Prediction of the structures in the family of La(IO3)3 iodates based on topology and symmetry analysis within the OD theory

Topology and symmetry analysis of the structures of the La (IO₃)₃ family is performed within the Dornberger-Schiff OD theory. Two-dimensional periodic blocks (“layers”) of two types are found in the monoclinic La (IO₃)₃ iodate; the local symmetry of one of these blocks is higher than the symmetry of the structure as a whole. This feature defines the possibility of varying the relative position of the pairs of “layers” and the existence of structures other than the structure studied. Three hypothetical polytypes with the maximum degree of ordering that belong to different crystal systems (triclinic, monoclinic, and trigonal) and disordered structures are predicted by the OD theory. This example demonstrates the possibilities of the OD theory for predicting structures.