A theoretical anisotropic material which was implied by Mullins' linear fourth-order equation for surface diffusion was used to model the redistribution, by surface diffusion, of a bicrystal which occupied a half-space and terminated along 2 planar surfaces which met at the grain boundary. Intersecting the junction of the 2 planes was an arbitrarily inclined grain boundary. The particular case where one of the bicrystal surfaces was initially coplanar with the grain boundary yielded a configuration that was locally representative of some joints among crystalline sintered particles. Closed-form solutions were derived for a family of orientations of either of the crystal lattices of the theoretical anisotropic material. Depending upon the initial geometry and surface environment, the bicrystal could either sinter together or divide apart. The theoretical material could model isotropic materials reasonably by choosing an appropriate orientation for the crystal lattice.

Thermal Grooving by Surface Diffusion for an Extended Bicrystal Abutting a Half-Space. P.Tritscher: Proceedings of the Royal Society A, 1999, 455[1986], 1957-77