Micromechanics of the sintering force in sintering by bulk diffusion

Densification in sintering originates from the relative approach of contacting particles, which is driven by the sintering force. This concept has been rigorously established for grain boundary diffusion, where the driving force is determined by the local curvature at the neck. For bulk diffusion, however, the diffusion potential is governed by the Laplace equation in the particle interior, so the driving force is inherently non-local and depends on the overall surface morphology of the particle; a rigorous definition of the sintering force has been lacking. Here, a microscopic theory of the sintering force for bulk diffusion is developed by decomposing the diffusion potential into non-densifying and densifying solutions. The sintering force takes the same form as that for grain boundary diffusion when the neck curvature is replaced by an effective curvature—a virtual curvature that would produce a chemical potential equal to the area-averaged value on the contact face. Front-tracking boundary-element simulations of two-particle sintering show that the sintering force exhibits a broad peak as a function of the contact radius and vanishes at the equilibrium shape. The effective curvature, sintering force, geometric factor, and relative velocity are presented as functions of the contact radius, so that the dynamics of sintering can be predicted from the particle geometry alone.