The effects of elastic stress on the kinetics of ostwald ripening: The two-particle problem

Abstract

We show that the kinetics of the classical two-particle Ostwald ripening problem can be altered radically by elastic stress induced by misfit (coherency) strains. The growth rates of the secondphase particles in the presence of elastic stress are shown to differ not only in magnitude but also in sign from the classical zero-stress treatment. For example, the larger particle does not always grow at the expense of the smaller particle, but there are large ranges of the thermophysical parameters in which inverse ripening occurs;i.e., the smaller particle grows at the expense of the larger particle. Elastic stresses also may induce significant morphological changes in the particles, as well as far stronger spatial correlations between the coarsening particles than in the classical zero-stress limit. The analysis is cast in terms of an initial value problem, allowing the growth rates of the particles to be determined as a function of readily obtainable materials parameters. We find that the influence of misfit strains on particle growth rates and regimes of inverse coarsening is significantly greater than that predicted from elastic energy analyses. We expect many of the qualitative features of the ripening behavior discussed herein to be observed in the multibody problem found in nature.