Strain of interatomic bonds and crystallochemical aspects of AB 1 2/′ B 1 2/″ O3 oxides with perovskite structure

A method for determining the strain characteristics of interatomic bonds in crystals of ternary oxides AB ₁ ^2/′ B ₁ ^2/″ O₃ with perovskite structure, i.e., AB ₁ ^2/′ B ₁ ^2/″ O₃ (B″ = Nb, Ta, Sb, Re, or Bi) and AB ₁ ^2/′2+ B ₁ ^2/″6+ O₃ (B″ = Mo, W, Re, Os, or U), is developed. A linear relationship is established between the effective lengths of unstrained B-O bonds (l _0BO) and the lengths of unstrained B′-O (l _0B′O) and B″-O (l _0B″O) bonds, which differs from the Vegard rule. The found values of l _0B″O for ternary oxides with perovskite structure turned out to be close to the average interatomic B″-O distances in crystals of polymorphic phases of low-symmetry simple oxides. It is shown that the average length of the unstrained Pb-O bond in PbB ₁ ^2/′ B ₁ ^2/″ O₃ perovskites corresponds to the length of the same bond in binary oxides PbBO₃. For ternary oxides with perovskite structure, a linear correlation between the bond-strain energy and the temperature of their transition to the cubic phase is established. A linear correlation is found between the ratios of the Curie temperatures and the bond-strain energy for lead niobates and tantalates.     

Crystal structure of new synthetic Ca,Na,Li-carbonate-borate

In the process of studying the phase formation in the Li₂CO₃-CaO-B₂O₃-NaCl system, new Ca,Na, Li-carbonate-borate has been synthesized under hydrothermal conditions. The crystal structure of carbonate-borate with the crystallochemical formula Ca₄(Ca_0.7Na_0.3)₃(Na_0.7□ _0.3)Li₅[B ₁₂ ^t B ₁₀ ^Δ O₃₆(O,OH)₆](CO₃)(OH) · (OH,H₂O) was refined to R _hkl = 0.0716 by the least squares method in the isotropic approximation of atomic thermal vibrations without the preliminary knowledge of the chemical composition and the formula (sp. gr. R3, a _rh = 13.05(2) Å, α = 40.32(7)]°, V = 838(2) ų, a _h = 8.99(2), c _h = 35.91(2) Å, V = 2513(2) ų, Z = 3, d _calcd = 2.62 g/cm³, Syntex P $\bar 1$ diffractometer, 3459 reflections, 2θ-θ method, λMo). The structure has a new boron-oxygen radical [B ₁₂ ^t B ₁₀ ^Δ O₃₆(O,OH)₆] _∞∞ ^15? , a double layer of nine-membered [B ₆ ^t B ₃ ^Δ O₁₅(O,OH)₃]^7.5?-rings bound by BO₃-triangles, and twelve-membered [B ₆ ^t B ₆ ^Δ O_19.5(O,OH)₃]^7.5? rings. This allows one to relate this compound to megaborates with complex boron-oxygen radicals. The structure is built from two types of blocks consisting of Ca,Na,B-and Li,B-polyhedra alternating along the c-axis, which explains the perfect cleavage of the crystals along the (0001) plane.     

Synthesis and crystal structures of bimetallic hydrogen sulfates M I M II [H(SO4)2](H2O)2 (M I = K, Cs; M II = Zn, Mn) and selenate KMg[H(SeO4)2](H2O)2

Single crystals of acid salt hydrates M ^I{M ^II[H(XO₄)₂](H₂O)₂}, where M ^I, M ^II, and X are K, Zn, and S (I); K, Mn, and S (II); Cs, Mn, and S (III); or K, Mn, and Se (IV), respectively, were synthesized and studied by X-ray diffraction analysis. Compounds I–IV (space group $P\bar 1$ ) are isostructural to each other and to hydrate KMg[H(SO₄)₂](H₂O)₂ (V) studied earlier. Structures I–V, especially, the M ^I-O, M ^II-O, and X-O distances and the O?H?O (2.44–2.48 Å) and O_w-H?O (2.70–2.81 Å) hydrogen bonds, are discussed.     

Insertion of ethyl isothiocyanate into tungsten hexachloride: Crystal structure of ethyl-(4-ethyl-5-thioxo[1.2.4]dithiazolidin-3-ylidene)ammonium oxopentachlorotungstate(VI)

A product of the insertion of two isothiocyanate molecules into the same W-Cl bond, namely, W-Cl-WCl₅{N(Et)C(S)N(Et)C(S)Cl} (I), is synthesized by the reaction of WCl₆ with EtNCS in a dichloroethane solution. The hydrolysis of compound I results in the formation of single crystals of the complex . The structure of crystals II is determined using X-ray diffraction. It is demonstrated that structural units of crystals II are the [W^VIOCl₅]^? anionic complexes and the ethyl-(4-ethyl-5-thioxo[1.2.4]dithiazolidin-3-ylidene)ammonium cations.     

