Geometrical grounds of mean field solutions for normal grain growth

The classical mean field approach for normal grain growth in polycrystalline materials is revisited. We re-drive and study possible self-similar solutions and show that the grain size distribution can be determined only by the geometry of neighbouring grains for any given configuration. In three dimensions, it is shown that a single index < R >(2)/< R-2 > can represent the geometrical characteristic of grains and has a one-to-one relationship with the mean field parameter gamma. We reinvestigate the results of our recent phase-field study [Darvishi Kamachali R, Steinbach I. Acta Mater 2012;60:2719] in the light of new analytical results and found a value gamma approximate to 3.5-3.2 for the stable regime. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.