Structural Analysis of Sr<Subscript>3</Subscript>NbFe<Subscript>3</Subscript>Si<Subscript>2</Subscript>O<Subscript>14</Subscript> Single Crystal from the Langasite Family and Finding of Negative Thermal Expansion in the Range of 83–110 K

Iron-containing Sr₃NbFe₃Si₂O₁₄ single crystals from the langasite family, which are interesting for researchers due to their magnetic ordering at T _N = 26 K, have been grown by the floating zone melting method. Accurate X-ray diffraction analysis is performed at 293 and 90.5 K using the data collected on a CCD diffractometer. To compensate for systematic errors, two data sets are collected at each temperature. The structure is refined based on averaged data set: sp. gr. P321, Z = 1, sin θ/λ ≤ 1.35 Å^–1; a = 8.2609(4) Å, c = 5.1313(3) Å at 293 K and a = 8.2344(6) Å, c = 5.1243(6) Å at 90.5 K; the agreement factors are R/wR = 1.18/1.03% and Δρ_min/Δρ_max =–0.57/0.25 e/Å3 for 3583 independent reflections at 293 K and R/wR = 1.18/1.13% and Δρ_min/Δρ_max =–0.54/0.23 e/Å3 for 3638 reflections at 90.5 K. Negative thermal expansion in the direction of the cell c axis is revealed in the range of 83–110 K.     

Electrical conductivity of CsCuCl<Subscript>3</Subscript> crystals at structural phase transition

The electrical conductivity σ of CsCuCl₃ single crystals synthesized by the crystallization method from aqueous solutions in the ternary CsCl–CuCl₂–H₂O system has been studied. The σ measurements for CsCuCl₃ crystals have been carried out in the temperature range of 397–455 K, which covers the structural phase transition from the low-temperature (sp. gr. P6₁22, Z = 6) to the high-temperature (sp. gr. P6₃mc, Z = 2) modification at T _tr = 423 ± 8 K. A jump of σ by a factor of ~3 is observed on the σ(T) dependence in the region of the structural transition, which indicates the existence of first-order phase transition. The electric transfer activation enthalpies ΔHσ are found to be 1.0 ± 0.1 eV at T > T _tr and 0.8 ± 0.1 eV at T < T _tr. The σ value for CsCuC_l3 crystals amounts to 7 × 10^–6 S/cm at 455 K.     

Crystal structure and microtwinning of monoclinic La<Subscript>3</Subscript>SbZn<Subscript>3</Subscript>Ge<Subscript>2</Subscript>O<Subscript>14</Subscript> crystals of the langasite family

The crystal structure of monoclinic La₃SbZn₃Ge₂O₁₄ crystals from the langasite family is determined by X-ray diffraction analysis [a = 5.202(1) Å, b = 8.312(1) Å, c = 14.394(2) Å, β = 90.02(1)°, sp. gr. A2, Z = 2, and R/R _w = (5.2/4.6)%]. The structure is a derivative of the Ca₃Ga₂Ge₄O₁₄-type structure (a = 8.069 Å, c = 4.967 Å, sp. gr. P321, Z = 1). The crystal studied is a polysynthetic twin with the twin index n = 2, whose monoclinic components are related by pseudomerohedry by a threefold rotation axis of the supergroup P321.     

X-ray and neutron diffraction studies of Rb<Subscript>4</Subscript>LiH<Subscript>3</Subscript>(XO<Subscript>4</Subscript>)<Subscript>4</Subscript><Emphasis Type="Italic">(X</Emphasis> = S,Se) single crystals

Rb₄LiH₃(SeO₄)₄ single crystals (1) are studied by the X-ray diffraction method at 180 K and Rb₄LiH₃(SO₄)₄ single crystals (2a–2c) are studied by the neutron diffraction method at 298 K (2a and (2b) and 480 K (2c). It is established that isostructural single crystals 1 and 2 (sp. gr. P4₁) have analogous systems of hydrogen bonds: chains of four XO₄ tetrahedra linked by three H bonds with the central bond (2.49 Å) being somewhat shorter than the terminal ones (2.52–2.54 Å). In the high-temperature 2c phase, the amplitudes of atomic thermal vibrations and the degree of proton disorder in the central hydrogen bond have somewhat elevated values.     

