Crystal structure of the Ca<Subscript>3</Subscript>TaGa<Subscript>3</Subscript>Si<Subscript>2</Subscript>O<Subscript>14</Subscript> compound

The absolute crystal structure of the Ca₃TaGa₃Si₂O₁₄ piezoelectric compound is refined using X-ray diffraction analysis. The unit cell parameters and final R factors are as follows: a = 8.112(1) Å, c = 4.9862(6) Å, space group P321, Z = 1, R = 0.98%, and R _w = 1.42%. It is shown that the configuration of the absolute crystal structure inherited from the seed material determines the positive sense of the optical activity of the crystal under investigation. The structural and acoustical characteristics of the Ca₃TaGa₃Si₂O₁₄ crystals are compared with those of the La₃Ga₅SiO₁₄ crystals.     

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-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.     

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.     

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.     

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.     

Crystal structure of a new synthetic Ca,Li pentaborate: CaLi<Subscript>4</Subscript>[B<Subscript>5</Subscript>O<Subscript>8</Subscript>(OH)<Subscript>2</Subscript>]<Subscript>2</Subscript>

When studying the phase formation in the CaO-Li₂O-B₂O₃-H₂O system, a new Ca,Li pentaborate was synthesized under hydrothermal conditions. The structure of a new compound with the crystallochemical formula CaLi₄[B₅O₈(OH)₂]₂ (sp. gr. Pb2n, a = 8.807(7), b = 9.372(7), c = 8.265(6) Å, V = 682.2(9) ų, Z = 2, d_calcd = 2.43 g/cm³, automated SYNTEX-\(P\bar 1\) diffractometer, 2690 reflections, 2θ/θ scan, λMo) is refined up to R_hkl = 0.0557 in the anisotropic approximation of atomic thermal vibrations with allowance for the localized H atoms. The structure of the Ca,Li pentaborate is formed by (010) open boron—oxygen layers formed by two independent [B₅O₈(OH)₂]^3? pentagroups, with each of them being formed by three B tetrahedra and two B triangles. The structure framework consists of the above boron—oxygen layers bound by isolated Li tetrahedra. The Ca cations are localized in the centers of eight-vertex polyhedra located in the [001] channels of the Li,B,O framework. Comparative crystallochemical analysis of the new Ca,Li pentaborate and Li pentaborate of the composition Li₃[B₅O₈(OH)₂]-II showed that the anionic matrices of both compounds are completely identical, whereas some of the cationic positions are different.     

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.     

Synthesis and structure of (Rb<Subscript>0.50</Subscript>Ba<Subscript>0.25</Subscript>)[UO<Subscript>2</Subscript>(CH<Subscript>3</Subscript>COO)<Subscript>3</Subscript>]

A new compound (Rb_0.50Ba_0.25)[UO₂(CH₃COO)₃] is synthesized and its crystal structure is studied by X-ray diffraction. The compound crystallizes in the form of yellow plates belonging to the cubic crystal system. The unit cell parameter a = 17.0367(1) Å, V = 4944.89(5) ų, space group I \(\bar 4\)3d, Z = 16, and R = 0.0182. The coordination polyhedron of the uranium atom is a hexagonal bipyramid with oxygen atoms of three acetate groups and the uranyl group in the vertices. The crystal chemical formula of the uranium-containing group is AB ₃ ⁰¹ (A = UO ₂ ²⁺ , B ⁰¹ = CH₃COO^?). The oxygen atoms of the acetate groups that enter the coordination polyhedron of uranium are bound to barium and rubidium atoms.     

Synthesis and an X-ray diffraction study of Rb<Subscript>2</Subscript>[(UO<Subscript>2</Subscript>)<Subscript>2</Subscript>(C<Subscript>2</Subscript>O<Subscript>4</Subscript>)<Subscript>3</Subscript>]

The synthesis and X-ray diffraction study of compound Rb₂[(UO₂)₂(C₂O₄)₃], which crystallizes in the monoclinic crystal system, are performed. The unit cell parameters are as follows: a = 7.9996(6) Å, b = 8.8259(8) Å, c = 11.3220(7) Å, β = 105.394(2)°, and V = 770.7(1) ų; space group P2₁/n, Z = 2, and R ₁ = 0.0271. [(UO₂)₂(C₂O₄)₃]^2? layers belonging to the AK _0.5 ⁰² T ¹¹ crystal chemical group of uranyl complexes (A = UO ₂ ²⁺ , K ⁰² = C₂O ₄ ^2? , and T ¹¹ = C₂O ₄ ^2? ) are uranium-containing structural units of the crystals. The layers are connected with outer-sphere rubidium cations by electrostatic interactions.     

