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

摘要

We conside4r 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 configuratins would contain facets divided by kcorners, and track the unstable evolution of an initially planar front to a faceted front. Regulrization by curvaturedependent sruface energy is posed, and in the nonlinear regime a convective Cahn-Hilliard eqation is derived. The emergence of facets is thus related to spinodal decompositon and subsequent coarsening. The presence of convective terms generated by the effect of kientics destroys the binodal construction and leads to a fast coarsening, that for large times t goes as t~1/2.