Ionic conductivity of ScF<Subscript>3</Subscript> single crystals (ReO<Subscript>3</Subscript> type)

Electrical conductivity σ of ScF₃ single crystals (sp. gr. \(Pm\overline 3 m\), ReO₃ structure type) has been studied by impedance spectroscopy and compared with the electrical conductivity of rare earth HoF₃ (β-YF₃ type) and LaF₃ (tysonite type) trifluorides. ScF₃ crystals obtained by Bridgman directional solidification have ionic conductivity σ = 4 × 10^–8 S/cm at 673 K. It is smaller than the σ values for LaF₃ (sp. gr. \(P\overline 3 c1\)) and HoF₃ (sp. gr. Pnma) single crystals by a factor of 10⁴–10⁵. The low conductivity of ScF₃ crystals is due to the weak coordinating ability (coordination number CN = 6) and low electronic polarizability (α_cat = 1.1 ų) of Sc³⁺ ions. Mobile V_F⁺ vacancies and less mobile interstitial V_i^- ions (defects are formed according to the Frenkel mechanism) are involved in the ion transport. HoF₃ and LaF₃ single crystals have a high coordinating ability (CN = 9 for Ho³⁺ and CN = 11 for La³⁺) and a high electronic polarizability of cations (α_cat = 1.6–1.9 ų for Ho³⁺ and α_cat = 2.2 ų for La³⁺). Only mobile V_F⁺ vacancies (defects are formed according to the Schottky mechanism) are involved in ion transport.     

Structural transformations in Cu<Subscript>1.95</Subscript>Ni<Subscript>0.05</Subscript>S crystals

A solid solution of the Cu_1.95Ni_0.05S composition has been synthesized for the first time due to the partial replacement of Cu with Ni atoms in Cu₂S. The polymorphic transformations in the polycrystalline samples in the temperature range of 300–1400 K have been investigated by X-ray diffraction and differential thermal analysis. It is established that, at room temperature, the synthesized Cu_1.95Ni_0.05S samples have an orthorhombic lattice with unit-cell parameters a = 26.50 Å, b = 15.39 Å, and c = 13.85 Å (sp. gr. Abm2). Heating to T = 379 ± 2 K leads to its transformation into a hexagonal lattice with parameters a = 3.960 Å and c = 6.78 Å (sp. gr. P6₃/mmc). At 750 ± 2 K, the hexagonal modification is transformed into a cubic one with period a = 5.788 Å (sp. gr. Fm\(\bar 3\)m). The phase transition in this crystal is enantiotropic.     

Structural study of new compound Bi<Subscript>2.53</Subscript>Li<Subscript>0.29</Subscript>Nb<Subscript>2</Subscript>O<Subscript>9</Subscript> by the powder neutron diffraction method

A new compound of composition Bi_2.53Li_0.29Nb₂O₉ was synthesized in the course of the search for new materials with high ionic conductivity. Its crystal structure was determined from the neutron diffraction data. The new compound Bi_2.53Li_0.29Nb₂O₉ is crystallized in the orthorhombic system, sp. gr. Cmc2₁, and unit-cell parameters a = 24.849(1) Å, b = 5.4536(3) Å, and c = 5.4619(2) Å at T = 290 K (a = 24.843(2) Å, b = 5.4456(5) Å, and c = 5.4546(5) Å at T = 10 K). Within the temperature range 10–870 K, no structural phase transitions were revealed. The atomic coordinates and the thermal factors in the isotropic approximation were refined by the Rietveld method at 290 and 10 K. The data obtained were analyzed based on the calculated local balance of bond strengths.     

X-Ray Structure Investigation of Sr<Subscript>3</Subscript>NbGa<Subscript>3</Subscript>Si<Subscript>2</Subscript>O<Subscript>14</Subscript> Langasite Family Crystal

An accurate structure analysis of Sr₃NbGa₃Si₂O₁₄ single crystals, belonging to the langasite family, has been performed. Two datasets are obtained on an Xcalibur S diffractometer equipped with a CCD detector. The structure is been refined using an averaged dataset: sp. gr. P 321, Z = 1, 295 K, sin θ/λ ≤ 1.35 Å^–1, a = 8.2797(3) Å, c = 5.0774(5) Å; the agreement factors between the model and experiment are found to be R/wR = 0.76/0.64% and Δρ_min/Δρ_max =–0.21/0.17 e/ų for 3820 independent ref lections. The Sr₃NbGa₃Si₂O₁₄ and Sr₃NbFe₃Si₂O₁₄ structures are compared, and the role of magnetic ions in the predicted P321 → P3 phase transition is analyzed.     

