Self-organization kinetics in finite precipitate ensembles during coarsening

A rate equation approach is applied for the description of the self-organization (layering) phenomenon predicted in recent computer experiments. This layering was observed in finite precipitate systems during annealing and is caused by Ostwald ripening. The onset of the layer formation is shown to be triggered by the inhomogeneity of the impurity concentration profile near the boundary of a precipitate system and not by the spatially uniform “nonlocal fluctuation instability” of precipitate parameters. The change of the spatial profile of precipitate size starts from the boundary of the system and occurs within a reaction shell having a thickness of the order of the diffusional screening length. During annealing this reaction shell shifts progressively into the system, leaving behind layers of precipitates. The layering is shown to occur only in sufficiently large systems with characteristic dimensions of at least several diffusional screening lengths. The reason for the weak sensitivity of interlayer distance to variations of system parameters is elucidated.