Monte Carlo Implementation for Simulation of Ostwald Ripening Via Long Range Diffusion in Two-Phase Solids

Abstract

Numerical simulations based on the Monte Carlo Potts model are used to study coupling of grain growth and Ostwald ripening in two-phase polycrystalline materials. The ratio of the grain boundary energy to the interphase boundary energy is used as an input parameter. It is shown that the grain growth in two-phase polycrystalline materials is controlled by long-range diffusion and the change of the mean grain size with time obeys the growth law,< R> n=< R> 0 n+ kt where n is the grain growth exponent. The value of n is calculated for a broad series of volume fractions. It is found that the inverse grain growth exponent, 1/n, in agreement with the theoretical value, 1/n= 1/3, noticed during computer simulations for volume fractions between 40% and 90%. However, the value of 1/n is smaller than 1/3 for volume fractions between 10% and 30%. Furthermore, the temporal development of the number of grains has been analyzed for the entire range of volume fractions. It is also seen that the quasi-stationary state is advanced at varied aging times depending on the volume fractions. Furthermore, it is shown that the simulated size distribution are symmetric and peaked at x= 1 for volume fractions differ between 50% and 90%; however, the simulated size distribution become asymmetric and skew to smaller grains for lower volume fractions change between 10% and 40%.