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, Ce1/2Cu3Ti4O12, 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.

中文翻译：

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1:3A位点有序钙钛矿形成的群论分析


四重钙钛矿AA′3B4X12具有极其广泛的有趣的物理性质，这使得它们成为各种应用的有吸引力的候选者。使用群论分析，发现了可能的 1:3A 位点有序低对称性相。它们可以由母体 Pm{\bar 3}m 钙钛矿结构（原型）形成，这是由于不同结构机制（原子的排序和位移、八面体的倾斜）导致的真实或假设（虚拟）相变的结果。对于每种类型的低对称性相，确定了全套序参数（真序参数和假序参数）、计算结构，包括空间群、原胞乘法、威科夫位置分裂和结构公式。所有有序相都根据母相（原型）空间群的不可约表示进行分类，并根据负责其形成的结构机制的类型进行系统化。特别关注从实验数据已知的化合物的低对称性相的形成结构机制，例如：CaCu3Ti4O12、CaCu3Ga2Sn2O12、CaMn3Mn4O12、Ce1/2Cu3Ti4O12、LaMn3Mn4O12、BiMn3Mn4O12等。第一次建立了正确顺序参数选​​择的可变性现象，该现象允许通过不同的群论路径获得相同的结构。这种现象强调了在描述相变时考虑全套有序参数的根本重要性。使用 Bärnighausen 树形式说明了从空间群 Pm{\bar 3}m 原型到所有 1:3A 位点有序钙钛矿的可能过渡路径。 这些结果可用于识别新相并解释实验结果，确定形成低对称性相的结构机制以及了解类钙钛矿相的结构起源。所获得的非模型群理论结果结合晶体化学数据和第一性原理计算可能成为设计具有钙钛矿结构的新型功能材料的起点。