The 3-D Aboav-Weaire relation from modified mean-field model

Grain-environment heterogeneity has been known to play a vital role in grain growth kinetics. In general, the topological correlation between grains and first nearest neighbors is described by the famous Aboav-Weaire law. However, its predictions in 3-D normal grain growth do not exactly match the results from experiments and simulations. In this work, with a 'maximum interval' assumption and an approximation of the MacPherson-Srolovitz law, an alternative approach of the Aboav-Weaire relation is developed from the modified mean-field model. The predictions are not only significantly close to the reality, but also successfully reflect the effect of grain-environment heterogeneity on the normalized grain growth rate.