Role of topological constraints on the statistical properties of grain boundary networks

Grain boundaries in polycrystalline materials form a topological network that evolves under dynamic processing conditions. Recent experimental results for a number of different materials have demonstrated that the statistical distribution of triple junction types (or node types) in polycrystals is highly nonrandom. These observations point to the critical role of local crystallographic constraints on the topology and evolution of grain boundary networks. Here we demonstrate that, within the context of percolation theory, a realistic local constraint applied at each junction can strongly influence the topology of networks in general. In the specific case of grain boundary networks, such constraint can account for the experimentally observed deviations from the random case.