A  -function Model for Equilibrium Crystals

1. q R c H A -function Model for Equilibrium Crystals Facets or planar surfaces appear often on crystalline solids, and need to be accurately modeled in studying surface evolution. Previous models of facets prescribe the surface free energy g as a function of crystallographic orientation q. However, when the anisotropic is strong, the reduced surface energy g + d2g/dq2 can become negative, which may induce ill-posedness in surface evolution problems. Here, we prescribe the reduced surface energy instead of the surface energy. This approach allows arbitrarily strong anisotropy, but avoids the ill-posedness. Further, a facet is represented by the Dirac delta function. This is the first time that the delta function is used to model facets. The new approach is demonstrated by modeling two-dimensional axially symmetric and three-dimensional axisymmetric equilibrium crystals. • Xin, T. and H. Wong "A -function model of facets," Surface Sci. 487, L529-L533 (2001). • Xin, T. and H. Wong "A spike-function model of facets," Materials Science & Engineering A364, 287-295 (2004). • Du, P. and H. Wong “A delta-function model for axially symmetric crystals,” Scripta Materialia 55, 1171-1174 (2006). • Du, P. and H. Wong " An analytic solution for three-dimensional axisymmetric equilibrium crystal shapes," Scripta Materialia 60, 631-634 (2009).