Growth and structure of La<Subscript>3</Subscript>Zr<Subscript>0.5</Subscript>Ga<Subscript>5</Subscript>Si<Subscript>0.5</Subscript>O<Subscript>14</Subscript> crystals

The complete X-ray structure determination of Czochralski grown La₃Zr_0.5Ga₅Si_0.5O₁₄ single crystals with the Ca₃Ga₂Ge₄O₁₄ structure is performed (sp. gr. P321, a = 8.226(1) Å, c = 5.1374(6) Å, Z = 1, Mo K_α1 radiation, 1920 crystallographically independent reflections, R = 0.0166, R_w = 0.0192). The absolute structure is determined. It is shown that possible transition of some of La atoms (～1.2%) from the 3e to 6g position may give rise to the formation of structural defects.     

Phase transitions in compounds with the Ca<Subscript>3</Subscript>Ga<Subscript>2</Subscript>Ge<Subscript>4</Subscript>O<Subscript>14</Subscript> structure

Possible structural changes described by the group-subgroup relationships in the Ca₃Ga₂Ge₄O₁₄-type structure (sp. gr. P321) are considered. The most probable phase transitions seem to be those accompanied by lowering of the symmetry to the maximal non-isomorphic subgroups P3 and C2. It is shown that only destructive phase transitions accompanied by symmetry rise up to the minimal non-isomorphic supergroups for the given structure type can take place. The change of the trigonal symmetry to monoclinic is revealed in La₃SbZn₃Ge₂O₁₄, whose crystal structure is refined as a derivative structure of the Ca₃Ga₂Ge₄O₁₄ structure type within the sp. gr. A2 (C2). At ～250°C, La₃SbZn₃Ge₂O₁₄ undergoes a reversible phase transition accompanied by symmetry rise, A2 ? P321. Similar phase transitions, P321 ? A2, are also observed in La₃Nb_0.5Ga_5.5O₁₄ and La₃Ta_0.5Ga_5.5O₁₄ under the hydrostatic pressures 12.4(3) and 11.7(3) GPa, respectively. The mechanisms of compression and phase transition are based on the anisotropic compressibility of a layer structure. With the attainment of the critical stress level in the structure, the elevated compressibility in the (ab) plane gives rise to a phase transition accompanied by the loss of the threefold axis. Attempts to reveal low-temperature phase transitions in a number of representatives of the langasite family have failed.     

Synthesis and electrophysical properties of some rare-earth molybdates with fluorite-like structure of the Nd<Subscript>5</Subscript>Mo<Subscript>3</Subscript>O<Subscript>16</Subscript> type

Polycrystalline samples of PbLn ₄Mo₃O₁₆ (Ln = La, Pr, Nd, or Sm), CdLn ₄Mo₃O₁₆ (Ln = La, Nd, Sm, Eu, or Tm), and PbLa_4–xNd_xMo₃O₁₆ (0 ≤ x ≤ 3) with the cubic fluorite-like structure and sp. gr. Pn n have been obtained by solid-phase synthesis in air. The specific conductivity of lead compounds is established to reach 10^–2 S/cm (which is an order of magnitude higher than that for cadmium compounds). The conductivity value is shown to reach a maximum at a concentration ratio of rare-earth elements of Nd: La = 1: 1.     

Accurate Refinement of the Crystal Structure of Ba<Subscript>3</Subscript>TaGa<Subscript>3</Subscript>Si<Subscript>2</Subscript>O<Subscript>14</Subscript> from Langasite Family and Analysis of Structural Transformations Due to Isomorphous Cation Substitutions

An accurate structure analysis of a Ba₃TaGa₃Si₂O₁₄ single crystal from langasite family was performed using four X-ray diffraction data sets collected on a diffractometer equipped with a CCD area detector (sp. gr. P321, Z = 1, sinθ/λ ≤ 1.35 Å^–1; at 295 K a = 8.516(1) Å, c = 5.1910(6) Å, R/wR = 0.58/0.56%, Δρ_min/Δρ_max =–0.73/0.42 e/ų, 4414 independent reflections; at 106 K a = 8.5109(9) Å, c = 5.1861(9) Å, R/wR = 0.75/0.86%, Δρ_min/Δρ_max =–0.81/1.06 e/ų, 4382 reflections). The distinguishing feature of the Ba₃TaGa₃Si₂O₁₄ structure is a strong disorder of the Ga atom at the 3f site. Structural transformations in the series of Сa₃TaGa₃Si₂O₁₄–Sr₃TaGa₃Si₂O₁₄–Ba₃TaGa₃Si₂O₁₄–Ba₃TaFe₃Si₂O₁₄ crystals were analyzed.     

