Evolution of two-dimensional crystal morphologies by surface diffusion with anisotropic surface free energies

The Wulff shape of a crystal surface in equilibrium under anisotropic surface free energy has been widely reported and a typical differentiable anisotropic free energy functional form has been used in illustrations. Here we study the evolution of an arbitrary initial two-dimensional crystal shape to equilibrium and we classify the anisotropy in three cases. We find that when the typical surface free energy is critically anisotropic, multiple equilibrium states exist and the evolved equilibrium shape depends on the initial crystal configuration. Numerical simulations show that corners and planar facets develop on the surface in evolution. In cases of severe anisotropy, small surface facets and coarsening can occur. In contrast, when the typical surface free energy is mildly anisotropic, the evolving surface is smooth and the equilibrium shape is unique for a variety of the initial crystal shapes.