On the problem of transient hydrodynamic instability of nematics in magnetic field: I. Instability at splay deformation

A dependence of the square of dimensionless magnetic-field (MF) strength on the square of dimensionless wave vector of the domain structure, $h^2 \left( {\tilde q^2 } \right)$ , is analytically derived for the transient hydrodynamic instability arising at splay deformation under a MF. The domain formation is related to the fold catastrophe; the square of the critical field of domain formation, h _D ² , is determined from the condition ${{\partial \left[ {h^2 \left( {\tilde q^2 } \right)} \right]} \mathord{\left/ {\vphantom {{\partial \left[ {h^2 \left( {\tilde q^2 } \right)} \right]} \partial }} \right. \kern-0em} \partial }\left( {\tilde q^2 } \right) = 0$ . In the general case, the function $h^2 \left( {\tilde q^2 } \right)$ is a ratio of two polynomials whose coefficients for calamitics are determined by combinations of four dimensionless viscosities ν₂/ν₁, ν₆/ν₁, ν₇/ν₁, and ν₈/ν₁. Under some assumptions, the quotient of the polynomials at large $\tilde q^2$ is a quadratic function which allows one to experimentally determine the dimensionless viscosities ν₂/ν₁, ν₆/ν₁, ν₇/ν₁, and α₂/ν₁.     

X-ray diffraction study of an as-grown crystal of a two-phase sample of Lu0.65Ca0.35F2.65

The X-ray diffraction study of an “as-grown” crystal of Lu_0.65Ca_0.35F_2.65 revealed for the first time two phases with a regular mutual orientation. The c axis of the hexagonal phase (a = 3.88 Å, c = 6.89 Å) is oriented along the body diagonal to the cubic phase (a = 5.50 Å). The hexagonal phase has a tysonite-type structure with a “small” unit cell (P6₃/mmc, Z = 2). The cubic phase has a fluorite structure ( \(Fm\bar 3m\) , Z = 4).     

New icosahedral nanoclusters in crystal structures of intermetallic compounds: Topological types of 50-atom deltahedra D50 in samson phases β-Mg2Al3 and ?-Mg23Al30

A database of intermetallic compounds has been compiled using the TOPOS program package. This database includes 514 topological types, containing 12- and 13-atom icosahedral i clusters. An isolated group of 1649 i clusters is described by 14 point groups and their maximum symmetry D _3d ( $\bar 3$ m) and T _h (m $\bar 3$ ) is established, respectively, in 47 and 25 types of crystal structures. A structural analysis of the outer quasispherical shells showed that local 63-atom i configurations 1@12@50, which contain 50 atoms in the second layer, are implemented in 8 out of 19 cases. Examples of new topologically different types of 50-atom D50 deltahedra in the Samson phases ?-Mg₂₃Al₃₀ and ??-Mg₂Al₃ are presented. Four topologically different sites with coordination numbers of 5, 6, 6, or 7 are established in the ? shell and seven sites with coordination numbers of 5, 5, 6, 6, 6, 6, or 7 are found in the ?? shell. The inner i clusters for the ??-Mg₂Al₃ structure (with the symmetry $\bar 3$ m) and the ?-Mg₂₃Al₃₀ structure (with the symmetry $\bar 3$ ) have a similar chemical composition, i.e., Mg₇Al₆ and Mg₆Al₇, and their 50-atom shells are chemically identical to 18Mg + 32Al. The configurations found supplement the series of known two-layer icosahedral Bergman and Mackay clusters in the form of deltahedra with 32- and 42-atom shells.     

Crystal structure of tisinalite Na2(Mn,Ca)1 − x (Ti,Zr,Nb,Fe3+)[Si6O8(O,OH)10]

Crystal structure of tisinalite from the Lovozero alkaline massif (the Kola Peninsula) was established by single-crystal X-ray diffraction analysis (SYNTEX $\bar P1$ diffractometer, λMoK_α radiation, 2θ/θ scanning mode). The structure solution (SHELX97 program package, R _hkl = 0.0565, 951 independent reflections, anisotropic refinement of thermal atomic displacements) confirmed that tisinalite belongs to the lovozerite structure type (sp. gr., $\bar P1$ , a = 10.036(5) Å, c = 12.876(9) Å, Z = 3). The difference between the structure of tisinalite and the structures of the minerals of the lovozerite group established earlier consists in the nature of the occupancy of both cation and anion positions.     

Flexoelectric effect and statistical properties in polar liquid crystals

The structural properties and flexoelectric coefficients e ₁ and e ₃ of polar liquid crystals (LCs) such as 4-n-pentyl-4′-cyanobiphenyl (5CB) are studied in the nematic phase by the molecular-dynamics and statistical-mechanics methods. A number of order parameters, $\bar P_{2L} (L = 1,2,3)$ and $\bar P_2 (r)$ , and orientational correlations ξ_λ for the nearest and next-nearest neighbors were investigated. The calculations show the absence of spontaneous polarization $(\bar P_1 \simeq 0)$ in the nondeformed polar 5CB liquid crystal over the entire range of temperatures corresponding to the nematic phase. The origination of spontaneous polarization (characterized by two independent flexoelectric coefficients e ₁ and e ₃) in response to an external deformation of a 5CB sample is studied. The calculated e ₁ and e ₃ coefficients agree well with the experimental data for 5CB obtained by the pyroelectric method.     