Crystal structure refinement of Sr<Subscript>3</Subscript>TaGa<Subscript>3</Subscript>Si<Subscript>2</Subscript>O<Subscript>14</Subscript>

An accurate X-ray diffraction study of Sr₃TaGa₃Si₂O₁₄ (STGS) crystal (a = 8.3023(10) Å, c = 5.0853(2) Å, sp. gr. P321, Z = 1, R/wR = 0.59/0.52%, 4004 independent reflections) is performed. The use of two independent data sets obtained on diffractometers with point and 2D detectors made it possible to determine the model structure characterized by the best reproducibility of parameters. The ordered distribution of atoms over crystallographic positions and the anharmonic character of displacements of all cations and one oxygen atom are established.     

Crystal chemistry of KCuMn<Subscript>3</Subscript>(VO<Subscript>4</Subscript>)<Subscript>3</Subscript> in the context of detailed systematics of the alluaudite family

The crystal structure of new manganese potassium copper vanadate KCuMn₃(VO₄)₃, which was prepared by the hydrothermal synthesis in the K₂CO₃–CuO–MnCl₂–V₂O₅–H₂O system, was studied by X-ray diffraction (R = 0.0355): a = 12.396(1) Å, b = 12.944(1) Å, c = 6.9786(5) Å, β = 112.723(1)°, sp. gr. C2/c, Z = 4, ρ_calc = 3.938 g/cm³. A comparative analysis of the crystal-chemical features of the new representative of the alluaudite family and related structures of minerals and synthetic phosphates, arsenates, and vanadates of the general formula A(1)A(1)′A(1)″A(2)A(2)′M(1)M(2)₂(TO₄)₃ (where A are sites in the channels of the framework composed of MО₆ octahedra and TО₄ tetrahedra) was performed. A classification of these structures into subgroups according to the occupancy of A sites is suggested.     

Crystal-structure refinement of Sr<Subscript>3</Subscript>Ga<Subscript>2</Subscript>Ge<Subscript>4</Subscript>O<Subscript>14</Subscript>

The accurate X-ray diffraction study of a Sr₃Ga₂Ge₄O₁₄ crystal was performed based on two X-ray diffraction data sets collected on a diffractometer equipped with a CCD area detector (a = 8.2776(2), c = 5.0415(1) Å, sp. gr. P321, Z = 1, R/wR = 0.78/0.69%, 3645 independent reflections). The structure of Sr₃Ga₂Ge₄O₁₄ is characterized by the presence of two mixed cation sites, which is accompanied by the anharmonic motion not only of cations, but also of two oxygen atoms in general positions. The structures and electromechanical characteristics of Sr₃Ga₂Ge₄O₁₄ and Sr₃TaGa₃Si₂O₁₄ were compared. The Sr₃Ga₂Ge₄O₁₄ structure is characterized by a larger elongation of the Sr polyhedron along the a axis and, simultaneously, by the smaller unit-cell parameter a compared with Sr₃TaGa₃Si₂O₁₄, which correlates with the ratio of the piezoelectric coefficients d ₁₁. The absence of thermally stable directions in the crystals of Sr₃Ga₂Ge₄O₁₄ and Sr₃TaGa₃Si₂O₁₄ is consistent with the absence of the anomalous temperature dependence of the dielectric constant ?₃₃.     

Accurate structural study of langasite-family Ca<Subscript>3</Subscript>TaGa<Subscript>3</Subscript>Si<Subscript>2</Subscript>O<Subscript>14</Subscript> crystal

An accurate X-ray diffraction study of Ca₃TaGa₃Si₂O₁₄ single crystal has been performed using two datasets obtained on a diffractometer equipped with a CCD area detector (a = 8.1056(2) Å, c = 4.9800(1) Å, sp. gr. P321, Z = 1, R/wR = 0.486/0.488%). A model structure is determined which is characterized by a high degree of reproducibility of structural parameters. Each site in Ca₃TaGa₃Si₂O₁₄ is occupied by atoms of only one type. Nevertheless, its structural feature is asymmetric disordering of sites of Ca, Ta, Ga, and two out of three oxygen atoms occupying special and general sites. A transition of some part of Ca atoms (~3%) from 3e sites on the twofold symmetry axis to general 6g sites is revealed.     

