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.