Synthesis and crystal structure of Na<Subscript>3</Subscript>(H<Subscript>3</Subscript>O)[UO<Subscript>2</Subscript>(SeO<Subscript>3</Subscript>)<Subscript>2</Subscript>]<Subscript>2</Subscript>· H<Subscript>2</Subscript>O

Single crystals of the compound Na₃(H₃O)[UO₂(SeO₃)₂]₂ · H₂O (I) have been synthesized, and their structure has been investigated using X-ray diffraction. Compound I crystallizes in the triclinic system with the unit cell parameters a = 9.543(6)Å, b = 9.602(7)Å, c = 11.742(8)Å, α = 66.693(16)°, β = 84.10(2)°, γ = 63.686(14)°, space group P \(\bar 1\), Z = 2, and R = 0.0734. The uranium-containing structural units of the crystals are [UO₂(SeO₃)₂]^2? chains, which belong to the crystal-chemical group AB ² B ¹¹ (A = UO ₂ ²⁺ , B ² = SeO ₃ ^2? , B ¹¹ = SeO ₃ ^2? ) of the uranyl complexes. The structures of the compounds containing the [UO₂(SeO₃)₂]^2? anionic complexes are compared.     

Synthesis and X-ray diffraction study of new uranyl malonate and oxalate complexes with carbamide

Two new malonate-containing uranyl complexes with carbamide of the formulas [UO₂(C₃H₂O₄)(Urea)₂] (I) and [UO₂(C₃H₂O₄)(Urea)₃] (II), where Urea is carbamide, and one uranyl oxalate complex of the formula [UO₂(C₂O₄)(Urea)₃] (III) were synthesized, and their crystals were studied by X-ray diffraction. The main structural units in crystals I are the electroneutral chains [UO₂(C₃H₂O₄)(Urea)₂]_∞ belonging to the crystal-chemical group AT¹¹M₂¹ (A = UO₂²⁺, T¹¹ = C₃H₂O₄^2-, M¹ = Urea) of uranyl complexes. Crystals II and III are composed of the molecular complexes [UO₂(L)(Urea)₃], where L = C₃H₂O₄^2- or C₂O₄^2-, belonging to the crystal-chemical group AB⁰¹M₃¹ (A = UO₂²⁺, B⁰¹ = C₃H₂O₄^2- or C₂O₄^2-, M¹ = Urea). The characteristic features of the packing of the uranium-containing complexes are discussed in terms of molecular Voronoi–Dirichlet polyhedra. The effect of the Urea: U ratio on the structure of uranium-containing structural units is considered.     

Theoretical study of structural phase transition in a RbMnCl<Subscript>3</Subscript> crystal by the Kim-Gordon method

Symmetry analysis of the low-temperature phase of RbMnCl₃ crystals with the monoclinic axis perpendicular to the sixfold axis of the high-temperature phase showed that its space group is either C _2h ³ or C _2h ⁶ The distribution of normal vibrations over the irreducible representations of the high-temperature phase is refined, and the symmetry relationships for normal vibrations of all possible low-temperature phases are tabulated. The model of the potential function of the crystal is obtained by the nonempirical Kim-Gordon method. This model allows one to establish the existence of the saddle point of the potential surface and several harmonically unstable modes corresponding to correlated rotations of rigid MnCl₆ and Mn₂Cl₉ polyhedra. The absolute energy minimum is determined by deforming the lattice along the eigenvector of the E_1g mode within the sp. gr.. C _2h ⁶ .     

X-Ray diffraction and IR-spectroscopic studies of UO2(n-C3H7COO)2(H2O)2 and Mg(H2O)6[UO2(n-C3H7COO)3]2

Single crystals of UO₂(n-C₃H₇COO)₂(H₂O)₂ (I) and Mg(H₂O)₆[UO₂(n-C₃H₇COO)₃]₂ (II) are synthesized. Their IR-spectroscopic and X-ray diffraction studies are performed. Crystals I are monoclinic, a = 9.8124(7) Å, b = 19.2394(14) Å, c = 12.9251(11) Å, β = 122.423(1)°, space group P2₁/c, Z = 6, and R = 0.0268. Crystals II are cubic, a = 15.6935(6) Å, space group $Pa\bar 3$ , Z = 4, and R = 0.0173. The main structural units of I and II are [UO₂(C₃H₇COO)₂(H₂O)₂] molecules and [UO₂(C₃H₇COO)₃]^? anionic complexes, respectively, which belong to AB ₂ ⁰¹ M ₂ ¹ (I) and AB ₃ ⁰¹ (II) crystal chemical groups of uranyl complexes (A = UO ₂ ²⁺ , B ⁰¹ = C₃H₇COO^?, and M ¹ = H₂O). A crystal chemical analysis of UO₂ L ₂ · nH₂O compounds, where L is a carboxylate ion, is performed.     

