Coupled grain boundary and surface diffusion in a polycrystalline thin film constrained by substrate

Abstract

Abstract It has recentlq been shown [1] that constrained grain boundary diffusion in a stressed polycrystalline thin film causes exponential relaxation of grain boundary traction, leading to formation of crack-like diffusion wedges vaa mass transport between the grain boundaries and the free surface of the film. It was assumed in [1] that surface diffusaon is very fast compared to grain boundary diffusion and surface tension is very large so that the film surface remains perfectly flat during the diffusion process. In this paper, we trq to relax some of these assumptions by extending the analysis of [1] to coupled grain boundary and surface diffusaon. We use Mullins' equation to describe surface evolution, with mass conservation and continuity of chemical potential strictly enforced at the junctions between grain boundaries and the free surface. The surface diffusaon is treated as a matter source or sink for the grain boundary diffusion and, assuming the surface slope is small, we neglect the effect of su...