A mean field theory of grain growth: II

Abstract

The initial part of a theory of normal grain growth previously published by Saetre (2002 Acta Mater. 50 1539) contained a minimum grain size of uncertain physical interpretation. In the accompanying paper to the present one, the theory has been improved by eliminating the constraint of a minimum size class and thus enabling the range u ϵ [0, umax), where u is the relative grain size. It has been shown that the resulting size distribution skews to the right in a manner similar to that of the Hillert distribution. The theory is further developed in this paper. Instead of assuming that all the grains in the ensemble have contiguous neighbouring grains of the same size, the present theory allows the contiguous grains to have sizes that vary as a function of the grain size. In principle, the smaller grains can be surrounded by larger grains and the larger grains can be surrounded by smaller grains, or vice versa. The distances between the triple junctions determine the neighbourhood of a grain. It is shown that a number of distribution functions exist that meet the Lifshitz and Slyozov quasi-stationary state criteria. Theoretical grain size distribution functions are compared with an experimental distribution found in the literature, and the theoretical distribution with the best agreement with the experimental data has been determined. The best theoretical distribution is skewed to the left and can account for major parts of the experimental distribution, but the tail towards the larger grain sizes approaches zero faster than does the experimental distribution.