Domain structure of a nematic-liquid-crystal layer in low-frequency Couette flow

The spatially periodic structure arising in a homeotropic nematic-liquid-crystal (NLC) layer in low-frequency Couette flow is described theoretically. The analysis of this phenomenon is based on the hydrodynamic equations for NLCs, from which a self-consistent system of equations is selected for perturbations of hydrodynamic variables: the steady-state angle of the molecule rotation, the liquid flow, and the velocity of oscillating vortex flows. The formation of the periodic structure is explained by the phase delay of the velocities of the vortex oscillating flows forming in the deformed structure with respect to the shear velocity in the Couette flow. It is shown that at low frequencies this difference in the velocities is caused by the orientational waves near the layer boundaries. In the case of fixed orientation of molecules at the boundaries, the dependence of the threshold shear amplitude on the frequency and layer thickness is given by the relation u_th ～ (ωh²)^?1/4. The influence of the conditions for the molecule orientation at the layer boundaries on the above phenomenon is analyzed.     

Relation between the bond lengths in an O-H…O bridge

The data in the literature on the bond lengths of O-H…O bridges formed in organic and inorganic crystals have been analyzed. The results of generalizations of these data on the basis of the generally accepted relation exp(?(r ₁ ? r ₀/b) + exp(?(r ₂ ? r ₀/b) = 1 are considered. The factors limiting its application are revealed and its limiting accuracy is estimated. A more universal expression relating the lengths of the same bonds is proposed: exp(?((r ₁ ? r ₀)/b) ^h ) + exp(?((r ₂ ? r ₀)/b) ^h ) = 1. On the basis of the generalization of all known neutron diffraction data on bridges with angles exceeding 165°, the coefficients in this relation are determined to be r ₀ = 0.950 ± 0.005, b = 0.33018 Å, and h = 5/3.     

Crystal structure of complex natural aluminum magnesium calcium iron oxide

The structure of a new natural oxide found near the Tashelga River (Eastern Siberia) was studied by X-ray diffraction. The pseudo-orthorhombic unit cell parameters are a = 5.6973(1) Å, b = 17.1823(4) Å, c = 23.5718(5) Å, β = 90°, sp. gr. Pc. The structure was refined to R = 0.0516 based on 4773 reflections with |F| > 7σ(F) taking into account the twin plane perpendicular to the z axis (the twin components are 0.47 and 0.53). The crystal-chemical formula (Z = 4) is Ca₂Mg ₂ ^IV Fe ₂ ^(2+)IV [Al ₁₄ ^VI O₃₁(OH)][Al ₂ ^IV O][Al^IV]AL^IV(OH)], where the Roman numerals designate the coordination of the atoms. The structure of the mineral is based on wide ribbons of edge-sharing Al octahedra (an integral part of the spinel layer). The ribbons run along the shortest x axis and are inclined to the y and z axes. The adjacent ribbons are shifted with respect to each other along the y axis, resulting in the formation of step-like layers in which the two-ribbon thickness alternates with the three-ribbon thickness. Additional Al octahedra and Mg and Fe²⁺ tetrahedra are located between the ribbons. The layers are linked together to form a three-dimensional framework by Al tetrahedra, Ca polyhedra, and hydrogen bonds with the participation of OH groups.     

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.     

Crystal structure of Сu<Subscript>2–<Emphasis Type="Italic">m</Emphasis></Subscript>Te (<Emphasis Type="Italic">m</Emphasis> = 0.25)

The Сu₂Te compound has been synthesized by alloying Сu and Te taken in stoichiometric ratios. A Сu₂Te sample has been homogenized by annealing at 773 K for 100 h. A pure copper phase in the form of thin filaments is found to segregate from the synthesized product (4 g) by the end of annealing. It is established by X-ray diffraction analysis that the copper-deficient sample is crystallized into the trigonal system with lattice parameters а = 8.328(1) Å, с = 7.196(1) Å, V = 432.2(1) ų, sp. gr. \(P\overline 3 m1\), Z = 8. The crystal structure is determined and the sample composition Сu_2–m Te (m = 0.25) is refined by the Rietveld method. The three independent copper atoms in the lattice are found to have different coordination numbers: 3, 4, and 5.     

