Shape evolution by surface diffusion and surface attachment limited kinetics on completely faceted surfaces

The evolution of two-dimensional shapes to equilibrium shapes is investigated for two kinetic mechanisms, surface diffusion and surface attachment limited kinetics. Qualitative differences are found that may be used in experiments for easy distinction among the two mechanisms, and find topological changes not expected for the corresponding isotropic problems. We take advantage of the mathematical developments for surface evolution and equilibration problems when surface energy anisotropy is “crystalline”, so extreme that crystals are fully faceted. We confirm the prediction that with this anisotropy these problems are more easily solvable than for lesser anisotropies, and the techniques developed may even be useful for approximating isotropic problems.