V. B. Shirokov

Tilting structures in spinels

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.

Atomic order in the spinel structure - a group- theoretical analysis

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.

Unique atom hyper‐kagome order in Na4Ir3O8 and in low‐symmetry spinel modifications

Group-theoretical and thermodynamic methods of the Landau theory of phase transitions are used to investigate the hyper-kagome atomic order in structures of ordered spinels and a spinel-like Na4Ir3O8 crystal. The formation of an atom hyper-kagome sublattice in Na4Ir3O8 is described theoretically on the basis of the archetype (hypothetical parent structure/phase) concept. The archetype structure of Na4Ir3O8 has a spinel-like structure (space group Fd\bar 3m) and composition [Na1/2Ir3/2](16d)[Na3/2](16c)O(32e)4. The critical order parameter which induces hypothetical phase transition has been stated. It is shown that the derived structure of Na4Ir3O8 is formed as a result of the displacements of Na, Ir and O atoms, and ordering of Na, Ir and O atoms, ordering dxy, dxz, dyz orbitals as well. Ordering of all atoms takes place according to the type 1:3. Ir and Na atoms form an intriguing atom order: a network of corner-shared Ir triangles called a hyper-kagome lattice. The Ir atoms form nanoclusters which are named decagons. The existence of hyper-kagome lattices in six types of ordered spinel structures is predicted theoretically. The structure mechanisms of the formation of the predicted hyper-kagome atom order in some ordered spinel phases are established. For a number of cases typical diagrams of possible crystal phase states are built in the framework of the Landau theory of phase transitions. Thermodynamical conditions of hyper-kagome order formation are discussed by means of these diagrams. The proposed theory is in accordance with experimental data.

Theory of structural phase transition in MgTi2O4

A theory of phase transition in MgTi2O4 is proposed based on a study of the order-parameter symmetry, thermodynamics, and mechanisms of formation of the atomic and orbital structure of the low-symmetry MgTi2O4 phase. The critical order parameter (which induces a phase transition) is determined. It is shown that the calculated MgTi2O4 tetragonal structure is a result of displacements of magnesium, titanium, and oxygen atoms; ordering of oxygen atoms; and the participation of dxy, dxz, and dyz orbitals. The contribution of noncritical representations to ion displacements is proven to be insignificant. The existence of various metal clusters in the tetragonal phase has been established by calculation in correspondence with experimental data. It is shown (within the Landau theory of phase transitions) that phase states can be changed as a result of both first- and second-order phase transitions: the high-symmetry phase borders two low-symmetry phases by second-order transition lines, while the border between low-symmetry phases is a first-order transition line.

Crystal chemistry and formation mechanism of tetragonal MgTi2O4

Symmetry methods of the theory of second-order phase transitions are used to clarify the structural mechanism of the transition from the cubic (Fd3m) to the tetragonal (P41212) phase of magnesium titanite. The proposed mechanism is consistent with all experimental structural data reported to date for magnesium titanite. We analyze the crystal-chemical features of the structure of tetragonal MgTi2O4 and infer the presence of metallic pico- and nanostructures: two types of Ti2 dimers, two types of helices along the twofold and fourfold axes of the tetragonal cell, and two types of infinite one-dimensional chains of titanium ions.

Anion order in perovskites: a group-theoretical analysis.

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.

Ferroelectric superlattice based on barium–strontium titanate solid solutions

A superlattice of the composition Ba0.8Sr0.2TiO3/Ba0.4Sr0.6TiO3 has been grown by rf cathode sputtering on a MgO(001) substrate. The unit cell parameters of the superlattice layers along the normal to the substrate, modulation period, and orientation relationships between the film and the substrate have been determined using X-ray diffraction. Based on the temperature dependences of the polarized Raman spectra, it has been revealed that the frequency of soft mode E(TO) increases from 79 to 97 cm–1 in the temperature range of 80–350 K. It has been found that there are no characteristic indications of a sequence of phase transitions, which take place in bulk samples of barium–strontium titanate solid solutions of identical compositions, and the transition from the ferroelectric to paraelectric phase in the superlattice occurs at a temperature of ∼350 K.

Group-theoretical study of cationic ordering in perovskite structure

Atomic ordering in the structure of cubic perovskite has been investigated by the group-theoretical method. The possibility of existence of 13 ordered phases in the 1(a) position (including four binary, two ternary, and five quaternary cationic superstructures) and 13 phases with different types of ordering in the 1(b) position (including four binary, two ternary, and five quaternary cationic superstructures) is established. Calculated structures of some types of ordered low-symmetry perovskite modifications are reported.

Unique hyper-kagome atomic order in the noncentrosymmetric structure of Na3Ir3O8

The formation of a unique hyper-kagome atomic order in the structure of the ordered spinel phase Na3Ir3O8 has been analyzed in terms of the Landau theory of phase transitions. We have identified a critical six-component order parameter generating a phase transformation of the spinel parent phase to ordered P4132 (P4332) spinel-like enantiomorphs and examined the structural mechanism behind the development of hyper-kagome order and the detailed crystal chemistry of Na3Ir3O8.

Physical properties of Ba0.8Sr0.2TiO3 thin films

The behavior of material constants in ferroelectric Ba0.8Sr0.2TiO3 thin films is studied depending on the misfit strain at room temperature in the context of nonlinear thermodynamic potential of the phenomenological theory. Some constants are found to undergo drastic changes with the alternating strain at the interfaces. The gathered results allow one to evaluate the material constants for a specific film and to outline the direction in searching the ways to synthesize films with the needed properties.