Contributions of Grain Boundary and Volume Diffusion to Shrinkage Rates during Sintering

Abstract

Previous sintering models (4), (6) that attempted to calculate the shrinkage rates associated with atom fluxes from grain boundary to neck have treated volume diffusion and grain boundary diffusion separately. In the present model the uniform shrinkage condition at the grain boundary is applied to the sum of the volume and grain boundary fluxes rather than to each flux separately. The assumption of the earlier models that each flux provided uniform shrinkage at the grain boundary cannot be justified on physical grounds. The present model also differs from previous ones in that the surface curvature of the neck surface is inserted in the problem in functional form; by this we mean that correct account is taken of the way in which surface curvature varies at the neck region. The ability to insert an arbitrary form and value for the surface curvature give this proposed solution a good deal of flexibility.