Refined crystal structure of parakeldyshite and the genetic crystal chemistry of zirconium minerals with [Si<Subscript>2</Subscript>O<Subscript>7</Subscript>] diorthogroups

The structure of the mineral parakeldyshite Na_1.93ZrSi₂O_6.93(OH)_0.07 is refined by X-ray diffraction analysis. The main crystallographic data are as follows: space group P \(\overline 1 \), a = 6.617(2) Å, b = 8.813(1) Å, c = 5.426(1) Å, α = 87.26(3)°, β = 85.68(3)°, γ = 71.45(3)°, and R _F = 0.0153. The initial structural model of this mineral is confirmed. Within this model, the structure of parakeldyshite is based on the heteropolyhedral framework formed by [Si₂O₇] diorthogroups, which are linked together through isolated zirconium octahedra. The fundamental difference between the structure under investigation and the initial structural model is associated with the arrangement of the extraframework cations. A comparative crystal chemical analysis of the zirconium silicates with [Si₂O₇] diorthogroups is performed.     

Ti/Zr isomorphism in wadeite: The crystal structure of the titanium-dominant K<Subscript>2</Subscript>(Ti<Subscript>0.55</Subscript>Zr<Subscript>0.45</Subscript>)Si<Subscript>3</Subscript>O<Subscript>9</Subscript> member of the series

The crystal structure of the titanium-rich mineral wadeite K₂(Ti_0.55Zr_0.45)Si₃O₉ from rischorrites of the Khibiny Alkaline Massif (Kola Peninsula, Russia) is studied by X-ray diffraction (XCalibur-S diffractometer, R = 0.0459): a = 6.8611(6) Å and c = 10.0611(9) Å; space group P6₃/m, Z = 6, D _x = 3.03 g/cm³. It is shown that the unit-cell parameters and volume of the mineral of mixed (Ti/Zr) composition are naturally intermediate between those of the terminal members of the isomorphous wadeite-based K₂ZrSi₃O₉–K₂(Ti_0.55Zr_0.45)Si₃O₉–K₂TiSi₃O₉ series. The expected correlation is due to the ionic radii of Zr⁴⁺ and Ti⁴⁺ which determine the lengths of Zr/Ti–O bonds in octahedra. The data of field observations and microscopic studies show that the Ti-dominant wadeite is formed on the basis of primary zirconium mineral in the course of a late imposed process under unique geochemical conditions.     

Crystal structure of Ga<Subscript>0.5</Subscript>In<Subscript>1.5</Subscript>Se<Subscript>3</Subscript> solid solution

A solid solution of the GaIn₃Se₆ (2Ga_0.5In_1.5Se₃) composition with a hexagonal lattice (a = 7.051(3) Å, c = 19.148(2) Å, sp. gr. P6₁, z = 6, V = 824.4332(4) ų, ρ = 5.379(2) g/cm³) has been synthesized as a result of alloying Ga, In, and Se elements with a metal ratio of 1: 3. It was established that six out of nine In atoms in the lattice are located in a trigonal bipyramid, while the other three In atoms and three Ga atoms have a tetrahedral coordination.     

Absolute structure of La<Subscript>3</Subscript>Ga<Subscript>5</Subscript>SiO<Subscript>14</Subscript> langasite crystals

The absolute structure of La₃Ga₅SiO₁₄ piezoelectric crystals (a = 8.1746(6) Å, c = 5.1022(4) Å, space group P321, Z = 1) with the positive sense of rotation of the plane of polarization is refined using X-ray diffraction analysis (R = 1.37%, R _w = 1.71%, 2413 unique reflections, max sinθ/λ = 1.15 Å^?1). The contributions from the anharmonicity of thermal vibrations of lanthanum atoms are calculated with the use of the components of the third-and fourth-rank tensors. It is demonstrated that these contributions can have a significant effect.     

