Elastic and dielectric properties of A<Superscript>II</Superscript>B<Stack><Subscript>2</Subscript><Superscript>V</Superscript></Stack> (<Emphasis Type="Italic">A</Emphasis> = Cd or Zn, <Emphasis Type="Italic">B</Emphasis> = P or As) single crystals

Elastic and dielectric properties of CdP₂, ZnP₂, and ZnAs₂ single crystals are investigated at frequencies of 10², 10³, 10⁴, 10⁶, and 10⁷ Hz in the [00l], [h00], and [hk0] directions in the temperature range 78–400 K. The elastic constants, the Gruneisen parameters, and the force constants of the crystals are calculated from the measured ultrasonic velocities. The elastic constants C_ij decrease with an increase in temperature and anomalously change in narrow (ΔT = 10–20 K) temperature ranges. The permittivity sharply increases from ε ≈ 7–14 at 78–150 K to ε ≈ 10²–10³ in the temperature range 175–225 K without any signs of a structural phase transition. The behavior of the temperature-frequency dependences of the complex permittivity ε*(f, T) is typical of relaxation processes. The dielectric relaxation in A^IIB ₂ ^V is considered on the basis of the model of isolated defects. The conuctivity σ of the single crystals under study is a sum of the frequency-dependent (hopping) conductivity σ_h and the conductivity σ_s that is typical of semiconductors. The hopping conductivity increases with an increase in frequency according to the law σ _h ～f^α, where α < 1 at low temperatures and α > 1 at high temperatures.     

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.     

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.     

Thermal Expansion of EuF<Subscript>2 + <Emphasis Type="Italic">x</Emphasis></Subscript> Single Crystals and Their Thermal Stability

Thermal expansion of an EuF_2.136 nonstoichiometric crystal with the fluorite structure type (Eu _0.864 ²⁺ Eu _0.136 ³⁺ F_2.136, lattice parameter 5.82171(5) Å) has been experimentally investigated in the temperature range of 9–500 K. The coefficient of thermal expansion is α = 15.8 × 10^–6 K^–1 at T = 300 K. The observed anomalies in the behavior of the coefficient of thermal expansion at T > 400 K are related to the oxidation processes with partition of Eu²⁺ ions. It is established by differential scanning calorimetry that the onset temperature of EuF_{2 + x} oxidation in air is 430 K and that this process occurs in three stages. X-ray diffraction analysis shows that the oxidation is accompanied by the formation of a phase mixture based on two modifications of the Eu _{1– y} ³⁺ Eu _y ²⁺ F_3–y solid solution with the structure types of tysonite (LaF₃), orthorhombic β-YF₃ phase, and europium oxyfluorides of variable composition EuO_1–xF_{1 + 2x}, with dominance of the latter.     

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.     

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.     

Synthesis and crystal chemical characteristics of the structure of <Emphasis Type="Italic">M</Emphasis><Subscript>0.5</Subscript>Zr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> phosphates

Double phosphates of zirconium and metals with an oxidation degree of +2 of the composition M_0.5Zr₂(PO₄)₃ (M = Mg, Ca, Mn, Co, Ni, Cu, Zn, Sr, Cd, and Ba) are synthesized and characterized by X-ray diffraction methods and IR spectroscopy. The crystal structures of all the compounds are based on three-dimensional frameworks of corner-sharing PO₄-tetrahedra and ZrO₆-octahedra. Phosphates with large Cd²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ cations octahedrally coordinated with oxygen atoms form rhombohedral structures (space group R3), whereas phosphates with small tetrahedrally coordinated Mg²⁺, Ni²⁺, Cu²⁺, Co²⁺, Zn ²⁺, and Mn²⁺-cations are monoclinic (space group P2₁/n). The effect of various structure-forming factors on the M_0.5Zr₂(PO₄)₃ compounds with a common structural motif but different symmetries are discussed.     

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.     

Specific features of the substitution of Fe<Superscript>3+</Superscript> impurity ions for Zr<Superscript>4+</Superscript> in NaZr<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript> single crystals

The EPR spectra of Fe³⁺ impurity ions in NaZr₂(PO₄)₃ single crystals at 300 K are investigated, and the spin Hamiltonian of these ions is determined. A comparative analysis of the spin-Hamiltonian and crystal-field tensors is performed using the maximum invariant component method. It is demonstrated that Fe³⁺ impurity ions substitute for Zr⁴⁺ ions with local compensator ions located in cavities of the B type. It is revealed that the invariant of the spin-Hamiltonian tensor B₄ and the crystal-field tensor V ₄ ⁴⁴ depend substantially on the mutual arrangement of ions in the first and second coordination spheres. The corresponding dependences are analyzed.     

Characteristic of spontaneous polarization in Pb<Subscript>5</Subscript>Ge<Subscript>3</Subscript>O<Subscript>11</Subscript> crystals

The temperature behavior of the spontaneous polarization of lead tetragermanate, a uniaxial ferroelectric, is studied in the range from 4.2 to 300 K. The results obtained along with the data from the literature make it possible to reconstruct a complete pattern of the behavior of P _s (T) both in the vicinity of the phase transition and at lower temperatures. In the range from 290 K to T_C, the crystal behavior is found to change from the dipole type (β = 1/2) to the pseudoquadrupole type (β = 1/4). This specific crossover manifests itself in the change in the behavior of P _s ^1/β as a function of (T_C-T). In the low-temperature range, weak anomalies in the dependenceP _s >(T) are found, which point to the occurrence of contributions from the dipole moments of separate structural fragments of Ge₂O₇ and GeO₄, which have internal degrees of freedom and are weakly bound to the dynamics of the crystal lattice.     

