Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures

Abstract

A new grain topology-size relationship in three-dimensional (3D) polycrystalline microstructures has recently been established by considering the effects of non-random first nearest neighbor grains. In this contribution, a generalized form for this relationship is presented by considering the interactions of kth (k=1, 2, 3...) nearest neighbor grains, and large scale Monte Carlo-Potts model simulation is used to investigate the general neighborhood topological effect on the topology-size relationship. The results show that, unlike their first nearest neighbors (k=1), the topological correlations of 3D grains with their kth layers (k≥2) of nearest-neighbors may have trivial effect on the topology-size relationship. © 2013 The Author(s).