Brownmillerites as members of the unified OD family with two-dimensional disorder: A topology and symmetry analysis, the prediction of structures, and the properties of crystals

Abstract

A topology and symmetry analysis of the structures of the brownmillerite family is performed within the OD theory. Blocks of two types with two-dimensional periodicity (“layers”) are revealed in two main structural types with Ibm2 and Pcmn symmetry. The high local symmetry of one layer is not characteristic of the other layer or of the structure as a whole. This feature determines the possibility of varying the arrangement of pairs of layers and the existence of one-dimensional disorder, as well as of structures with a maximum degree of order, periodic structures, and disordered structures. A symmetry analysis allows one to reveal the second direction of disordering (two-dimensional disorder), which is comparatively uncommon. The structure law of the family, which allows the systematic predicting of commensurate structural models without applying the fourth dimension, is described. Structure-property relationships are considered.