Modeling and simulation of grain growth in Si 3N 4—I. Anisotropic Ostwald ripening

Abstract

The anisotropic Ostwald ripening model has been developed for completely faceted crystals. This model has been applied to the simulation of grain growth in β-Si 3N 4 with a highly anisotropic rod-like grain shape developed in the liquid phase. The reduction of aspect ratio after the phase transformation observed by previous studies is proved to be a consequence of the anisotropic Ostwald ripening. This model predicts a growth exponent n=3 for totally interfacial reaction controlled kinetics, and higher values when the diffusion constant approaches the interfacial reaction constants. This would explain the puzzling results reported by previous works that growth exponents n=3 or higher have been observed in the grain growth of faceted crystals. While the length distribution becomes wider with time, the reduced radius distribution approaches the shape that is known as the asymptotic distribution function derived from the LSW theory.