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 .     

Synthesis,Crystal Structure,and Luminescent Properties of Ag(I) Coordination Polymer with Tricarboxylic Acid and Flexible N-donor Ligand

The reaction of AgNO₃ with combinations of 1,3-bis(4-pyridyl)propane (bpp) and 1,3,5-benzenetricarboxylic acid (H₃btc) in aqueous alcohol/ammonia at room temperature produces crystals of {[Ag₆(H₂O)₂(bpp)₆] · (btc)₂ · 25H₂O} _n (Ι). Single crystal X-ray diffraction analysis reveals that the complex Ι consists of 1D infinite cationic chains of [Ag(bpp)] _n ⁿ⁺ and [Ag(H₂O)(bpp)] _n ⁿ⁺ which are further linked into the cation layer of [Ag(bpp)] _n ⁿ⁺ by Ag···π interactions. The noncoordinated btc^3? serves as template driving surrounding water molecules to aggregate into the anionic water layer. The neighboring anionic water layer and cationic layer were further alternately joined into a 3D sandwich-like framework by hydrogen bonding. In addition, the luminescent properties of Ι were investigated.     

Unstrained bond lengths and corresponding cation radii in crystals with perovskite structure

A method for determining average lengths of unstrained bands A-X (l_0AX) and B-X (l_0BX) and the ratio of the rigidity constants of these bonds for ABX₃ compounds with perovskite structure is proposed. The values of l_0AX and l_0BX correspond to the minimum energies of cation-anion interaction of the crystal sublattices. Values of l_0AX and l_0BX are obtained for several groups of halide and oxide compounds: A⁺B²⁺F₃, Cs⁺B²⁺Cl₃, A⁺B⁵⁺O₃, A²⁺B⁴⁺O₃, and A³⁺B³⁺O₃. It is ascertained that, for most compounds studied, the values of l_0AX and l_0BX are equal or close to the interatomic distances in crystals of binary compounds. The values of l_0AX and l_0BX are compared with the sums of the radii of the corresponding cations (R _A , R _B ) and anions (\(^{VI} R_{O^{2 - } } ,^{VI} R_{F^ - } ,^{VI} R_{Cl^ - }\)). It is found that the differences \(l_{0AO^ - } ^{VI} R_{O^{2 - } } (L_{0AF^ - } ^{VI} R_{F^ - } )\) and \(l_{0BO^ - } ^{VI} R_{O^{2 - } } (l_{0BF^ - } ^{VI} R_{F^ - } )\), regarded as the radii of the A and B cations in unstrained bonds, are close to the Shannon radii for a coordination number of six. It is shown that the rigidity constant for A-X bonds is several times smaller than that for B-X bonds.     

Synthesis and Structure of Di(1,2,4,6-tetraphenylpyridinium) Octachlorodirhenate(III)

The (NC₅H₂(C₆H₅)₄)₂[Re₂Cl₈] · 2CH₃CN compound was prepared by the reaction of (n-Bu₄N)₂[Re₂Cl₈] with the 1,2,4,6-tetraphenylpyridinium tosylate in the acetonitrile; it crystallizes upon cooling of the solution at –15°C. The structure consists of the ((C₆H₅)₄C₅H₂N)⁺ cation and Re₂Cl ₈ ^2? anion with virtual D_4h symmetry. The average Re–Re and Re–Cl bond distances are 2.2205 and 2.3431 Å, respectively. In the structure, the Re₂Cl ₈ ^2? anions are disordered, such that 71.34% of the Re–Re units are aligned in one direction while 28.66% are aligned orthogonal to it. The principal crystallographic data are as follows: sp. gr. R?3; a = 26.554(1) Å, c = 23.666(1) Å; V = 14451.6(1) ų; Z = 9; D_x = 1.643 g cm^–3.     

