Theory of the size distribution in three-dimensional grain growth.

Abstract

The evolution of a three-dimensional grain boundary network is calculated in terms of a modified version of the classic theory of Hillert [M. Hillert, Acta Metall. 13, 227 (1965)]. This has been extended beyond the mean field approximation to account for the size dependence of the incoming flux to grains embedded in the network. The prediction for the scaling distribution of grain sizes shows good agreement with that observed in Potts model simulations. At small volumes the distribution follows a power-law behavior, whereas at larger volumes it falls exponentially.