Solution to the multi-particle diffusion problem with applications to ostwald ripening—II. Computer simulations

Abstract

The multi-particle diffusion solution developed in Paper I is used to determine the collective behavior of a system of dispersed second phase particles undergoing Ostwald ripening. Since the multi-particle diffusion solution was employed to determine the diffusion field within the matrix, interparticle diffusional interactions are specifically included in the treatment. Both the transient and long-time behavior of given initial distributions of particle sizes were examined over a wide range of volume fractions of the coarsening phase. It was found in the transient region that the collective behavior of the coarsening ensemble was highly dependent on the initial distribution. When these distributions were scaled by the average particle radius, they all eventually evolved to identical time-independent distributions which were functions of the volume fraction of the coarsening phase. These time-independent distributions are, in general, significantly different from the classic Lifshitz-Slyozov-Wagner distribution, and become progressively broader and more symmetric with increasing volume fraction. The ripening kinetics were also found to be a function of the volume fraction, the kinetics increasing by a factor of five upon changing the volume fraction from zero to 0.5. The statistical nature of Ostwald ripening was investigated by examining the influence of the volume fraction on the distribution of individual particle source/sink strengths. This statistical information is used to show the self-consistency of the numerical approach.