On the Aboav-Weaire-law for junction limited grain growth in two dimensions

In the present work the validity of the Aboav-Weaire-relation in polycrystalline grain microstructures obtained by junction limited grain growth as it may occur in nanocrystalline materials is tested. To that aim, two-dimensional Monte Carlo Potts model simulations have been performed, and it follows that while the kinetics as well as the grain size-topology-relationship shows significant differences for grain boundary controlled grain growth and triple junction controlled growth, the Aboav-Weaire-relation is fulfilled independent of the grain feature controlling the growth kinetics.