Structure of (Ga2O3)2(ZnO)13 and a unified description of the homologous series (Ga2O3)2(ZnO)(2n + 1).

The structure of (Ga(2)O(3))(2)(ZnO)(13) has been determined by a single-crystal X-ray diffraction technique. In the monoclinic structure of the space group C2/m with cell parameters a = 19.66 (4), b = 3.2487 (5), c = 27.31 (2) Å, and ß = 105.9 (1)°, a unit cell is constructed by combining the halves of the unit cell of Ga(2)O(3)(ZnO)(6) and Ga(2)O(3)(ZnO)(7) in the homologous series Ga(2)O(3)(ZnO)(m). The homologous series (Ga(2)O(3))(2)(ZnO)(2n + 1) is derived and a unified description for structures in the series is presented using the (3+1)-dimensional superspace formalism. The phases are treated as compositely modulated structures consisting of two subsystems. One is constructed by metal ions and another is by O ions. In the (3 + 1)-dimensional model, displacive modulations of ions are described by the asymmetric zigzag function with large amplitudes, which was replaced by a combination of the sawtooth function in refinements. Similarities and differences between the two homologous series (Ga(2)O(3))(2)(ZnO)(2n + 1) and Ga(2)O(3)(ZnO)(m) are clarified in (3 + 1)-dimensional superspace. The validity of the (3 + 1)-dimensional model is confirmed by the refinements of (Ga(2)O(3))(2)(ZnO)(13), while a few complex phenomena in the real structure are taken into account by modifying the model.

The structural phase transition in SrV(6)O(11).

Single-crystal X-ray diffraction and specific heat studies establish that strontium hexavanadium undecaoxide, SrV(6)O(11), undergoes a P6(3)/mmc to inversion twinned P6(3)mc structural transition as the temperature is lowered through 322 K. The P6(3)/mmc and P6(3)mc structures have been determined at 353 K and at room temperature, respectively. For the room-temperature structure, seven of the ten unique atoms lie on special positions, and for the 353 K structure all of the seven unique atoms sit on special positions. The P6(3)/mmc to P6(3)mc structural phase transition, accompanied by a magnetic transition, is a common characteristic of AV(6)O(11) compounds, independent of the identity of the A cations.

Characterization of the pressure-induced second-order phase transition in the mixed-valence vanadate BaV6O11.

The pressure dependence of the structure of the mixed-valence vanadate BaV6O11 was studied with single-crystal X-ray diffraction in a diamond-anvil cell. The compressibility data could be fitted with a Murnaghan equation of state with the zero-pressure bulk modulus B0 = 161 (7) GPa and the unit-cell volume at ambient pressure = 387.1 (3) A3 (B' = 4.00). A phase transition involving a symmetry reduction from P6(3)/mmc to P6(3)mc can be reliably detected in the high-pressure data. The estimated transition pressure lies in the range 1.18 < P(c) < 3.09 GPa. The transition leads to a breaking of the regular Kagomé net formed by part of the V ions. While in the ambient pressure structure all V-V distances in the Kagomé net are equal, they split into inter-trimer and intra-trimer distances in the high-pressure phase. In general, these changes are comparable to those observed in the corresponding low-temperature transition. However, the pressure-induced transition takes place at a lower unit-cell volume compared with the temperature-induced transition. Furthermore, overall trends for inter-trimer and intra-trimer V-V distances as a function of the unit-cell volume are clearly different for datapoints obtained by variation of pressure and temperature. The behavior of BaV6O11 is compared with that of NaV6O11. While in the latter compound the transition can be explained as a pure volume effect, in BaV6O11 an additional degree of freedom related to the valence distribution among the symmetrically independent vanadium sites has to be taken into account.

Isosymmetrical phase transition in alpha-YbV4O8.

The structure of YbV4O8 is related to the CaFe2O4 structure type. VO6 octahedra form a three-dimensional framework with tunnels in which the Yb3+ ions are incorporated. Two different polymorphs alpha and beta are known and differ mainly in the arrangement of the Yb ions within the framework. We studied the structure and magnetic properties of alpha-YbV4O8 as a function of temperature. At approximately 70 K alpha-YbV4O8 undergoes a first-order isosymmetrical phase transition (P2(1)/n --> P2(1)/n). While in the high-temperature alpha phase the three V3+ and one V4+ are disordered over the four symmetrically independent octahedral sites, in the low-temperature alpha' phase complete charge ordering is observed. The transition is accompanied by a paramagnetic-paramagnetic anomaly in the magnetic susceptibility data which can be interpreted on the basis of spin-gap formation. The transition mechanism in the alpha polymorph is very similar to that observed earlier in the beta polymorph at 185 K.

Structure of Ga2O3(ZnO)6: a member of the homologous series Ga2O3(ZnO)m.

The structure of Ga(2)O(3)(ZnO)(6) was determined using single-crystal X-ray diffraction techniques in the space group Cmcm. The metal ion sublattice resembles some of the Zn ions in the wurtzite ZnO structure. The oxygen ion sublattice in Ga(2)O(3)(ZnO)(6) also resembles some of the O ions in ZnO. Structural relationships between Ga(2)O(3)(ZnO)(6) and ZnO are discussed, illustrating the process for obtaining the centrosymmetric Ga(2)O(3)(ZnO)(6) structure from the noncentrosymmetric ZnO. Structures of phases in the homologous series Ga(2)O(3)(ZnO)(m) are predicted on the basis of the structural data for Ga(2)O(3)(ZnO)(6). The structures of even m are constructed by simply extending the structure units seen in Ga(2)O(3)(ZnO)(6), while those of odd m consist of structure units which are of different types from those used for even m.

Structural characterization of YV(4)O(8): simultaneous analysis of coexisting polytypes and simulation of diffuse scattering for a stacking disorder model.

The structure of a crystal of newly synthesized YV(4)O(8) was refined on the assumption that two polytypes and their respective twin forms intergrow. The model was expressed as a commensurate composite crystal with two types of subsystem: one is a V(4)O(8) framework with rather large tunnels and the other consists of Y ions. In the tunnels, Y ions and vacancies are located at every second site in an ordered manner that is characteristic of each polytype. Refinement was performed using a high-dimensional formalism and all reflections from all domains. Diffuse streaks observed in the X-ray and electron diffraction patterns were simulated using the matrix method that has been used for one-dimensional disorder such as stacking faults. The unusual diffraction phenomena that occur in a crystal of YV(4)O(8) are explained as arising from a multiple-domain structure of coexisting polytypes.