Coarsening kinetics of grain-boundary precipitates: a reanalysis based on the multiple pairwise interaction model of Ostwald ripening

The topological structure of the recently developed MultiParticle (MP) model of Ostwald ripening based on direct pairwise interactions has been extended to describe the coarsening of grain-boundary (GB) precipitates by introducing a 2D diffusion geometry. In agreement with previous studies in the literature, the model predicts that the mean radius grows proportionally to t(1/4). The analysis carried out in this work originates from the observation that in some cases the t(1/3) kinetics, typical of a process controlled by bulk diffusion, is recovered also in systems where almost all particles are located on grain boundaries. In order to investigate this discrepancy, an ideal system with small volume fraction of second phase (0.05) where all precipitates are on GBs has been considered. By calculating the ratio between the coarsening rate predicted when the system is controlled by GB diffusion and that of the same system controlled by bulk diffusion it is found that, even by imposing a diffusion coefficient at GBs 100 times that in the bulk, GB diffusion dominates only when the mean particle size is below a limiting value. Since the system is anyway undergoing coarsening, eventually the bulk diffusion mechanism will prevail. This provides a possible explanation of the experimental results. For the sake of completeness, a kinetic equation describing the true 2D Ostwald ripening of island-like cylindrical particles within the framework of the MP model is also developed. As expected, it is characterised by a t(1/3) coarsening law.