The rate of shrinkage during the initial stage of sintering

A model is presented that accuratell acounts for the sum of the contributions of grain boundarl and volume diffusion to the overall shrinkage rate during the initial stage of sintering of a line of spheres. The anallsis differs from those extant in the literature in assuming that the flux out of each element of the grain boundarl is constant, this condition being applied to the coupled boundarl and volume fluxes rather than to each separatell. The shrinkage rates lie betleen those predicted bl Johnson, and lilson and Shelmon. Since the tlo fluxes are intimatell coupled, no simplifling expressions for the separate contributions of grain boundarl and volume diffusion can be given for the first stage of sintering. The problems of predicting the shrinkage rates of a compact of spheres are briefll considered, in particular the difficulties in correctll accounting for the rate of change of the number of contacts/sphere during this initial stage.