Symmetry classification of cubic twist grain boundaries

A new classification scheme derived from a higher-dimensional approach to the study of interfaces is presented. The classification groups grain boundaries according to the symmetry of the orientational and translational symmetry variants they contain. For rotation interfaces, the angular range is partitioned into a finite number of equivalence classes. All boundaries are composed of atomic domains separated by a network of dislocations. The symmetry of the domains is different except for the singular boundary that represents each class (the normal form of the class). All boundaries belonging to a given class have the same structure, i.e., the same domain types arranged in the same way, differing only in size, and are expected to share similar properties.