An unusual case of the structural mechanisms of inorganic crystals formation is considered theoretically on the example of the AlV₂O₄ and CuZr_1.86(1)S₄ isosymmetric rhombohedral spinels with the same character of the atom distribution on the Wyckoff positions. It is shown that the difference in structures is due to the critical influence of the order parameter value that describes the real (in the case of AlV₂O₄) and virtual (in the case of CuZr_1.86(1)S₄) structural phase transitions. Owing to the low value of the order parameter, the phase transition to the rhombohedral AlV₂O₄ structure is associated with relatively small atomic displacements and the formation of heptamer structural blocks in the V sublattices. In contrast, the virtual phase transition to the rhombohedral CuZr_1.86(1)S₄ structure is associated with high value of the order parameter and giant atomic displacements. As a result, the Cu and Zr atoms form metal nanoclusters—a “bunch” of dimers. The CuZr_1.86(1)S₄ is a second substance (the first example is CuTi₂S₄) with a new type of self-organization of atoms, in which the metal clusters are formed by the atoms from two (but not one, as in the known materials) geometrically frustrating spinel sublattices.

中文翻译：

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菱面体尖晶石结构中金属簇形成的两种不同机理：AlV ₂ O ₄和CuZr _1.86（1） S ₄

理论上，以AlV ₂ O ₄和CuZr _1.86（1） S _4等对称菱形六面体尖晶石为例，从理论上考虑了无机晶体形成的结构机理的异常情况，该尖晶石具有相同的Wyckoff位置上的原子分布特征。结果表明，结构上的差异是由于顺序参数值的关键影响，顺序参数值描述了真实（在AlV ₂ O ₄的情况下）和虚拟（在CuZr _1.86（1） S ₄的情况下）结构阶段过渡。由于阶跃参数的值较低，相变到菱形AlV ₂ O ₄结构与相对较小的原子位移和V亚晶格中七聚体结构嵌段的形成有关。相反，到菱形CuZr _1.86（1） S ₄结构的虚拟相变与高阶的阶跃参数值和巨大的原子位移有关。结果，Cu和Zr原子形成了金属纳米团簇-二聚体的“束”。CuZr _1.86（1） S ₄是具有新的原子自组织类型的第二种物质（第一个示例是CuTi ₂ S ₄），其中金属簇是由两个（但不是一个， （如已知材料）在几何上令人沮丧的尖晶石亚晶格。