Domain structure in a nematic layer under oscillatory Couette flow

The formation of a spatially modulated structure (domains) in a homeotropically aligned layer of a nematic liquid crystal (NLC) under an oscillatory Couette flow are described theoretically by using the hydrodynamic equations for an NLC which are linearized with respect to perturbations. The shear frequencies at which the phenomenon is determined by the inertial properties of the medium are considered. It is shown that the domain size is equal to the thickness h of an NLC layer and that the dependence of the threshold value of the shear amplitude u _th on the frequency ω and the layer thickness h is described by the expression u _th = const/(ωh²). The calculated results are compared with the experimental data.     

Identification of nematic lymoesophases with discotic and cylindrical micelles in lyotropic amphiphilic systems

Nematic lyomesophases with discotic (N _D) and cylindrical (N _C) micelles in complex multicomponent lyotropic systems based on alkyltrimethylammonium bromide detergents have been identified by the ¹H-²H-, and ¹³C-NMR methods and polarizationoptical microscopy. The difference in the structures of the N _D and N _C nematic phases is especially pronounced in the ¹³C-NMR spectra. Addition of chiral dopants to the lyomixture facilitates formation of the Ch _D and Ch _C cholesteric phases. According to the ¹³C-NMR spectra, the micellar mobility in the cholesteric lyomesophases decreases in comparison with the nematic ones. The alignment of lyocholesterics under the action of an external magnetic field is found.     

Relationship between the temperature dependence of the induced helical pitch and the anisometry of molecules of chiral dopants

The regularities of changes in the temperature dependence of the helical pitch P and the parameter dP/dt are analyzed for induced cholesteric liquid-crystal systems based on nematic 4-pentyl-4′-cyanobiphenyl, including chiral arylidene derivatives of (S)-1-phenylethylamine and (1R),(4R)-isomenthone. In the molecules of these compounds, the length of the π-electron arylidene fragment, the nature of the bridge group between its benzene rings and of the lateral substitution in the cyclohexanone ring, and the length of the terminal alkyl or oxyalkyl substituent are varied. The statistical molecular anisometry of the chiral dopants is calculated using the density functional method and the semiempirical AM1 method. It is shown that the temperature dependence of the induced helical pitch and, correspondingly, its quantitative characteristic dP/dt and the parameter dt _t /dC, characterizing the effect of a chiral dopant on the thermal stability of the mesophase, are determined by the molecular anisometry of the chiral component.     

Gosset helicoids: I. 8D crystallographic lattice <Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript> and crystallographic,quasi-crystallographic,and fractional helicoidal axes determined by this lattice

It is shown that mapping of substructures of a semiregular Gosset polytope, whose 240 vertices form the first coordination sphere of a 8D lattice E ₈, determines the orders of p/d axes of helicoids that are set only by invariants of (sub)algebras. Axes of such (Gosset) helicoids are derived. These axes perform rotation by an angle (360°/p(d; can be crystallographic, quasi-crystallographic (p = 2, 3, 4, 5, 6, …; d = 1), or fractional (1 < d < p/2); and may belong to regular polytopes (conventional, starlike, etc.). Formation of ordered structures is considered as a formation of Gosset helicoids (rods) with their subsequent assembly. Helicoids with axes 15/4 and 15/7 are considered as examples. They correspond to crystallographic approximants—helicoids with axes 4₁ and 2₁ composed of deformed icosahedra (dodecahedra)—in a β-Mn crystal (clathrate IX).     

Structural characteristics of a new cation-deficient representative of the labuntsovite group

The crystal structure of a new representative of the labuntsovite group from the Khibiny massif (the Kola Peninsula) has been refined. The unit-cell parameters are a = 14.298(7) Å, b = 13.816(7) Å, c = 7.792(3) Å, β = 116.85(5)°, V = 1373.3 ų, sp. gr. C2/m, R^aniso = 0.047, 1084 reflections with F > 4σ (F). The mineral differs from lemmleinite-Ba and other members of the group by the predominance of the vacancies in two key cationic positions—C position is occupied by Ba cations (37%) and D position is occupied mainly by Mn cations (47%).     

