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

The quadruple perovskitesAA′₃B₄X₁₂are characterized by an extremely wide variety of intriguing physical properties, which makes them attractive candidates for various applications. Using group-theoretical analysis, possible 1:3A-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, Ce_1/2Cu₃Ti₄O₁₂, LaMn₃Mn₄O₁₂, BiMn₃Mn₄O₁₂and 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 1:3A-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.