Low-temperature X-ray diffraction studies of [(CH<Subscript>3</Subscript>)<Subscript>2</Subscript>NH<Subscript>2</Subscript>]<Subscript>5</Subscript>Cd<Subscript>3</Subscript>Cl<Subscript>11</Subscript> crystals

[(CH₃)₂NH₂]₅Cd₃Cl₁₁ crystals are grown by the method of isothermal evaporation from saturated aqueous solutions containing dimethylamine and cadmium chlorides, [(CH₃)2NH₂]Cl and CdCl_2.5H₂O. The crystal grown are studied by the X-ray diffraction method. It is established that the crystals are orthorhombic with the unit-cell parameters at room temperature a = 18.115 ± 0.004 Å, b = 11.432 ± 0.002 Å, and c = 15.821 ± 0.003 Å. The unit-cell parameters a, b, and c of the [(CH₃)₂NH₂]₅Cd₃Cl₁₁ crystals are measured as functions of temperature in the temperature range 100–320 K. The data obtained were used to determine the thermal expansion coefficients along the main crystallographic axes. The temperature curves of the unit-cell parameters and thermal expansion coefficients showed pronounced anomalies in the vicinity of the temperatures T ₁ = 120, T ₂ = 150, and T ₃ = 180 K corresponding to the phase transitions in the [(CH₃)₂NH₂]₅Cd₃Cl₁₁ crystals. The crystals are also characterized by a pronounced anisotropy of thermal expansion.     

Polymorphism of the borophosphate anion in K(Fe,Al)[BP<Subscript>2</Subscript>O<Subscript>8</Subscript>(OH)] and Rb(Al,Fe)[BP<Subscript>2</Subscript>O<Subscript>8</Subscript>(OH)] crystal structures

The crystal structure of two borophosphates, Rb(Al,Fe)[BP₂O₈(OH)] (a = 9.381(6), b = 8.398(5), c = 9.579(6) Å, β = 102.605(10)°, sp. gr. P2₁/c) and K(Fe,Al)[BP₂O₈(OH)] (a = 5.139(2), b = 8.065(4), c = 8.290(4)Å, α = 86.841(8)°, β = 80.346(8)°, γ = 86.622(8)°, sp. gr. P \(\bar 1\)), obtained by hydrothermal synthesis in the AlCl₃: FeCl₃: K₃PO₄(Rb₃PO₄): B₂O₃: H₂O system has been established using X-ray diffraction (Bruker Smart diffractometer, T = 100 K). Hydrogen atoms are located and their coordinates and thermal parameters are refined. It is shown that the polymorphism of the [BP₂O₈(OH)]^4? borophosphate anion has a morphotropic nature and is related to the substitutions both in the cationic part of the structure and in the octahedral position of the anionic mixed framework. The synthesis of new isotypic triclinic compounds under hydrothermal conditions is predicted.     

New multicell model for describing the atomic structure of La<Subscript>3</Subscript>Ga<Subscript>5</Subscript>SiO<Subscript>14</Subscript> piezoelectric crystal: Unit cells of different compositions in the same single crystal

Accurate X-ray diffraction study of langasite (La₃Ga₅SiO₁₄) single crystal has been performed using the data obtained on a diffractometer equipped with a CCD area detector at 295 and 90.5 K. Within the known La₃Ga₅SiO₁₄ model, Ga and Si cations jointly occupy the 2d site. A new model of a “multicell” consisting of two different unit cells is proposed. Gallium atoms occupy the 2d site in one of these cells, and silicon atoms occupy this site in the other cell; all other atoms correspondingly coordinate these cations. This structure implements various physical properties exhibited by langasite family crystals. The conclusions are based on processing four data sets obtained with a high resolution (sin θ/λ ≤ 1.35 Å^–1), the results reproduced in repeated experiments, and the high relative precision of the study (sp. gr. P321, Z = 1; at 295 K, a = 8.1652(6) Å, c = 5.0958(5) Å, R/wR = 0.68/0.68%, 3927 independent reflections; at 90.5 K, a = 8.1559(4) Å, c = 5.0913(6) Å, R/wR = 0.92/0.93%, 3928 reflections).     

Crystal structure of Rb<Subscript>2</Subscript>[Ti(VO<Subscript>2</Subscript>)<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript>]

The crystal structure of the new compound Rb₂[Ti(VO₂)₃(PO₄)₃] obtained by hydrothermal synthesis in the RbCl-TiPO₄-V₂O₅-B₂O₃-H₂O system (a = 13.604(2) Å, c = 9.386(2) Å, sp. gr. P6cc, Z = 4, ρ_calcd = 3.32 g/cm³) has been studied by X-ray diffraction (Xcalibur-S-CCD diffractometer, R = 0.038). It is shown that the isotypism of Rb₂[Ti(VO₂)₃(PO₄)₃] and Cs₂[Ti(VO₂)₃(PO₄)₃] is caused by the flexibility of a mixed anionic framework composed of phosphorus tetrahedra, vanadium five-vertex polyhedra, and titanium octahedra (bases of the crystal structures of these compounds). The topological correlations between the structures of titanium-vanadyl phosphates and benitoite and beryl silicates are analyzed.