Magnetoplastic effect: Basic properties and physical mechanisms

This paper presents a review of the main results of investigations into the magnetoplastic effect, which manifests itself in motion of dislocations in crystals exposed to magnetic fields. The dependences of the mean free path of dislocations on the induction and direction of the magnetic field, the magnetic treatment time, the temperature, and the type and concentration of impurities are studied for NaCl, LiF, CsI, Zn, Al, and InSb crystals. The threshold magnetic field B _c below which the effect is absent, the saturation field B₀ above which the mean free paths of dislocations remain constant with an increase in the magnetic induction B, and the critical frequency v _c of rotation of a sample in the magnetic field above which the effect disappears are examined. The quantities B _c , B₀, and v _c are investigated as functions of the basic physical parameters. It is found that the magnetoplastic effect is highly sensitive to X-ray radiation at low doses and to simultaneous action of an electric field or mechanical loading. The hardening of NaCl(Pb) crystals in the magnetic field is revealed. The theoretical interpretation is proposed for all the findings and dependences observed.     

Crystal structures of oxalate-bearing cancrinite with an unusual arrangement of CO<Subscript>3</Subscript> groups and sulfate-rich davyne

The crystal structures of two unusual varieties of cancrinite-group minerals—oxalate-bearing cancrinite from the Kovdor massif (Kola Peninsula) and the sulfate end member of the davyne series from the Sar-e Sang mine (Badakhshan, Afghanistan)—were studied by single-crystal X-ray diffraction. The unit-cell parameters of the hexagonal cells are a = 12.688(4) Å, c = 5.189(1) Å and a = 12.773(1) Å, c = 5.334(1) Å, sp. gr. P6₃; the R factors are 0.034 and 0.035, respectively. The presence of oxalate groups in cancrinite as admixtures is one of the factors responsible for the shift of CO₃ groups in wide channels.     

X-ray structure analysis of 4-cyano-4′-<Emphasis Type="Italic">n</Emphasis>-undecyloxybiphenyl

The structure of a liquid crystal of 4-cyano-4′-n-undecyloxybiphenyl (C₂₄H₃₁NO) is determined by X-ray diffraction. The compound crystallizes in the monoclinic crystal system (space group C2/c) with the unit cell parameters a = 84.108(7) Å, b = 7.159(2) Å, c = 6.922(2) Å, and β = 91.6(4)°. The structure has been solved by direct methods and refined to the residual index R₁ = 0.067. Both phenyl rings are almost planar, and the dihedral angle between these rings is 31.5(6)°.     

Viscous and elastic properties of the nematic in the tetrapalladium organyl-pentadecane system

Temperature dependences of the dielectric anisotropy ?_a, effective rotational viscosity \(\tilde \gamma \), and elastic modulus K ₁₁ of the nematic phase of the tetrapalladium organyl-pentadecane system containing 55 wt % pentadecane have been experimentally studied. The quantities ?_a, \(\tilde \gamma \), and K ₁₁ are shown to decrease: ?_a decreases by a factor of about 2.5; \(\tilde \gamma \), by almost two orders of magnitude; and K ₁₁, by more than an order of magnitude. It is found that an applied electric field induces growth of tetrapalladium organyl crystals at 6–9°C above the nematic-crystallosolvate phase transition temperature.     

Crystal structure of zinc(II) hydrated trinuclear complex with monoprotonated ethylenediaminetetraacetate anion(3−), [Zn<Subscript>3</Subscript>(H<Emphasis Type="Italic">Edta</Emphasis>)<Subscript>2</Subscript>(H<Subscript>2</Subscript>O)<Subscript>6</Subscript>]

