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A system of mutual relationships (a hierarchy) is constructed between various perovskite-like crystal structures based on available structural data. All the perovskite-like structures are characterized by a common indicator of their relationship—the presence of layers, stacks, or frameworks made up of BX6 octahedra linked at their vertices (where B is a cation, X is an anion) or fragments of octahedra in the form of BX5 pyramids or BX4 squares in aniondeficient compounds. In layered structures, these stacks are joined to each other by various intermediate blocks. It is well known that one homological series of compounds is constructed by increasing the number of layers in a stack while preserving the same kind of connecting block. Crystals of various series that contain identical stacks (but different blocks of one or two types) can also be related to one another via this feature. The hierarchical system includes compounds with small distortions in their structures for various reasons.
Aleksandrov et al. (Thu,) studied this question.