Date Published: March 01, 2019
Publisher: International Union of Crystallography
Author(s): Mikhail V. Talanov.
A group-theoretical analysis of 1:3 A-site-ordered perovskite structures is reported.
A-site-ordered quadruple AA′3B4X12 perovskites occupy a special place among a large variety of functional materials (Mitchel, 2002 ▸; Tilley, 2016 ▸; King & Woodward, 2010 ▸; Aleksandrov & Beznosikov, 1997 ▸; Shimakawa, 2008 ▸; Yamada, 2017 ▸; Long, 2016 ▸; Vasil’ev & Volkova, 2007 ▸). This numerous family of materials is characterized by intriguing physical properties such as a giant dielectric constant (Subramanian et al., 2000 ▸; Homes et al., 2001 ▸), positive and negative magnetodielectricity (Imamura et al., 2008 ▸), low- and high-field magnetoresistance (Chen et al., 2014 ▸; Kida et al., 2012 ▸), multiferroic properties (Wang et al., 2015 ▸; Zhou et al., 2017 ▸), large negative and positive thermal expansion (Long, Hayashi et al., 2009 ▸; Zhang et al., 2014 ▸; Long & Shimakawa, 2010 ▸) and heavy Fermion-like behavior (Kobayashi et al., 2004 ▸).
The space group of the ABX3 cubic perovskite structure is . In this structure, A cations occupy Wyckoff position 1a with cubo-octahedral coordination and with local symmetry , octahedral B cations occupy Wyckoff position 1b with local symmetry and X anions occupy Wyckoff position 3c with local symmetry 4/mm.m. Perovskites are referred to as anion-octahedral-type structures, i.e. BX6 octahedra act as building blocks which are connected together by common vertices in three directions and are separated by A cations located in cubo-octahedral voids. Note that 1a and 1b positions in the perovskite structure are symmetrically equivalent. They are connected by an external automorphism, i.e. origin shift (½ ½ ½) of the unit cell. This means that the origin can be chosen both at A- (like in this work) and B-cation sites. The fact that the irreps responsible for these two descriptions are different must be taken into account.
Using group-theoretical methods of the phase transitions theory, possible 1:3 A-site-ordered structures are derived from more than 2600 low-symmetry perovskite-like phases obtained by different paths and then analyzed. These phases can be formed from a high-symmetry parent perovskite structure (archetype) as a result of real or virtual structural phase transitions connected with different OPs: atom orderings, atom displacements (polar and non-polar), tilts of octahedra and their combinations. From these phases all 1:3 A-site-ordered low-symmetry phases are identified and classified by irreps of the space group (Fig. 1 ▸, Table 2 ▸). Proper and improper OPs, as well as theoretically calculated structures (space groups, multiplications of primitive cells, Wyckoff position splitting) are presented for each of these phases. The structural mechanisms of the formation of some experimentally known 1:3 A-site-ordered low-symmetry phases from an archetype perovskite phase have been studied in detail: CaCu3Ti4O12 (the phase structure is characterized by the tilts of anion octahedra), CaCu3Ga2Sn2O12 (the phase structure can be represented by a combination of the tilts of anion octahedra and 1:1 B-site ordering), CaMn3Mn4O12 (the structure of the phase can be considered as a combination of the tilts of anion octahedra and 1:3 B-site ordering), Ce1/2Cu3Ti4O12 (the phase structure is characterized by a combination of tilts of anion octahedra and additional 1:1 A-site ordering) and others.