Structures of Tris(2-hydroxyethyl)ammonium Salts of Succinic Acid

Succinic acid salts-tris(2-hydroxyethyl)ammonium succinate (C₆H₁₆NO₃) ₂ ⁺ C₄H₄O ₄ ^2? (monoclinic crystals, sp. gr. P2₁/c, Z = 4) and tris(2-hydroxyethyl)ammonium hydrogen succinate (C₆H₁₆NO₃)⁺C₄H₅O ₄ ^? (monoclinic crystals, sp. gr. P2₁/c, Z = 4)—were synthesized and structurally characterized. The specific features of the three-dimensional structures of tris(2-hydroxyethyl)ammonium salts of succinic acid are considered. The role of interionic electrostatic interactions in the structure stabilization and the formation of products of composition 1: 1 and 1: 2 derived from succinic acid is discussed.     

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.     

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.     

Molecular and crystal structures of 1R,4R-cis-2-(4-hydroxybenzylidene)-p-menthan-3-one

The molecular and crystal structures of chiral 1R, 4R-cis-2-(4-hydroxybenzylidene)-p-menthan-3-one (I) are determined by X-ray diffraction analysis. Single crystals of I are orthorhombic, a = 8.997(2) Å, b = 11.314(2) Å, c = 14.847(3) Å, V = 1511.3(5) ų, Z = 4, and space group P2₁2₁2₁. The cyclohexanone ring in molecules of compound I has a chair-type conformation with the axial methyl and equatorial isopropyl groups. The enone and benzylidene groupings are nonplanar. The considerable distortion of bond angles at the sp ² carbon atoms of the benzylidene grouping and the puckering parameters of the cyclohexanone ring in the structure of I are close to those observed for the previously studied compound with the p-methoxy substituent. In the crystal, molecules I are linked by very short intermolecular hydrogen bonds .     

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 structures of cesium and dimethylammonium cupradecaborates, Cs[CuB10H10] and (CH3)2 NH2[CuB10H10]

The crystal structures of Cs[CuB₁₀H₁₀] (I) and (CH₃)₂NH₂[CuB₁₀H₁₀] (II) are studied (R = 0.0398 and 0.0510 for 1225 and 2728 observed reflections in I and II, respectively). Crystals I and II are built of [(CuB₁₀H₁₀)^?]∞ anionic chains and cations. The distorted tetrahedral coordination of the Cu⁺ ions is formed by four pairs of B-H atoms from two polyhedral anions. The Cu-B bond lengths in I and II are 2.159–2.287(6) and 2.130–2.285(9) Å, respectively. The coordination of the Cu⁺ ions in II includes only edges between apical and equatorial vertices of the anions. In I, both the edges of the apical belt and those between two equatorial vertices are involved in coordination. The ability of the B₁₀H ₁₀ ^2? anion to coordinate metals by the equatorial edge is established for the first time.     

Crystal structure and IR spectroscopic study of (CN3H6)2[(UO2)2(C2O4)(CH3COO)4]

Compound (CN₃H₆)₂[(UO₂)₂(C₂O₄)(CH₃COO)₄] is synthesized and characterized by IR spectroscopy and single-crystal X-ray diffraction [a = 8.5264(2) Å, b = 13.8438(4) Å, c = 10.7284(2) Å, β = 103.543(1)°, space group P2₁/n, Z = 2, and R = 0.0258]. The main structural units of the crystals are binuclear [(UO₂)₂C₂O₄(CH₃COO)₄]^2? groups, which belong to the A ₂ K ⁰² B ₄ ⁰¹ crystal chemical group of uranyl complexes (A = UO ₂ ²⁺ , K ⁰² = C₂O ₄ ^2? , and B ⁰¹ = CH₃COO^?). The coordination polyhedron of the uranium atom is the UO₈ hexagonal bipyramid with the oxygen atoms of the uranyl ion at the axial positions. Uranium-containing groups and guanidinium cations are connected by electrostatic interactions and by the hydrogen bond system, which involves hydrogen atoms of guanidinium cations and oxygen atoms of oxalate and acetate anions. The results of the spectroscopic study of the compound agree with the X-ray diffraction data.     

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.     

