Determination of composite crystal structures and superspace groups

Abstract

Superspace groups introduced for usual modulated structures have recently been applied to the analysis of composite crystals. This review describes the method of composite-crystal analysis based on the superspace group. This method is efficient for the analysis of any (incommensurate or commensurate) composite crystals. The method is analogous to that for the modulated structure in many respects. The description of composite crystals in superspace, determination of their superspace groups and unified setting of the unit vectors are mentioned. Two possible approximations and a relation between the superspace and space groups for commensurate composite crystals are discussed. Space groups of chimney-ladder structures with different periods are derived from a single superspace group by the application of this relation. Possible superspace groups for known composite structures are deduced from the space groups of average substructures. Finally, the refinement method is discussed.