Sintering by coupled grain boundary and surface diffusion was analyzed in terms of mechanics. The shrinkage was a result of the relative motion of particles caused by grain boundary diffusion. The center of mass of a particle also moved due to spheroidization of the particles by surface diffusion. The mobility and sintering force for both processes were calculated during sintering of two identical particles until they reached equilibrium. The particle velocity was proportional to the mobility and the thermodynamic driving force generally. For relative motion the sintering force and the effective viscosity, which was the inverse of mobility, were calculated from the neck radius and the neck curvature during sintering of two identical particles until they reached equilibrium. The thermodynamic driving force and mobility were defined for the velocity of the mass center caused by surface diffusion and interface controlled surface diffusion. Surface diffusion was responsible for spheroidization of the particle pair in the later stages of sintering. The contribution of grain boundary diffusion to the final shrinkage increased with increasing ratio of grain boundary diffusion coefficient to surface diffusion coefficient and the ratio of grain boundary energy to surface energy.

Mechanics of Sintering for Coupled Grain Boundary and Surface Diffusion. F.Wakai, K.A.Brakke: Acta Materialia, 2011, 59[14], 5379-87