Crystal chemistry of Li,GeVI-germanates: Combinatorial-topological analysis and modeling of crystal structures

The combinatorial-topological analysis of the structures of framework Li,Ge-germanates of the compositions Li₂Ge^VIGe ₂ ^IV O₆(OH)₂ (sp. gr. B ₂/b), Li₂Ge^VIGe ₃ ^IV O₉ (sp. gr.Pcca), Li₄Ge ₂ ^VI Ge ₇ ^VI O₂₀ (sp. gr. C2), and Li₂Ge^VIGe ₆ ^IV O₁₅ (sp. gr. Pbcn) has been made with the separation of subpolyhedral structural units (SPSUs) built by octahedra and tetrahedra. The topologically invariant SPSUs are separated in three-dimensional frameworks of the structures. A possible mechanism of the matrix assemblage from the SPSU invariants in crystal structures of the framework Li,Ge-germanates is suggested.     

Alkali-metal hydrogen selenate-phosphates M 2 H 3(SeO4)(PO4) (M = Rb or K) and M 4H5(SeO4)3(PO4)(M = K or Na)

Crystalline hydrogen selenate-phosphates M ₂H₃(SeO₄)(PO₄) [M = Rb (I) or K (II)] and M ₄H₅(SeO₄)₃(PO₄) [M = K (III) or Na (IV)] were obtained by reactions of Rb, K, and Na carbonates with mixtures of selenic and phosphoric acid solutions. The X-ray structure study of single crystals revealed that I and II are isostructural (sp. gr. Pn). In these structures, SeO₄ and H₃PO₄ tetrahedra are linked by hydrogen bonds to form corrugated layers. Structures III and IV (sp. gr. $P\bar 1$ ) have similar arrangements of non-hydrogen atoms but different hydrogen-bond systems. In III = K₄(HSeO₄)₂{H[H(Se,P)O₄]₂}, the HSeO₄ groups branch from the infinite anionic {H[H(Se,P)O₄]₂} chains. In IV = Na₄[H(SeO₄)₂]{H[H_1.5(Se, P)O₄]₂}, the anionic {H[H_1.5(Se,P)O₄]₂} chains are crosslinked by hydrogen bonds formed by the [H(SeO₄)₂] dimers.     

Phase transitions in Cs5(HSO4)2(H2PO4)3 crystal

The symmetry (sp. gr.I $\bar 4$ 3d) and lattice parameters have been determined for the first time for Cs₅(H₂SO₄)₂(H₂PO₄)₃ crystals in the temperature range from 172 to 390 K. The thermal and optical properties of crystals, as well as their conductivity, have been investigated at elevated temperatures. It is shown that a crystal heated to T = 365 K undergoes a phase transition with symmetry lowering to the tetragonal phase (with the parameters a = 4.965(1) Å and c = 5.016(1) Å), while at T ≈ 390 K a phase transition to the cubic phase is presumably observed. With a decrease in temperature, a phase transition without a change in symmetry occurs at T = 240 K.     

Ba1−x R x F2 + x Phases (R = Gd-Lu) with distorted fluorite-type structures—products of crystallization of incongruent melts in the BaF2-RF3 Systems (R = Gd-Lu). III. Defect Ba0.75Lu0.25F2.25 structure. A new {Lu8[Ba6F71]} supercluster of defects

The structure of Ba_0.75Lu_0.25F_2.25 crystals grown from melt has been studied by X-ray diffraction analysis (4729 measured reflections, 269 independent reflections with I > σ (I), R = 1.1%, R _w = 0.7%). The crystals are crystallized in the cubic system, sp. gr. Pm $\bar 3$ m, with the lattice parameter a = 5.9870(9) Å. A new complex of defects is singled out—a supercluster of the composition {R ₈[Ba₆F₇₁]}. This supercluster differs from the well-known rare earth octahedral supercluster of the composition {Ba₈[R ₆F_68-69]} because its nucleus is formed not by RE cations but by an alkali earth cation, Ba. The {R ₈[Ba₆F₇₁]} supercluster has a configuration close to that of the [B₁₄F₆₄] fragment of the fluorite structure and can replace the latter isomorphously. The model of the Ba_0.75Lu_0.25F_2.25 crystals consisting of coherently intergrown isostructural microphases having different chemical compositions is characterized by the good agreement of the calculated and experimentally determined occupancies of the F^1? positions. The comparison of the Ba_0.8Yb_0.2F_2.2 (phase studied earlier) and Ba_0.75Lu_0.25F_2.25 structures demonstrates the evolution of the defect structure along the series of rare earths with the corresponding change of the sp. gr. Fm $\bar 3$ m by the sp. gr. Pm $\bar 3$ m.