GEOMETRIC .1. MODELS OF CRYSTAL-GROWTH

Recent theoretical advances in the mathematical treatment of geometric interface motion make more tractable the theory of a wide variety of materials science problems where the interface velocity is not controlled by long-range-diffusion. Among the interface motion problems that can be modelled as geometric are certain types of phase changes, crystal growth, domain growth, grain growth. ion beam and chemical etching, and coherency stress driven interface migration. We provide an introduction to nine mathematical methods for solving such problems, give the limits of applicability of the methods, and discuss the relations among them theoretically and their uses in computation. Comparisons of some of them are made by displaying how the same physical problems are treated in the various applicable methods.