Refinement of the crystal structure of rhombohedral KU<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> as a representative of orthophosphates with the NaZr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> structure

The crystal structure of the high-temperature β modification of synthetic orthophosphate KU₂(PO₄)₃ was refined from powder X-ray diffraction data by the Rietveld method: sp. gr. \(R\bar 3c\), the unit-cell parameters a= 9.113(1) Å and c= 24.997(1) Å. The isotropic refinement converged to R _wp = 6.15, R _B = 2.14, R _F = 3.52, and S = 0.42. It was confirmed that β-KU₂(PO₄)₃ belongs to the structure type of sodium zirconium phosphate containing an actinide atom in a sixfold (octahedral) coordination formed by oxygen atoms, which is unusual for orthophosphates. The principal interatomic distances and bond angles in the structure are reported.     

Multicell model of La<Subscript>3</Subscript>Ga<Subscript>5</Subscript>GeO<Subscript>14</Subscript> crystal: A new approach to the description of the short-range order of atoms

The multicell model alternative to the model of mixed atomic sites used now is proposed for a single crystal of La₃Ga₅GeO₁₄ belonging to the langasite family. The multicell consists of four unit cells. In three identical cells of the structure, atoms adapt to the Ge atom occupying one of the two 2d positions on the threefold symmetry axis. In the fourth cell, atoms surround the Ge atom located at the 1a position. The multicell model allows one to study the short-range order of atoms by the methods of classical structure analysis based on Bragg scattering. Four high-resolution data sets measured at 295 and 111.5 K are used in the study. The results are obtained with high relative precision (space group P321, Z = 1; at 295 K a = 8.2020(6) Å and c = 5.1065(6) Å, R/wR = 0.81/0.73% for 3829 unique ref lections; at 111.5 K a = 8.1939(1) Å and c = 5.1022(4) Å, R/wR = 0.85/0.76% for 3880 reflections).     

Accurate crystal structure refinement of La<Subscript>3</Subscript>Ta<Subscript>0.25</Subscript>Ga<Subscript>5.25</Subscript>Si<Subscript>0.5</Subscript>O<Subscript>14</Subscript>

An accurate X-ray diffraction study of an La₃Ta_0.25Ga_5.25Si_0.5O₁₄ single crystal has been performed using two data sets obtained independently for the same sample in different orientations on a diffractometer with a 2D CCD detector. This structure was refined with an averaged set of these data (a = 8.1936(15) Å c = 5.1114(6) Å, sp. gr. P321, Z = 1, R/wR = 0.75/0.71%, 4030 independent reflections). This analysis was aimed at determining the character of the occupancies of the cation position in the structure. The octahedra at the origin of coordinates turned out to be statistically occupied by gallium and tantalum ions of similar sizes, whereas the tetrahedra on the threefold symmetry axes are occupied by gallium and silicon whose ionic radii differ significantly. The latter circumstance caused the splitting of oxygen positions and made it possible to reliably establish the structural position of statistically located [SiO₄] and [GaO₄] tetrahedra of different sizes.     

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.     

New type of borophosphate anionic radical in the crystal structure of CsAl<Subscript>2</Subscript>BP<Subscript>6</Subscript>O<Subscript>20</Subscript>

The crystal structure of a new borophosphate CsAl₂BP₆O₂₀ obtained by spontaneous crystallization in a multicomponent Cs–Cu–B–P–O system is determined by X-ray diffraction (a = 11.815(2), b = 10.042(2), and c = 26.630(4) Å; space group Pbca, Z = 8, V = 3159.5(10) ų; R₁ = 0.043). A new type of borophosphate anionic 2D radical characterized by the lowest B: P = 1: 6 ratio and containing P₃O₁₀ phosphate groups is found in the compound. A mixed-type anionic framework consisting of vertex-sharing BO₄ and PO₄ tetrahedra and AlO₆ octahedra is distinguished in the structure. Large cesium atoms are located in the channels of the framework. Topological relationships are revealed between the structures of the CsAl₃(P₃O₁₀)₂ and CsAl₂BP₆O₂₀ phases having different cationic compositions. These compounds can be considered quasi-polytypic phases.