Surface motion of single crystals driven by anisotropic surface diffusion

In this paper we compute a mathematical model for the evolution of single crystal with a particular kind of anisotropic surface free energies that yields equilibrium crystal shapes close to octahedrons. Employing the developed model we exhibit the entire evolution path of single crystals to equilibrium with different levels of anisotropic surface free energy. We find that with a mildly anisotropic surface free energy, the crystal morphology is smooth in evolution and evolves to a unique equilibrium crystal shape. With a severely anisotropic surface free energy, edges, corners and faceting by hill-and-valley structures on crystal surface occur. The equilibrium crystal shape reached in computation approaches the analytic octahedron Wulff shape as the anisotropy in the surface free energy becomes more severe.