials. 

Coble, R.L. (1961) Sintering crystalline solids 1. Intermediate and final stage models II. Experimental test of diffusion models in powder compacts, J. Appl, Phys, 32, 787. 

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... 

Some of the main parameters associated with the three idealized stages of sintering are summarized in Table 8.4, and examples of the microstmctures (planar section) of real powder compacts in the initial, intermediate, and final stages are shown in Fig. 8.9. 

For the two-sphere model appropriate to the initial stage of sintering (Fig. 8.10), Coble assumed that cj) is 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., 4> = Aa / nXf, whereas for both the intermediate and final stages, Coble argued that 4) = 1/p, where p is the relative density of the body. 

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