Length Scale of Correlations in Grain Boundary Networks

Statistical descriptions of grain boundary networks tend to focus upon the connectivity among “special” grain boundary types, such as low-angle or coincidence boundaries. Recent results from experiments, computer simulations and analytical models have shown that the distribution of such special boundaries is nonrandom at the nearest-neighbor level, but the discussion has not yet been extended to the study of longer-range correlations. In the present work, we explore the correlations among special and general (i.e., non-special) boundaries at longer length scales by calculating the configurational entropy of grain boundary structures. We find that correlations among grain boundary types exist to at least the third nearest-neighbor level even when there is no spatial correlation in the crystallographic texture of the material. Furthermore, we show that the percolation threshold for special boundary connectivity is strongly affected by these higher-order crystallographic constraints.