A generalized kinetic equation for crystal growth

A kinetic equation describing the growth of a crystal is formulated in the spirit of the time-dependent Ginzburg-Landau theory. The equation, which is applicable to two and three-dimensional problems, takes into account the anisotropy of the edge free energy γ and of a transport coefficient D as well as spatial and temporal variations in the chemical-potential difference. Anisotropic expressions for γ and D are obtained from a microscopic model. Numerical solutions of the generalized kinetic equation are presented which show the influence of the anisotropy on the two-dimensional growth spiral of a screw dislocation.