A delta-function model for axially symmetric crystals

A surface energy polar plot contains two possible singularities: the cusps that give facets on an equilibrium crystal, and the circular arcs connecting the cusps that can lead to missing orientations. The common approach of specifying the surface energy usually cannot handle both singularities simultaneously. We model the surface stiffness to avoid missing orientations. Furthermore, a facet is represented by the Dirac delta function. Thus, both singularities are treated precisely. We demonstrate our approach by modeling two axially symmetric crystals.