Arrangement of polyhedral units for [0001]-symmetrical tilt grain boundaries in zinc oxide

Polycrystalline ZnO is used in a wide variety of electrical applications, and its properties are largely influenced by crystalline defects, such as grain boundaries (GBs). Therefore, in this study, the atomic structures of [0001]-symmetrical tilt GBs in ZnO have been characterized by scanning transmission electron microscopy, and the misorientation dependence of the atomic structures around GBs is thoroughly discussed based on the polyhedral-unit model. In addition to theoretical calculations, the polyhedral-unit arrangements for arbitrary tilt angles are described and predicted by a number-theory-based approach. The predicted structural-unit arrangements agreed well with those experimentally observed, indicating that geometrical restrictions determine the ZnO GB structures. Owing to the crystallographic relationship between the structural-unit Burgers vector and the GB-plane normal, the structural-unit arrangement was transformed at approximately 30∘, which is associated with a rigid-body translation from one grain to another.