Invariant distributions and stationary correlation functions of simulated grain growth processes

This paper first reviews and highlights a relatively large number of distributions and correlation functions that are characteristic for normal grain growth. Attention is then paid to the correlation between the average size of an n-sided grain and the average size of a grain next to an n-sided grain. Size correlations between neighbouring grains are examined using a nearest-neighbour Q=40 Potts model on a triangular 500x500 lattice. We show that few-sided grains tend to be surrounded by large grains, while the neighbours of six-sided grains are typically average-sized. The neighbours of many-sided grains tend to be somewhat smaller than an average-sized grain. This confirms the existence of spatial grain size correlations, which have previously been reproduced by the use of a fundamentally different simulation technique. Finally, the robustness of the stationary correlation functions, is examined by incorporating artificial correlations into the starting pattern. (C) 2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.