The spinel oxide AlV₂O₄ is a unique material, in which the formation of clusters is accompanied by atomic, charge and orbital ordering and a rhombohedral lattice distortion. In this work a theory of the structural phase transition in AlV₂O₄ is proposed. This theory is based on the study of the order‐parameter symmetry, thermodynamics, electron density distribution, crystal chemistry and mechanisms of formation of the atomic and orbital structures of the rhombohedral phase. It is established that the critical order parameter is transformed according to irreducible representation k₉(τ₄) (in Kovalev notation) of the space group. Knowledge of the order‐parameter symmetry allows us to show that the derived AlV₂O₄ rhombohedral structure is a result of displacements of all atom types and the ordering of Al atoms (1:1 order type in tetrahedral spinel sites), V atoms (1:1:6 order type in octahedral sites) and O atoms (1:1:3:3 order type), and the ordering of d_xy, d_xz and d_yz orbitals. Application of the density functional theory showed that V atoms in the Kagomé sublattice formed separate trimers. Also, no sign of metallic bonding between separate vanadium trimers in the heptamer structure was found. The density functional theory study and the crystal chemical analysis of V—O bond lengths allowed us to assume the existence of dimers and trimers as main clusters in the structure of the AlV₂O₄ rhombohedral modification. The trimer model of the low‐symmetry AlV₂O₄ structure is proposed. Within the Landau theory of phase transitions, typical diagrams of possible phase states are built. It is shown that phase states can be changed as a first‐order phase transition close to the second order in the vicinity of tricritical points of the phase diagrams.

中文翻译：

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在几何受挫的尖晶石氧化物AlV2O4中形成钒簇。

尖晶石氧化物AlV ₂ O ₄是一种独特的材料，其中团簇的形成伴随着原子，电荷和轨道的排序以及菱形的晶格畸变。在这项工作中，提出了AlV ₂ O _4中结构相变的理论。该理论基于对阶参数对称性，热力学，电子密度分布，晶体化学以及菱形面相的原子和轨道结构形成机理的研究。经确定的临界顺序参数是根据不可约表示变换ķ ₉（τ ₄）（以科瓦列夫符号）的空间群。对阶数参数对称性的了解使我们能够证明，得出的AlV ₂ O ₄菱面体结构是所有原子类型的位移和Al原子（四面体尖晶石位点为1：1阶数），V原子（八面体位点的1：1：6顺序类型）和O原子（1：1：3：3顺序类型），以及d _xy，d _xz和d _yz的顺序轨道。密度泛函理论的应用表明，Kagomé亚晶格中的V原子形成了独立的三聚体。另外，在七聚体结构中的分离的钒三聚体之间没有发现金属结合的迹象。密度泛函理论研究和V-O键长度的晶体化学分析使我们能够假设二聚体和三聚体作为AlV ₂ O ₄菱面体修饰结构的主要簇而存在。低对称AlV ₂ O ₄的三聚体模型建议的结构。在Landau相变理论中，建立了可能的相态的典型图。结果表明，在相图的三临界点附近，相态可以作为接近二阶的一阶相变而改变。