Thermal grooving by surface diffusion for an extended bicrystal abutting a half–space

Abstract

A theoretical anisotropic material implied from Mullin's linear fourthorder equation for surface diffusion is used to model redistribution by surface diffusion of a bicrystal occupying a halfspace, terminated along two planar surfaces meeting at the grain boundary. Intersecting the junction of the two planes is an arbitrarily inclined grain boundary. The particular case where one of the bicrystal surfaces is initially coplanar with the grain boundary yields a configuration that is locally representative of some joints among crystalline sinter particles. Closedform solutions for a family of orientations of either of the crystal lattices of the theoretical anisotropic material are derived. Dependent upon the initial geometry and the surface environment, the bicrystal may either sinter together or divide apart. The theoretical material may reasonably model isotropic materials by appropriate orientation of the crystal lattice.