A CONVECTIVE CAHN-HILLIARD MODEL FOR THE FORMATION OF FACETS AND CORNERS IN CRYSTAL-GROWTH

We consider solidification into a hypercooled melt in which kinetic un dercooling and anisotropic surface energy are present. We allow the an isotropy to be strong enough that missing orientations would be presen t in equilibrium configurations, and track the unstable evolution of a n initially planar front to a facetted front. Regularization by curvat ure-dependent surface energy is posed, and in the nonlinear regime a c onvective Cahn-Hilliard equation is derived. The emergence of facets i s thus related to spinodal decomposition and subsequent coarsening. Th e presence of convective terms generated by the effect of kinetics des troys the binodal construction and leads to a fast coarsening, that fo r large times t goes as t(1/2). (C) 1998 Elsevier Science B.V.