Modeling and simulation of grain growth in Si3N4 - I. Anisotropic Ostwald ripening

The anisotropic Ostwald ripening model has been developed for completely fa ceted crystals. This model has been applied to the simulation of grain grow th in beta-Si3N4 With a highly anisotropic rodlike grain shape developed in the liquid phase. The reduction of aspect ratio after the phase transforma tion observed by previous studies is proved to be a consequence of the anis otropic Ostwald ripening. This model predicts a growth exponent n = 3 for t otally interfacial reaction controlled kinetics, and higher values when the diffusion constant approaches the interfacial reaction constants. This wou ld explain the puzzling results reported by previous works that growth expo nents n = 3 or higher have been observed in the grain growth of faceted cry stals. While the length distribution becomes wider with time, the reduced r adius distribution approaches the shape that is known as the asymptotic dis tribution function derived from the LSW theory. (C) 1998 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.