The Fe<Superscript>2+</Superscript>/Fe<Superscript>3+</Superscript> ratio in natural and heat-treated iron-rich eudialytes

The structures of natural iron-rich eudialyte (specimen 3458 from the Khibiny massif, the Kola Peninsula) and two heat-treated samples of this mineral calcined at 700 and 800°C were determined by X-ray diffraction. The trigonal unit-cell parameters (sp. gr. R3m) are as follows: a = 14.2645(1) Å, c = 29.9635(5) Å; a = 14.1307(1) Å, c = 30.1229(3) Å; a = 14.1921(2) Å, c = 30.2417(5) Å, respectively. It was found that Fe³⁺ ions in the calcined eudialytes, as well as impurities in the starting specimen, occupy the square-pyramidal Fe³⁺(V) sites, whereas Fe²⁺ ions are in the planar-tetragonal Fe²⁺(IV) sites.     

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.     

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.     

Structure and some properties of [UO<Subscript>2</Subscript>(C<Subscript>5</Subscript>H<Subscript>12</Subscript>N<Subscript>2</Subscript>O)<Subscript>5</Subscript>](ClO<Subscript>4</Subscript>)<Subscript>2</Subscript>

Compound [UO₂(C₅H₁₂N₂O)₅](ClO₄)₂ is synthesized and characterized by thermogravimetry, IR spectroscopy, and X-ray diffraction. The compound crystallizes in the monoclinic crystal system; a = 15.2985(9) Å, b = 26.9676(15) Å, c = 20.6962(11) Å, β = 100.697(1)°, space group P2₁/c, Z = 8, and R = 0.0445. Discrete [UO₂(C₅H₁₂N₂O)₅]²⁺ groups belonging to the AM ₅ ¹ crystal chemical group of uranyl complexes (A = UO ₂ ²⁺ and M ¹=C₅H₁₂N₂O) are uranium-containing structural units of the crystals.     

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.     

Synthesis and Electrical Properties of a Fluorite-Like Nd<Subscript>5</Subscript>Mo<Subscript>3</Subscript>O<Subscript>16</Subscript> Compound with Partial Substitution of Molybdenum by Tungsten,Niobium, or Vanadium

The phase formation of Nd₅Mo_{3 – x}W _x O_16.5, Nd₅Mo_{3 – x}Nb _x O_{16.5 – х/2}, and Nd₅Mo_{3 – x}V _x O_{16.5 – х/2} solid solutions based on a fluorite-like Nd₅Mo₃O_16.5 compound (mixed conductor with interstitial oxygen conductivity) has been studied. The electrical conductivity of doped compounds obeys the Arrhenius law and, at a low impurity content, is as high as 0.03–0.08 S/cm at 800°C. Substitution of Mo⁶⁺ cations by V⁵⁺ and Nb⁵⁺ cations reduces the interstitial oxygen content, which causes a decrease in the solid-solution electrical conductivity by 1–2 orders of magnitude and a decrease in the cubic unit-cell parameter. A wide diffuse anomaly with a maximum of about 1500–4000 has been observed in the temperature dependence of the permittivity for all single-crystal and polycrystalline samples in the range of 300–900°C.     

Structure refinement of cadmium cerium(IV) phosphate Cd<Subscript>0.5</Subscript>Ce<Subscript>2</Subscript>(PO<Subscript>4</Subscript>)<Subscript>3</Subscript>

Cadmium cerium orthophosphate Cd_0.5Ce₂(PO₄)₃ is synthesized by precipitation from aqueous solutions. The structure refinement from powder X-ray diffraction data is preceded by the sample preparation and structure solution. The refinement is carried out by the Rietveld method (ADP-2 diffractometer, Cu _Kα radiation, Ni filter, 15° < 2θ < 120°, 2θ-scan step 0.02°, counting time 10 s per step). All calculations are carried out using the WYRIET program (version 3.3) within the sp. gr. P2₁/n. The structure is refined with anisotropic displacement parameters for cations and isotropic displacement parameters for oxygen atoms.     

Birefringence of (NH<Subscript>4</Subscript>)<Subscript>2</Subscript>SO<Subscript>4</Subscript> crystals under the action of uniaxial pressures

The influence of uniaxial mechanical pressure σ _m ≤ 150 bar on the spectral (300–800 nm) dependence of the birefringence Δn _i of (NH₄)₂SO₄ crystals is studied. The dispersion Δn _i (λ) is shown to be normal and greatly increases when approaching the absorption edge. Uniaxial pressure changes the value of dispersion dΔn _i /dλ but not its character. It is found that the simultaneous action of pressures σ _x ～ σ y ～ 560 bar results in the occurrence of a uniaxial isotropic state. Piezoelectric constants of the crystals are estimated.     

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.     

Growth,structure, and magnetic properties of CuFeTe<Subscript>2</Subscript> single crystals

CuFeTe₂ single crystals were grown and the temperature dependence of their magnetic susceptibility in the temperature range 1.8–400 K was investigated. It is found that the magnetic susceptibility shows anomalies at temperatures T _s = 65 and T _N = 125 K. At T > 125 K, the crystal is in the paramagnetic state controlled by Fe²⁺ and Cu²⁺ ions with an effective magnetic moment of 1.44 μB.