Abstract
The quadruple perovskites AA'3B4X12 are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3 A-site-ordered low-symmetry phases have been found. They can be formed from a parent Pm{\bar 3}m perovskite structure (archetype) as a result of real or hypothetical (virtual) phase transitions due to different structural mechanisms (orderings and displacements of atoms, tilts of octahedra). For each type of low-symmetry phase, the full set of order parameters (proper and improper order parameters), the calculated structure, including the space group, the primitive cell multiplication, splitting of the Wyckoff positions and the structural formula were determined. All ordered phases were classified according to the irreducible representations of the space group of the parent phase (archetype) and systematized according to the types of structural mechanisms responsible for their formation. Special attention is paid to the structural mechanisms of formation of the low-symmetry phase of the compounds known from experimental data, such as: CaCu3Ti4O12, CaCu3Ga2Sn2O12, CaMn3Mn4O12, Ce1/2Cu3Ti4O12, LaMn3Mn4O12, BiMn3Mn4O12 and others. For the first time, the phenomenon of variability in the choice of the proper order parameters, which allows one to obtain the same structure by different group-theoretical paths, is established. This phenomenon emphasizes the fundamental importance of considering the full set of order parameters in describing phase transitions. Possible transition paths from the archetype with space group Pm{\bar 3}m to all 1:3 A-site-ordered perovskites are illustrated using the Bärnighausen tree formalism. These results may be used to identify new phases and interpret experimental results, determine the structural mechanisms responsible for the formation of low-symmetry phases as well as to understand the structural genesis of the perovskite-like phases. The obtained non-model group-theoretical results in combination with crystal chemical data and first-principles calculations may be a starting point for the design of new functional materials with a perovskite structure.
Highlights
A-site-ordered quadruple AA03B4X12 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)
To obtain the list of all possible 1:3 A-site-ordered phases resulting from the combination of B-site ordering and tilts of anion octahedra, it is necessary to consider the order parameters (OPs) which is transformed according to the direct sum of irreps entered into the permutation representation of perovskite structure on the 1b Wyckoff position and in the enumeration (2)
CaMn7O12 (CaMn3Mn4O12) (Bochu et times referred to as 1322 perovskites (Senn et al, 2014). This al., 1980) is one of the compounds with such structure; it phase has a structure with eightfold primitive cell volume demonstrates a giant improper ferroelectricity as a result of (Fig. 4). It is generated by a two-component OP, which is transformed by the direct sum of two irreps k115(M2+) and k134(R2À) [or k115(M2+) and k102(X1À) from the same full set of OPs], linked with the in-phase tilts of anion octahedra the magnetic phase transition to an incommensurate helical magnetic structure below 90 K (Zhang et al, 2011a; Johnson et al, 2012; Perks et al, 2012)
Summary
A-site-ordered quadruple AA03B4X12 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). The possible structures of A-site-ordered quadruple AA03B4X12 perovskites have been found based on powerful group-theoretical methods of Landau phase transition theory (Howard & Stokes, 2005; Howard et al, 2003; Aroyo et al, 2006; Perez-Mato et al, 2010; Toledano & Toledano, 1987; Toledano & Dmitriev, 1996; Birman, 1978; Vinberg et al, 1974; Aleksandrov & Bartolome, 2001; Bock & Muller, 2002; Balachandran & Rondinelli, 2013; Stokes & Hatch, 1988; Chechin, 1989; Talanov et al, 2015, 2018; Talanov & Shirokov, 2014; Talanov, 2007, 2018; Stokes & Campbell, 2017). The aim of this study is a group-theoretical analysis of possible pathway formation and structural genesis of 1:3 A-site-ordered perovskites using the ITC and R-approaches
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