The crystal structure of the [Zn₃(HEdta)₂(H₂O)₆] complex (I) is determined by X-ray diffraction analysis. The crystals are orthorhombic, a = 14.780 Å, b = 29.699 Å, c = 7.032 Å, Z = 4, and space group Pna2₁. The structural units of crystals I are trinuclear linear molecules, in which the peripheral atoms Zn(1) and Zn(2) each coordinate two N atoms and three O atoms of the HEdta ^3? ligand and the O(w) atom of the H₂O molecule, whereas the central Zn(3) atom coordinates four O(w) atoms of the H₂O molecules and two terminal O atoms of the two HEdta ^3? ligands. The HEdta ^3? ligand fulfills a hexadentate chelating—bridging function. The bond lengths are as follows: Zn-O(HEdta), 2.006(4)–2.123(4) Å; Zn-N, 2.214(6) and 2.128(5) Å; and Zn-O(w), 2.006(6)–2.225(5) Å. In structure I, there is a specific contact formed by hydrogen bonds, owing to which the distance between the central atoms of individual molecules appears to be shorter than that in covalently bonded complexes.     

Zinc oxide single crystals: Influence of temperature and orientation of crystals on their mechanical properties

Zinc oxide single crystals are grown hydrothermally and their microhardness is measured on different {hkil} faces in the temperature range from liquid nitrogen temperature to 900°C. The coefficient K_1C of fracture roughness and the surface energy γ of fracture are estimated. The (0001) plane of a positive monohedron is characterized by the maximum hardness and plasticity over the whole temperature range studied. The shape of indenter prints and dislocation rosettes on the planes of monohedra, hexagonal prisms, and the pyramid are studied. The indenter print on the basal plane has an isotropic shape, whereas on the planes of prisms and the pyramid the prints indicate the first-kind anisotropy of mechanical properties. The first-kind anisotropy coefficient k equal to H_max/H_min increases with an increase in the temperature for the \(\{ 10\bar 10\} , \{ 11\bar 20\} \), and \(\{ 10\bar 11\} \) planes. For the \(\{ 10\bar 10\} \) plane, the coefficient k varies from ～1.4 at room temperature to ～2 at 900°C.     

Crystal structure of a new representative of the cancrinite group with a 12-layer stacking sequence of tetrahedral rings

The crystal structure of a 12-layer tounkite-like mineral of the cancrinite group was determined for the first time by single-crystal X-ray diffraction analysis (the unit-cell parameters are a = 12.757 Å, c = 32.211 Å). The structure was refined in the space group P3 to R = 0.035 using 3834 reflections with | F| > 2σ(F). Si and Al atoms occupy tetrahedral framework positions in an ordered fashion. The average distances in the tetrahedra are 〈Si-O〉 = 1.611 Å and 〈Al-O〉 = 1.723 Å. The stacking sequence of the layers is described as CACACBCBCACB, where A, B, and C are six-membered rings arranged around the [2/3 1/3 z], [1/3 2/3 z], and [0 0 z] axes, respectively. In the structure of the mineral, the columns along the [0 0 z] axis are composed of cancrinite cages. The columns along the [2/3 1/3 z] and [1/3 2/3 z] axes contain alternating cancrinite, bystrite, and liottite cages.     

X-ray mapping in heterocyclic design: XV. Tricyclic heterocycles based on 2-oxo-2,5,6,7-tetrahydro-1<Emphasis Type="Italic">H</Emphasis>-cyclopenta[<Emphasis Type="Italic">b</Emphasis>]pyridine-3-carbonitrile

