Effective diffusion coefficients in solid-state sintering

A numerical analysis of the sintering neck growth rate between rigid spherical particles of the same size is carried out. The contributions of the surface, grain-boundary and volume diffusion transport into sintering kinetics during the first and the second stages of sintering are estimated. It is shown that the three-dimensional problem of the matter redistribution during sintering can be reduced to a two-dimensional problem if the effective diffusion coefficients are introduced. The effective diffusion coefficients are the grain-boundary diffusion coefficients that include the contribution of volume diffusion. The effective diffusion coefficients are sensitive to the stage of sintering: they have different form during the first and the second stages. During the second stage of sintering, the unified effective diffusion coefficient is determined. It is demonstrated that the effective diffusion coefficients can be used also for the description of the pressure-assisted sintering.