Uniqueness and self similarity of size distributions in grain growth and coarsening

The late stage statistical self-similarity or scaling observed in normal grain growth and coarsening are derived from a model for their evolution using a Fokker–Planck equation obtained from stochastic considerations. Using a suitably generalized H-theorem, it is shown that there is indeed a unique state (self-similar state) evolving from an arbitrary initial state. The time dependence of the appropriate average sizes in normal grain growth, bubble growth, and coarsening are deduced from this model. Multiple self-similar states in some previous models based on mean field treatment do not appear in the present analysis.