Percolation and statistical properties of low- and high-angle interface networks in polycrystalline ensembles

Percolation theory is often used to model intergranular or transgranular phenomena in polycrystals by treating low- and high-angle interfaces as strong and weak links, respectively. Here we demonstrate that triple-junction coordinations and percolation thresholds of such interfacial networks are significantly different from those of randomly assembled lattices, which invalidates the use of standard percolation theory for these problems. This departure is due to local crystallographic constraints for low- and high-angle boundary coordinations at triple junctions, which we understand here through (i) two-dimensional simulations of polycrystals with various textures and (ii) an analytical model using local transition probabilities. Both methods capture the tendency for high-angle boundaries to cluster, and the computational method also provides percolation threshold values for general and fiber-textured microstructures.