Coarsening in the presence of vacancies

Using Monte Carlo simulations, we explore the effect of vacancy-mediated diffusion on the kinetics of coarsening of a two-phase (matrix and precipitate) alloy system. When a vacancy diffuses into the vicinity of a minority-phase (precipitate) cluster, the further time development of its trajectory is dictated by the interplay of the cluster–matrix interface energy and the thermal fluctuations. For low temperatures, the vacancy takes a position at the interface; while with increasing temperatures, thermal fluctuations favor a random location of the vacancy. Thus, at low temperatures, the probability is relatively higher for minority-phase atoms that evaporate from a cluster, aided by a vacancy, to recondense onto the same cluster, deforming the shapes of the clusters. The consequent shift in the center of mass causes random motion of clusters as a whole. This gives rise to coarsening via cluster–cluster aggregation (CCA) as the clusters encounter one another. As thermal fluctuations increase, the tendency of an atom to diffuse far from the original cluster, aided by a vacancy, increases. Thus, with increasing temperature, the coarsening mechanism gradually changes to Ostwald ripening (OR). At the early stages of coarsening, for sufficiently low temperature and sufficiently high minority-phase concentration, there is a third process, which is a variant of CCA. At sufficiently low minority-phase cluster spacing, the vacancy interfacial diffusion, and the consequent particle reshaping, leads to CCA without the need for any further diffusive motion of the minority-phase clusters. As we describe in detail, this leads to a more complicated time evolution than in the lower concentration and/or higher temperature regime. We include this discussion as part of our overall detailed discussion of the time evolution of the length-scale in coarsening.