General schema for [0 0 1] tilt grain boundaries in dense packing cubic crystals

Atomic resolution Z-contrast images from a series of CeO2 [0 0 1] tilt grain boundaries at coincident site lattice (CSL) or near-CSL misorientations can all be explained within a structural unit model. These structural units (which cover all boundaries from 0° to 90°) show striking similarities to comparable CSL boundaries observed in cubic crystal structures that are also derived from dense packing (face centered cubic metal; rocksalt, perovskite, etc.). A general model for the structure of grain boundaries in such similarly structured materials systems has been developed that is based on the crystallography of the parent structures. Changes away from these predicted grain boundary symmetries can be interpreted as showing the frustration of symmetry caused by the incorporation of point defects (vacancies and impurities). This general model for grain boundary structures can, in principle, provide a means to infer the structure–property relationships in broad classes of materials.