The effect of volume fraction of precipitate on ostwald ripening

Abstract

The classical theory of the coarsening of precipitate particles by competitive growth (Ostwald ripening) is extended to include the effect of encounters between growing particles using the method outlined by Lifshitz and Slyosov [ J. phys. Chem. Solids 19, 35 (1961)]. In the modified theory the rate of change of the mean particle size is still proportional to the cube root of the time but the rate constant is a function of volume fraction and so is the relative particle size distribution. The effect of encounters is to increase the growth rate although the effect is not great; the rate constant varying by a factor of approximately three over the whole volume fraction range. This is in broad agreement with current experimental evidence but contradicts alternative modifications of the classical theory. The relative particle size distributions are greatly altered in the modified theory, becoming flattened, more symmetrical and having a much broader range of particle sizes than the unmodified theory. The broadening of the relative particle size distribution is also in good accord with experiment and is rather greater than predicted by alternative modifications.