Verification of a generalized Aboav-Weaire law via experiment and large-scale simulation

Topological correlations in grain boundary networks are investigated on the basis of more than 14000 experimental grains and 9000 Monte Carlo-Potts model simulation grains. A generalized Aboav-Weaire law which serves as a description of the short- and long-range nearest-neighbor topological correlations, is proved to hold both in 2D grain structures and 2D cross-section structures. However, the nearest-neighbor topological correlations have no obvious influence on the rate of 2D grain growth, which is explicitly different from the case in three dimensions that was previously reported in Wang H., Liu G. Q., Song X. Y. and Luan J. H., EPL, 96 (2011) 38003.