Synthesis and structure of Cs[UO<Subscript>2</Subscript>(SeO<Subscript>4</Subscript>)(OH)] · <Emphasis Type="Italic">n</Emphasis>H<Subscript>2</Subscript>O (<Emphasis Type="Italic">n</Emphasis> = 1.5 or 1)

The synthesis and single-crystal X-ray diffraction study of Cs[UO₂(SeO₄)(OH)] · 1.5H₂O (I) and Cs[UO₂(SeO₄)(OH)] · H₂O (II) are performed. Compound I crystallizes in the monoclinic crystal system, a = 7.2142(2) Å, b = 14.4942(4) Å, c = 8.9270(3) Å, β = 112.706(1)°, space group P2₁/m, Z = 4, and R = 0.0222. Compound II is monoclinic, a = 8.4549(2) Å, b = 11.5358(3) Å, c = 9.5565(2) Å, β = 113.273(1)°, space group P2₁/c, Z = 4, and R = 0.0219. The main structural units of crystals I and II are [UO₂(SeO₄)(OH)]^? layers which belong to the AT ³ M ² crystal chemical group of uranyl complexes (A = UO ₂ ²⁺ , T ³ = SeO₄ ^2?, and M ² = OH^?). In structure I, johannite-like layers are found. Structure II is a topological isomer of I. The two structures differ in the number of U(VI) atoms bound to the central atom by all bridging ligands.     

Molecular structures of chalcone podands: A prognosis of photoinduced transformations in the crystals

A series of chalcone podands with the propenone group in the ortho position of the bridging aryl substituent with respect to the oxyethylene fragment is synthesized. The influence of the preorganization of the chalcone podand molecules in crystals on their ability to participate in topochemical reactions is investigated. From analyzing the X-ray structural data, the highest probability of the solid-state photochemical [2 + 2]cycloaddition is predicted for podands with phenyl substituents and the oxyethylene fragment containing two or three oxygen atoms. The X-ray structural data for the chalcone podand C₃₂H₂₆O₄ (3a) are as follows: a = 7.904(9) Å, b = 14.92(2) Å, c = 21.30(3) Å, β = 91.7(1)°, monoclinic system, space group P2₁/c, Z = 4, V = 2510(5) ų, ρ = 1.26 g/cm³, and R = 0.046; C₃₄H₃₀O₅ (3b): a = 15.738(9) Å, b = 11.889(2) Å, c = 15.0830(15) Å, β = 105.47(14)°, monoclinic system, space group C2/c, Z = 4, V = 2720.0(9) ų, ρ = 1.266 g/cm³, and R = 0.0418; C₃₂H₂₄N₂O₈ (4a): a = 17.9416(18) Å, b = 10.9703(8) Å, c = 41.699(2) Å, β = 105.970(11)°, monoclinic system, space group P2₁/c, Z = 4, V = 2781.4(5) ų, ρ = 1.348 g/cm³, and R = 0.0426; C₃₆H₃₂N₂O₁₀ (4c): a = 7.6286(5)Å, b = 17.9398(10) Å, c = 11.5890(3)Å, β = 95.287(4)°, monoclinic system, space group P2₁/n, Z = 2, V = 1579.27(14) ų, ρ = 1.372 g/cm³, and R = 0.0377; and C₂₈H₂₂O₆ (5a): a = 15.6032(10) Å, b = 8.1131(5) Å, c = 17.7334(11) Å, β = 91.381(5)°, monoclinic system, space group C2/c, Z = 4, V = 2244.2(2) ų, ρ = 1.345 g/cm³, and R = 0.0309.     

