Low-Σ twist and tilt grain boundaries in cubic materials

Knowledge of the geometry of grain boundaries in polycrystalline materials is essential for predicting boundary properties. The issue of cataloging the geometrically characterized groups of twist and tilt boundaries is addressed. All distinct types of pure-twist and pure-tilt boundaries are determined for misorientations corresponding to highly coincident (3 ≤ Σ ≤ 13) lattices of cubic symmetry. For these particular misorientations, the number of distinct twist boundaries and zones of tilt boundaries ranges from 5 (Σ = 3) to 11 (Σ = 9 or 11). Maps displaying the locations of twist and tilt boundary planes indicate boundaries having particular geometries with two-dimensional periodicities. This is of significance for identification of special boundary structures. Moreover, the maps allow for relating peaks on experimentally determined grain boundary distributions to particular types of twist or tilt boundaries.