The effect of imposing a corner condition on the evolution of two-dimensional crystal morphologies by surface diffusion with anisotropic surface free energies

Continuity of the chemical potential is required from the physics of the evolution of crystal morphology by surface diffusion and in equilibrium crystal shapes (ECS). With an anisotropic surface free energy, multiple ECS with corners have been reported and instability developed in computing evolution of crystal morphology. For a cornered ECS that minimizes the total surface free energy, a corner condition is needed. Hence, in addition to continuity of the chemical potential, we add the corner condition in the evolution of crystal morphology and ensure the condition is satisfied in the numerical computation of the evolving surfaces. The evolution is governed by a nonlinear 4th order time dependent partial differential equation. By enforcing the corner condition, we obtain better stability in the evolution, which leads to ECS having lower total surface free energies than those obtained previously without satisfying the corner condition. Our study shows that the corner condition plays an important role for the cases of critically and severely anisotropic surface free energies that yield surface corners and facets.