Nonrandom percolation behavior of grain boundary networks in high-Tc superconductors

The grain boundary networks of tetragonal and orthorhombic superconductors are shown to be nonrandom through computer simulations of polycrystalline structures. For biaxially textured microstructures, the distribution of low-angle grain boundaries around triple junctions is measurably deviant from the expectations for a randomly constructed lattice. Percolation thresholds are calculated for the unhindered flow of superconducting current through a polycrystal, and are found to be significantly different from the standard random percolation threshold in two dimensions. These deviations are explained as a result of crystallographic constraints on the network topology.