Anion order in perovskites: a group-theoretical analysis

Abstract

Anion ordering in the structure of cubic perovskite has been investigated by the group-theoretical method. The possibility of the existence of 261 ordered low-symmetry structures, each with a unique space-group symmetry, is established. These results include five binary and 14 ternary anion superstructures. The 261 idealized anion-ordered perovskite structures are considered as aristotypes, giving rise to different derivatives. The structures of these derivatives are formed by tilting of BO6 octahedra, distortions caused by the cooperative Jahn-Teller effect and other physical effects. Some derivatives of aristotypes exist as real substances, and some as virtual ones. A classification of aristotypes of anion superstructures in perovskite is proposed: the AX class (the simultaneous ordering of A cations and anions in cubic perovskite structure), the BX class (the simultaneous ordering of B cations and anions) and the X class (the ordering of anions only in cubic perovskite structure). In most perovskites anion ordering is accompanied by cation ordering. Therefore, the main classes of anion order in perovskites are the AX and BX classes. The calculated structures of some anion superstructures are reported. Comparison of predictions and experimentally investigated anion superstructures shows coherency of theoretical and experimental results.

Group-theoretical analysis of 1:3A-site-ordered perovskite formation

“…The idealized perovskite structure is the archetype (this word originates from the ancient Greek one '"o' which means 'prototype') and/or aristotype (from the ancient Greek word 'o', 'highest') for low-symmetry modifications (Megaw, 1957(Megaw, , 1973Aleksandrov et al, 1981;Talanov et al, 2016). 1 Atom displacements (including ordered tilts or rotations of the BX 6 octahedra) and orderings, as well as their combinations, result in lower-symmetry superstructures.…”

“…We have shown previously that the ordering in the B sublattice of the perovskite structure, described by a single OP, cannot lead to simultaneous ordering in the A sublattice ). Yet, the proposed ordering mechanism can be 386 Mikhail V. Talanov realized with anion ordering in the X sublattice (Talanov et al, 2016). Of all the phases that are formed as a result of the anion ordering (induced by only one OP without the contribution of additional structural mechanisms), only three phases show 1:3 A-site ordering.…”

“…The former are formed with an eightfold increase in primitive cell volume, and the latter with a fourfold increase. In these structures, there is an ordering in the B sublattice induced by improper OPs that are transformed by irreps k 10 4 (X 3 À ), k 11 7 (M 4 + ), k 13 4 (R 2 À ), which enter into the permutation representation of perovskite structure on the 1b Wyckoff positions (Talanov et al, 2016). The Pn " 3 3 phase can be induced by a combination of several OPs only (see the next section).…”

“…The diverse and unique physical properties of 1:3 A-siteordered perovskites are mainly due to the ordered structure of these crystals. We have previously carried out a study of cation-and anion-ordered low-symmetry modifications of the parent Pm " 3 3m perovskite structure Talanov et al, 2016). In this article, we emphasize the systematic study of perovskite-like structures with an order of 1:3 in the A sublattice which are formed as a result of real or hypothetical (virtual) structural phase transitions from the parent phase through various structural mechanisms.…”

“…In this article, we consider the ideal perovskite structure as an archetype, and ideal cation and anion superstructures of perovskites as aristotypes [see details on this issue in the work ofTalanov et al (2016)]. By definition, groupsubgroup relations necessarily exist between the space groups of the parent structure (archetype and aristotype) and the observed one.…”