Kinetics of hydrothermal crystallization of quartz in Na2CO3 solutions

The kinetics of crystallization of the {0001}c, {01 $\bar 1$ 1}r, and {10 $\bar 1$ 1}R faces of quartz in 0.5 M Na₂CO₃ (M is molarity) aqueous solutions has been studied in the temperature range 200–450°C. It is established that the dependence of the crystal growth rate on temperature in the logV-1/T, K coordinates is of a parabolic nature. It is most probable that the nonlinearity of this dependence is associated with a deficiency in the solution of silica monomers, taking part in the elementary event of quartz crystallization. The causes of a jumpwise decrease in the activation energy of the growth of the c, r, and R faces at t > 280–325°C are considered.     

Refinement of the crystal structure of sanidine-like feldspar

The crystal structure of sanidine-like feldspar of the composition KAlSi₃O₈ from the Khibiny alkaline massif (the Kola Peninsula) has been refined (X-ray diffraction analysis; automated Syntex $P\bar 1$ diffractometer; 2θ: θ scanning technique; 2320 reflections; R _(hkl) = 0.0409; anisotropic refinement; AREN program package). The data obtained for KAlSi₃O₈ are: a = 8.615(9), b = 13.030(7), c = 7.200(5) Å, α = 89.99(5)°, β = 116.01(6)°, γ = 89.98(7)°, Z = 4, sp. gr. $C\bar 1$ . Microtwinning revealed in the crystal structure of the mineral explains the simultaneous existence of two structural-optical types in one sample—“high” and “low” sanidines.     

Anisotropy of microhardness of β-BaB2O4 single crystals

The anisotropy of microhardness of β-barium borate single crystals β-BaB₂O₄ (BBO) is studied by the sclerometry method on the (0001) basal plane, the $(10\bar 10)$ plane of the hexagonal prism, and the $(11\bar 20)$ plane of the trigonal prism. It is shown that the anisotropy observed in the crystal is determined by the directions of covalent B-O bonds. It is established that the anisotropy of microhardness correlates with the system of cleavage planes.     

Formation of zinc oxide quasibicrystal structures

Quasibicrystal structures with interblock boundaries of epitaxial zinc oxide layers on a sapphire substrate along a given direction have been obtained for producing submicron electronic devices. It is shown that the use of the buffer technique allows one to grow on one (10 $\bar 1$ 2) α-Al₂O₃ substrate ZnO layers oriented in the (11 $\bar 2$ 0)and (0001) planes with clearly pronounced interlayer boundaries. The morphology and structural characteristics of these layers are studied.     

Program for calculating the scattering parameters used in the X-ray standing wave method

A computer program for calculating the complex kinematic scattering parameters χ₀, χ_h, and $\chi _{\bar h} $ of X rays, which are Fourier components of the crystal complex susceptibility, as well as some of their combinations, is presented. The values calculated by the program can be used for computer simulation of experimental results obtained by the X-ray standing-wave method. Methods for calculating these parameters on the basis of well-known tables are described in detail. For crystals of complex structure, it is necessary to know their structure and the Debye temperature or specific heat capacity in order to calculate χ_h and $\chi _{\bar h} $ . To calculate χ₀, it is sufficient to know the chemical formula and the density of a material.     

Structure of Tl18Pb2Ti7S25 as a masterpiece of crystallographic symmetry

A crystallographic analysis of the cubic structure of Tl₁₈Pb₂Ti₇S₂₅ has established the arrangement of all cations and anions according to the law of the 27-fold (with respect to volume) structure type of PbS(NaCl) with strictly fixed anionic vacancies. The nonintersecting axes of symmetry \(\bar 3\) of four directions organizing the structure distribute cations differing in sizes, charges, and amounts over general and particular sites of the sp. gr. Pa3 to form a high-symmetry design in the simple atomic matrix.     

Refined crystal structure of iron-rich triclinic astrophyllite

Crystal structure of Fe-rich triclinic astrophyllite K₂NaFe₇ [Ti₂Si₈O₂₆F](OH)₄ is refined (a Syntex P $\bar 1$ automatic diffractometer, 3809 reflections, 2θ/θ scan, R = 0.041): a = 5.365(2), b = 11.88(1), c = 21.03(2) Å, α = 84.87(6)°, β = 92.25(5)°, γ = 103.01(4)°, sp. gr. A $\bar 1$ , Z = 2, d _calcd = 3.29 g/cm³. The refined structure is identical to that reported earlier. The structure is built by three-layer TOT sheets in which an O layer of Fe-octahedra is sandwiched between the T layers consisting of Si-tetrahedra and Ti-octahedra. It is established that differently chosen unit cells of the mineral are interrelated.     

