A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth

Abstract

We consider solidification into a hypercooled melt in which kinetic undercooling and anisotropic surface energy are present. We allow the anisotropy to be strong enough that missing orientations would be present in equilibrium configurations, 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 .