A spike-function model of facets

Facets appear often on crystalline solids and affect surface evolution. Previous models of facets prescribe the surface energy γ as a function of crystallographic orientation θ. However, when the anisotropy is strong, the reduced surface energy γ+d2γ/dθ2 can become negative, which may make surface-evolution problems ill-posed. Recently, a new model has been proposed in which the reduced surface energy is prescribed instead of the surface energy [Surf. Sci. 487 (2001) L529]. In this approach, a facet is represented by the Dirac delta function, and the anisotropy can be arbitrarily strong, but it does not induce ill-posedness. The delta-function model is illustrated in this work by an octagonal crystal with unequal sides. To facilitate numerical simulations, the delta function is replaced by a spike function with width ε. A square crystal is simulated to show the effect of varying ε. We also demonstrate that, given a measured equilibrium crystal shape, the new model can calculate the surface energy if the temperature is at or above the roughening temperature.