Models of Idealized Grain Growth: Critique of Stochastic Theories and Implications of Scaling

摘要

Using a Fokker-Planck analysis, we derive the equation of continuity describing grain growth. By analysis of coarse graining, it is shown that ther is no diffusion term in this equation and therefore that stochastic theories based on this term are not valid descriptions of grain growth. Then, using the continuity equation and assuming scaling holds for the uniform grain boundary model in two dimensions, we apply an analysis of Hunderi and Ryum to show that the Hillert grain size distribution always flows if there is no correlation of neighboring grain sizes in the sense that the average number of neighbors of a given grain is a linear function of the size (e.g. perimeter) of that grain. Hence, non-Hillert distributions requrie departures from this linearity. Soem examples of neighbor grain correlations that produce grain size distributions in close agreement with simulations will be given.