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.

Group-theoretical methods of the Landau theory of phase transitions are used to investigate the structures of ordered spinels. The possibility of the existence is determined of 305 phases with different types of order in Wyckoff position 8a (including seven binary and seven ternary cation substructures), 537 phases in Wyckoff position 16d (including eight binary and 11 ternary cation substructures), 595 phases in Wyckoff position 32e (including seven binary and four ternary anion substructures) and 549 phases with simultaneous ordering in Wyckoff positions 8a and 16d (including five substructures with binary order in tetrahedral and octahedral sublattices, two substructures with ternary order in both spinel sublattices, and nine substructures with different combined types of binary and ternary order). Theoretical results and experimental data are compared. Calculated structures of the spread types of ordered low-symmetry spinel modifications are given.

The possible distortions in the spinel structure resulting from rotation of the tetrahedra and octahedra have been investigated by a group-theoretical method. The possibility of the existence of 28 phases of rotation of the tetrahedra and five phases of rotation of the octahedra has been shown. In all these phases the polyhedra are equivalent, but their orientation can be different. Among the phases of the tetrahedra rotation there is one phase of pure rotation, i.e. not accompanied by additional (not rotation) distortions of the structure. Of the five phases of the rotation of the octahedra three phases can be obtained only by pure rotation of the octahedra.

The nature of the phonon and magnon modes in the CoCr 2 O 4 multiferroic with a cubic spinel structure has been studied using submillimeter spectroscopy and infrared Fourier spectroscopy. This paper reports on the first measurement of the evolution with temperature of the exchange optical magnon in the ferrimagnetic (T C = 94 K) and two low symmetry (T S ≈ 26 K, T lock in = 14.5 K) phases of CoCr 2 O 4 down to T = 5 K in zero magnetic field. It has been shown that the detected magnon is not a ferrimagnetic order parameter and originates, most probably, from spin precession in the cobalt sublattices. At the points of the magnetic phase transitions, the oscillator parameters of the two lowest frequency phonon modes reveal an anomalous temperature behavior, thus evidencing the presence of significant interaction between the mag netic and phonon subsystems. The increase by 25% of the damping parameter of the phonon mode originat ing from vibrations of the CoO 4 tetrahedra during the transition of CoCr 2 O 4 to the multiferroic state (T < T S ) suggests structural changes in the lattice involving loss of spatial central symmetry of the medium.

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.