In this contribution, we attempted a theoretical analysis on the validity of the widely-accepted idea that rough and singular surfaces can coexist in a crystal at equilibrium. By manipulating the Cahn and Hoffman capillarity vector, the conclusion that a crystal at equilibrium should be composed either of singular surfaces or of rough ones was reached.

The growth process of solid grains in a liquid matrix is usually explained in tem1S of Ostwald ripening. The variation of growth (dissolution) rate as a function of grain size during Ostwald ripening predicted that the dissolution rate becomes very large as grain size decreases but the growth rate of a large grain is rather limited. Therefore. a rather uniform size distribution of grain size is maintained once after the quasi-equilibrium state is reached. Quite frequently, however, the exaggerated grain growth (EGG) is observed to occur: only a limited number of grains grow exceptionally. From the observation that the EGG occurs only for the faceted grains with apparently straight solid-liquid interfaces, the EGG is suggested to be the consequence of growth process controlled by 2-dimensional nucleation. In this study, the result by computer calculation on the grain growth process controlled by various mechanisms will be given.