Crystal structure of the new radical cation salt (<Emphasis Type="Italic">DOET</Emphasis>)<Subscript>4</Subscript>[Fe(CN)<Subscript>5</Subscript>NO]<Subscript>1.25</Subscript>(C<Subscript>6</Subscript>H<Subscript>5</Subscript>Cl)<Subscript>0.75</Subscript>

A new radical cation salt based on 4,5-(1,4-dioxanediyl-2,3-dithio)-4′,5′-ethylenedithiotetrathiafulvalene (DOET) with the photochromic anion [Fe(CN)₅NO]^2?, namely, (DOET)₄[Fe(CN)₅ NO]_1.25(C₆H₅Cl)_0.75, is synthesized. Single crystals of this salt are studied using X-ray diffraction [a = 10.398(2) Å, b = 11.168(2) Å, c = 18.499(4) Å, α = 103.14(3)°, β = 92.80(3)°, γ = 106.02(3)°, V = 1996.3(7) ų, space group \(P\bar 1\), and Z = 1]. In the structure, radical cation layers alternate with anion layers along the c axis. The centrosymmetric dimers are formed by DOET radical cations in the donor layer with packing of the β type. Like the vast majority of DOET-based salts, the new salt possesses semiconductor properties.     

Structural features and isomorphous substitutions in chromium- and magnesium-containing beryls and chromium-containing beryllian indialite grown by the flux method

Beryls and beryllian indialite {the general formula M ^VI ₂ T(2)^IV ₃ T(1)^IV ₆O₁₈} synthesized in magnesium-containing flux systems saturated with chromium are investigated using X-ray diffraction. The isovalent schemes of the isomorphous incorporation of chromium into Moctahedra of these compounds and the simultaneously realized heterovalent schemes with the participation of other components are revealed from the occupancies of the positions. It is demonstrated that an increase in the average bond lengths in the M positions leads predominantly to an increase in the parameter α. In the beryllian indialites, the T(1) tetrahedra are substantially closer to perfect tetrahedra, the T(2) tetrahedra are distorted to a lesser extent, and the M octahedra are distorted to a greater extent than those in beryls. The structural indications of the ability of compounds with a beryl structure to congruently melt are distinguished.     

Structural chemistry of peroxo compounds of group VI transition metals: I. Peroxo complexes of chromium (a review)

The specific features revealed in the structure of the d ³ Cr(III), d ² Cr(IV), d ¹Cr(V), and d ⁰ Cr(VI) peroxo complexes with the ratios M:O₂ = 1:1, 1:2, and 1:4 are considered. It is noted that, in eleven compounds of the general formula Cr(O₂)_nO_m A _p (n = 1, 2, 4; m = 0, 1; p = 0–4), the metal atoms can be in four oxidations states: +3 (d ³), +4 (d ⁴), +5 (d ¹), and +6 (d ⁰). This property distinguishes chromium peroxo compounds from molybdenum and tungsten dioxygen complexes, which, with one exception, are represented by the d ⁰ M(VI) compounds.     

Coordination dimers constructed from metal(II) halides and the organic ligand 1,2-dimethoxy- 4,5-bis(2-pyridylethynyl)benzene

A series of new coordination compounds has been synthesized using the organic ligand 1,2-dimethoxy-4,5-bis(2-pyridylethynyl)benzene (dmpeb). The compounds all form dimers consisting of two metal cations bridged by two ligand molecules. Charge balance is provided by halide ligands, and the four-coordinate metal centers are distorted from the ideal tetrahedral environment. [CoCl₂(dmpeb)]₂ (1) crystallizes in the monoclinic space group P2₁/n with a = 8.5272(6) Å, b = 18.3653(13) Å, c = 13.3493(9) Å, β = 103.574(2)^°, V = 2032.2(2) ų, Z = 2. [ZnCl₂(dmpeb)]₂ (2) is isostructural to 1 and has the cell parameters a = 8.5495(4) Å, b = 18.4049(8) Å, c = 13.3692(6) Å, β = 103.4460(10)^°, V = 2046.01(16) ų, Z = 2. [ZnBr₂(dmpeb)]₂ (3) is also isostructural to 1 with a = 8.7882(5) Å, b = 18.7260(12) Å, c = 13.3857(8) Å, β = 102.5990(10)^°, V = 2149.8(2) ų, Z = 2. Additionally, the compounds [ZnI₂(dmpeb)]₂ (4, cell parameters: a = 8.9650(5) Å, b = 19.1251(10) Å, c = 13.4160(7) Å, β = 101.1660(10)^°, V = 2256.7(2) ų, Z = 2), [HgCl₂(dmpeb)]₂ (5, cell parameters: a = 8.8457(7) Å, b = 18.4030(15) Å, c = 13.3711(11) Å, β = 104.246(2)^°, V = 2109.7(3) ų, Z = 2), and [HgBr₂(dmpeb)]₂ (6, cell parameters: a = 9.0576(5) Å, b = 18.8634(11) Å, c = 13.4535(8) Å, β = 102.9780(10)^°, V = 2239.9(2) ų, Z = 2) are also isostructural to 1. A seventh dimeric compound, [HgI₂(dmpeb)]₂, not isostructural to the others was also characterized by X-ray crystallography. [HgI₂(dmpeb)]₂ (7) crystallizes in the triclinic space group P-1 with a = 8.8028(5) Å, b = 12.0990(7) Å, c = 12.4082(7) Å, α = 109.7240(10)^°, β = 107.3680(10)^°, γ = 93.0880(10)^°, V = 1169.57(12) ų, Z = 1.     

