Evolution of multiple asymptotic grain face and volume distributions during grain growth- connection to the initial distribution and asymptotic stabilization of the topological event rates

There has long been a question concerning the existence of a single vs. multiple asymptotic grain size distributions in normal grain growth. The goal of this study has been to address this topic by investigating the underlying mechanisms by which grain face and volume distributions evolve from transient to asymptotic states during grain growth. This investigation employs 3D Monte Carlo simulations to quantify the topological mechanisms of this transition, i.e., grain separation, encounter and loss, and examine their mutual evolution with the distributions from a wide range of initial states towards their multiple final asymptotic states. In the initial transient growth stage, the topological event rates fluctuate markedly, seeking balance among themselves and with the face/volume distributions. In the asymptotic stage this balance is indicated by asymptotic behavior of the ratios of the rates, as well the mean face class 〈 f〉, and normalized widths, CV, of the face and size distributions. It was found that a moderate range of initial distributions evolved through relatively short transient periods towards asymptotic states less spread from each other but with those same relative orders of width. Initial distributions much wider or narrower than these evolved through longer transient periods with trajectories crossing the paths of the more moderate ones, with the widest initial distributions becoming the narrowest and the initially narrowest becoming the widest. These behaviors are explained by their interactive evolution with the topological event rates.