Modeling the formation of facets and corners using a convective Cahn–Hilliard model

Abstract

We consider solidification into a hypercooled melt in the presence of kinetic undercooling and anisotropic surface energy. We allow the anisotropy to be strong enough that equilibrium configurations would contain facets divided by corners, and track the unstable evolution of an initially planar front to a facetted front. Regularization by curvature-dependent surface energy is posed, and in the nonlinear regime a convective Cahn–Hilliard equation is derived. The emergence of facets is thus related to spinodal decomposition and subsequent coarsening. The presence of convective terms generated by the effect of kinetics destroys the binodal construction and leads to a fast coarsening, that for large times t goes as t 1/2.