Anion ordering in the structure of cubic perovskite has been investigated by the group-theoretical method. The possibility of the existence of 261 ordered low-symmetry structures, each with a unique space-group symmetry, is established. These results include five binary and 14 ternary anion superstructures. The 261 idealized anion-ordered perovskite structures are considered as aristotypes, giving rise to different derivatives. The structures of these derivatives are formed by tilting of BO6 octahedra, distortions caused by the cooperative Jahn-Teller effect and other physical effects. Some derivatives of aristotypes exist as real substances, and some as virtual ones. A classification of aristotypes of anion superstructures in perovskite is proposed: the AX class (the simultaneous ordering of A cations and anions in cubic perovskite structure), the BX class (the simultaneous ordering of B cations and anions) and the X class (the ordering of anions only in cubic perovskite structure). In most perovskites anion ordering is accompanied by cation ordering. Therefore, the main classes of anion order in perovskites are the AX and BX classes. The calculated structures of some anion superstructures are reported. Comparison of predictions and experimentally investigated anion superstructures shows coherency of theoretical and experimental results.

By slow cooling of the melt, large Bi2Ti2O7 single crystals with a composition close to stoichiometric were grown. No traces of impurity phases were found on the X-ray diffraction patterns. A structural model with the space group Fd m and displacive disorder in Bi-sublattice was proposed based on X-ray single crystal diffraction data. The dielectric properties of Bi2Ti2O7 single crystals as a function of temperature at different frequencies were studied for the first time. As in the case of ceramic samples, a step-like frequency-dependent anomaly was detected at a temperature of about 220 K at a frequency of 1 kHz. It was found that attempts to describe the dielectric relaxation using the Arrhenius equation do not lead to physically significant values of the fitting parameters. However, the relaxation behavior is well described by the empirical Vogel–Fulcher relation, which is typical for many dipole and spin glasses, as well as relaxor ferroelectrics. Based on the value of fitting parameters, Bi2Ti2O7 occupies an intermediate position between the canonical relaxor PbMg1/3Nb2/3O3 on one hand and lead-free weakly coupled relaxors based on BaTiO3 on the other one. Possible mechanisms of the observed relaxor-like behavior of the Bi2Ti2O7 single crystal are discussed in terms of correlated hopping of bismuth cations and geometric frustration of the pyrochlore lattice.

The structural diversity of breathing pyrochlore lattices was investigated on the example of ordered pyrochlores in terms of group-theoretical analysis, Landau thermodynamics and crystal chemistry.

The theory of structural phase transition in CuTi2S4 is proposed. The symmetry of order parameters, thermodynamics and the mechanism of the atomic structure formation of the rhombohedral Cu-Ti-thiospinel have been studied. The critical order parameter inducing the phase transition has been found. Within the Landau theory of phase transitions, it is shown that the phase state may change from the high-symmetry cubic disordered Fd3[combining macron]m phase to the low-symmetry ordered rhombohedral R3[combining macron]m phase as a result of phase transition of the first order close to the second order. It is shown that the rhombohedral structure of CuTi2S4 is formed as a result of the displacements of all types of atoms and the ordering of Cu-atoms (1 : 1 order type in tetrahedral spinel sites), Ti-atoms (1 : 1 : 6 order type in octahedral spinel sites), and S-atoms (1 : 1 : 3 : 3 order type). The Cu- and Ti-atoms form metal nanoclusters which are named a "bunch" of dimers. The "bunch" of dimers in CuTi2S4 is a new type of self-organization of atoms in frustrated spinel-like structures. It is shown that Ti-atoms also form other types of metal nanoclusters: trimers and tetrahedra.

Pyrochlores belong to a numerous family of crystalline materials with a rich variety of technologically important functional properties and developed structural diversity of possible transformations including isosymmetric, reconstructive, and phase transitions of second order (and first order close to second order). Here, using a combination of group-theoretical and crystallographic analysis, we report a uniform classification of 343 types of possible ordered phases, which are theoretically derived from only one initial A 2 B 2 X 6 Y pyrochlore structure by different specific physical mechanisms (order parameters or its combinations) and show a hierarchical relationship between them. A symmetry analysis of the intrinsic relationships between structural degrees of freedom and atomic order in pyrochlore crystals made it possible to highlight six nominal classes of atomic order depending on the ordered sublattice, and by taking into account the role of the improper ordered parameters, only four classes remain: X, XY, ABX, and ABXY. For each of these abstract classes of atomic order the modified Barnighausen tree, illustrating the symmetry pathways of group−subgroup relation and participation of relevant order parameters, was constructed. Three fundamental structural features of the ordered pyrochlores have been established: (a) the impossibility of "pure" (not accompanied by atomic displacements) cation ordering at the A and B pyrochlore sublattices (16d and 16c Wyckoff positions, respectively); (b) the impossibility of "pure" ordering of anions at the X sublattice (48f Wyckoff position); (c) atomic ordering in the A sublattice which is always accompanied by atomic ordering in the B sublattice. A brief review of experimentally known ordered pyrochlores consistent with our structural predictions is given. Finally, the main directions of the theoretical results application including interpretation of the phase transition origins, experimental property predictions, the choice of a model for structural refinement or for materials design as a starting point for energy calculations, and a classification of the hierarchical relationship between phases are discussed. This study provides a symmetry guide for the extensive family of ordered pyrochlores and shows the origin of its structural diversity.

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The spinel oxide AlVO 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 AlVO 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 k(τ) (in Kovalev notation) of the Fd \bar{3}m space group. Knowledge of the order-parameter symmetry allows us to show that the derived AlVO 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, d and d 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 AlVO rhombohedral modification. The trimer model of the low-symmetry AlVO 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.

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