Structure analysis of O,O’-propane-1,3-diyl bis[diphenyl(phosphinothioate)]

A new diphosphine disulphide compound with the formula C₂₇H₂₆O₂|P₂S₂, was synthesized from the reaction between PPh₂SCl and 1,3-propanediol and characterized with different spectroscopic methods. Its structure has also been studied by X-ray diffraction. The compound crystallizes in the triclinic space group $P\bar 1$ . Pentavalent phosphorus atoms in the molecule are in distorted tetrahedral environments.     

On crack nucleation in zinc upon interaction of basal and pyramidal dislocations

The interaction of intersecting basal and pyramidal dislocation pileups in single-crystal zinc has been analyzed. Different versions of the formation of sessile (1/3[4 $ \bar 2\bar 2 $ 3]) and cleavage ([0001]) dislocations (microcrack nuclei) are considered. The merging of the head dislocations in pyramidal pileups is shown to be preferred. The conditions for thermally activated dislocation merging are derived. The conditions for crack opening according to the Gilman-Rozhanski? mechanism are discussed. It is analytically established that the breaking stress, normal to the (0001) plane in the region of microcrack nucleation, exceeds the theoretical strength.     

Polytypism and superstructure in CoInGaS4

It is established that a one-layer polytype 1T with the unit-cell parameters a = 3.758, c = 12.135 Å, sp. gr. P3m1 and the structure module _hT_hO_hT_hE is mixed with the three-layer polytype 3R with the unit-cell parameters a = 3.758, c = 36.405 Å, sp. gr. R3m and the structure module _hT_cO_cT_hE, where T and O are two-dimensional nets of tetrahedra and octahedra, respectively, E is the empty intermediate layer, and h and c indicate the hexagonal and cubic packings of atomic planes S. The microdiffraction pattern in the hexagonal basis shows a monoclinic superlattice with the parameters $A = \sqrt {19} a, B = \sqrt {13} a, \gamma = 110.485^\circ$ related to the main hexagonal lattice as A = [520] and $B = [\bar 130]$ .     

Synthesis, crystal structure, and magnetic properties of a Li8FeSm22O38 single crystal

Li₈FeSm₂₂O₃₈ single crystals have been grown by spontaneous flux crystallization, and their structure has been identified by X-ray diffraction analysis as follows: cubic crystals, a = 11.9078(5) Å, sp.gr. $Im\bar 3m$ , Z = 2. Fe atoms occupy two mixed positions. Magnetic ions have different ligand environments: a regular octahedron (Sm/Fe)O₆, a three-cap trigonal prism SmO₉, and a square antiprism SmO₈. The rather low Neel temperature (～3 K) can be explained by the considerable variation in the angles and lengths of exchange couplings between magnetic ions.     

Regular domain structure in a lithium niobate crystal—Period stabilization

High stability of the period and homogeneity of a regular domain structure was attained in Nd: Mg: LiNbO₃ crystals grown from melt with an excess of lithium oxide by the Czochralski method along the normal to the close-packed $\{ 01\bar 12\} $ face.     

The first observation of dislocation blocking in pure metal without external stress

Self-blocking of c + a edge dislocations at second-order pyramidal slip in magnesium single crystals whose axis is parallel to the c axis has been found. Self-blocking is confirmed by the dislocation extension along a selected direction in the absence of external stress. Transmission electron microscopy (TEM) images of (c + a) dislocations extended in the $\left\langle {1\bar 100} \right\rangle$ directions are obtained. A model of a two-valley potential relief in Mg is proposed: the Peierls relief determines the second-order slip of (c + a) dislocation in the pyramid plane, while the immersion in deep valleys is related to splitting of the c + a edge segment (or the spread of its core) in the basal plane.     

Crystal structure of Rb-elpasolite Rb2NaAlF6

Single crystals of Rb₂NaAlF₆, the Rb analogue of the mineral elpasolite, are obtained in the NaF-Rb₂CO₃-Al₂O₃-Rb₃PO₄-H₂O system under hydrothermal conditions, and their structure is determined by X-ray diffraction (R = 0.0188): a = 8.3087(1) Å, space group $Fm\bar 3m$ , Z = 4, and ρ_calcd = 3.88 g/cm³. The hypothesis that Rb elpasolite exists in nature in late associations of pegmatites enriched in rubidium is proposed.     

Synthesis, crystal structure and DFT studies of N-(4-acetyl-5,5-dimethyl-4,5-dihydro-1,3,4-thiadiazol-2-yl)acetamide

The title compound N-(4-acetyl-5,5-dimethyl-4,5-dihydro-1,3,4-thiadiazol-2-yl)acetamide (III) was obtained from the reaction of 2-(propan-2-ylidene)hydrazinecarbothioamide (II) with acetic anhydride instead of formation of the desired thiosemcarbazide derivative of Meldrum acid. The structures of II and III were established by elemental analysis, IR, NMR, Mass and X-ray crystallographic studies. II crystallizes in triclinic system, sp. gr. $P - \bar 1$ Z = 2; III crystallizes in the monoclinic system, sp. gr. P2₁/c, Z = 8. Density functional theory (DFT) calculations have been carried out for III. ¹H and ¹³C NMR of III has been calculated and correlated with experimental results.