Structure of 1-(2,6-dimethylphenyl)-<Emphasis Type="Italic">N</Emphasis>-hydroxy-4,4-dimethyl-2,5-dioxo-<Emphasis Type="Italic">N</Emphasis>-phenyl-3-pyrrolidine carboxamide

The title compound is crystallized in the monoclinic space group P2₁/c with cell parameters a = 7.499, b = 13.336, c = 19.390 Å, β = 99.716°, V = 1911.4 ų, Z = 4, D _cal = 1.273 Mg/m³ at T = 120 K. The structure is refined by full-matrix least-squares procedures to final R ₁ = 0.0548 and wR ₂ = 0.1089 for 3424 reflections. Two phenyl rings are noncoplanar with regard to each other and pyrrolidine core. The structure contains intramolecular hydrogen bond.     

Crystallographic analysis of the structure of livingstonite HgSb<Subscript>4</Subscript>S<Subscript>8</Subscript> from refined data

An X-ray diffraction study of mineral livingstonite (HgSb₄S₈) from Khaydarkan (Kyrgyzstan) has been performed on a Bruker Nonius X8Apex diffractometer with a 4K CCD detector (R = 0.031). The unit-cell parameters were found to be a = 30.1543(10) Å, b = 3.9953(2) Å, c = 21.4262(13) Å, β = 104.265(1)°, V = 2501.7(2) ų, Z = 8, d _calcd = 5.013 g/cm³, and sp. gr. A2/a. It was confirmed that livingstonite belongs to rod-layers structures. In one type of layer, two double Sb₂S₄ chains are bound by disulfide groups [S₂]^2? (S-S 2.078(2) Å); in the other type, these chains are bound via Hg²⁺ cations. A crystallographic analysis confirmed the existence of independent pseudotranslational ordering in the cation and anion matrices, which is characteristic of the lozenge-like structures of sulfides and sulfosalts.     

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.     

Crystal and molecular structure of phenanthrolinium peroxodisulfate dihydrate (C<Subscript>12</Subscript>H<Subscript>9</Subscript>N<Subscript>2</Subscript>)<Subscript>2</Subscript>S<Subscript>2</Subscript>O<Subscript>8</Subscript> · 2H<Subscript>2</Subscript>O

The crystal structure of (HPhen)₂S₂O₈ · 2H₂O is studied using X-ray diffraction. The crystals are monoclinic, a = 23.716(5) Å, b = 10.220(2) Å, c = 13.103(3) Å, β = 128.03(2)°, V = 2501.6(9) ų, Z = 4, space group C2/c, and R = 0.0745 for 1579 reflections with I > 2σ(I). The crystal is built of S₂O ₈ ^2? centrosymmetric anions, HPhen ⁺ cations, and molecules of crystallization water. Hydrogen bonds link the structural units into chains. Within a chain, stacking interactions are observed between the phenanthroline rings (the interplanar spacing between the rings is 3.8 Å, and the dihedral angle between their planes is 8°). The data of IR spectroscopy confirm the formation of the N(Phen)-H bond.