Model for faceting in a kinetically controlled crystal growth

A two-dimensional anisotropic nonlinear evolution equation is derived to mo del the formation of facets and corners in the course of kinetically contro lled crystal growth. The equation is solved numerically in particular cases corresponding to the faceting of [001], [111], and [110] growing crystal s urfaces, and the formation of hill-and-valley structures in the form of squ are, triangular, and rhombic pyramids; grooves are observed as well. The py ramidal slopes far from the vertices are found analytically, and in particu lar cases exact solutions of the equation are found. The pyramidal structur es coarsen in time, and the rate of coarsening is studied. [S1063-651X(99)0 7401-2].