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

The late stage statistical self-similarity or scaling observed in normal gr ain growth and coarsening are derived from a model for their evolution usin g a Fokker-Planck equation obtained from stochastic considerations. Using a suitably generalized H-theorem, it is shown that there is indeed a unique slate (selfsimilar state) evolving from an arbitrary initial state. The tim e dependence of the appropriate average sizes in normal grain growth, bubbl e 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. Published by Elsevier Science Ltd on behalf of Ac ta Materialia Inc.