The structures of five compounds are studied using single-crystal X-ray diffraction: 2-oxo-2,5,6,7-tetrahydro-1H-cyclopenta[b]pyridine-3-carbonitrile [a = 15.641(8) Å, b = 9.373(5) Å, c = 7.387(4) Å, β = 92.91(5)°, Z = 4, space group P2₁/c]; 1-[2-(4-chlorophenyl)-2-oxoethyl]-2-oxo-2,5,6,7-tetrahydro-1H-cyclopenta[b]pyridine-3-carbonitrile [a = 4.728(4) Å, b = 28.035(11) Å, c = 11.184(3) Å, Z = 4, space group P2₁2₁2₁]; 2-[2-(4-chlorophenyl)-2-oxoethoxy]-6,7-dihydro-5H-cyclopenta[b]pyridine-3-carbonitrile [a = 10.1202(13) Å, b = 11.2484(18) Å, c = 13.4323(19) Å, β = 102.05(1)°, Z = 4, space group P2₁/c]; 2-(4-chlorophenyl)-3a, 6,7,8-tetrahydrocyclopenta[e][1.3]oxazolo[3.2-a]pyridine-4-carboxamide perchlorate [a = 7.702(2) Å, b = 9.599(3) Å, c = 23.798(5) Å, β = 93.44(2)°, Z = 4, space group P2₁/c]; and (3-amino-6,7-dihydro-5H-cyclopenta[b]furo[3.2-e]pyridin-2-yl)(4-chlorophenyl)methanone [a = 7.3273(2) Å, b = 13.390(3) Å, c = 28.792(8) Å, Z = 8, space group Pbca]. The structures are solved using direct methods and refined by the full-matrix least-squares procedure in the anisotropic approximation to R = 0.0580, 0.0724, 0.0469, 0.0477, and 0.0418, respectively.     

X-ray mapping in heterocyclic design: XII. X-ray diffraction study of 2-pyridones containing cycloalkane fragments annelated to the C(5)-C(6) bond

The structures of 4,6-dimethyl-1H-pyridin-2-one [a = 6.125(2) Å, b = 15.153(4) Å, and c = 14.477(4) Å, Z = 8, space group Pbca], the 2: 1: 1 complex of 4-methyl-1,5,6,7-tetrahydro-2H-cyclopenta[b]pyridin-2-one with phosphoric acid and methanol [a = 11.181(2) Å, b = 14.059(6) Å, c = 13.593(4) Å, β = 97.78(2)°, Z = 8, space group P2₁/n], 4-methyl-1,5,6,7,8,9-hexahydro-2H-cyclohepta[b]pyridin-2-one [a = 12.565(6) Å, b = 5.836(6) Å, c = 13.007(3) Å, β = 93.10(3)°, Z = 4, space group P2₁/n], and 4-methyl-5,6,7,8,9,10-hexahydrocycloocta[b]pyridin-2(1H)-one [a = 12.955(3) Å, b = 6.1595(15) Å, c = 13.038(3) Å, β = 95.50(2)°, Z = 4, space group P2₁/n] are determined by single-crystal X-ray diffraction. The structures are solved by direct methods and refined by the full-matrix least-squares procedure in the anisotropic approximation to R = 0.0755, 0.0644, 0.0754, and 0.0569, respectively. The structures of 4-methyl-1,5,6,7-tetrahydro-2H-cyclopenta[b]pyridin-2-one [a = 7.353(4) Å, b = 8.176(4) Å, c = 13.00(1) Å, β = 105.64(2)°, Z = 4, space group P2₁/c] and 2-oxo-1,2,5,6,7,8-hexahydroquinoline-3-carbonitrile [a = 5.9870(2) Å, b = 16.5280(5) Å, c = 9.6540(3) Å, β = 111.52(4)°, Z = 4, space group P2₁/c] are studied by the powder diffraction technique. The structures are solved using the grid search procedure and refined by the Rietveld method to R _wp = 0.108 and 0.058, R_exp = 0.032 and 0.027, R _p = 0.076 and 0.043, R _b = 0.123 and 0.077, and χ² = 7.9 and 3.64, respectively. In all the structures, hydrogen bonds involving the N, H, and O atoms of the pyridone fragment are formed.     

<Emphasis Type="Italic">P</Emphasis>-wave ray velocities and the inverse acoustic problem for anisotropic media

The specific features of the calculation of ray velocities of quasi-longitudinal waves in anisotropic media have been considered. A technique for calculating elastic constants using P-wave ray velocities measured in an ultrasonic experiment on spherical samples is presented. It is shown by an example of tabular data that elastic constants С₁₁, С₂₂, and С₃₃ and combinations of constants (С₁₂ + 2С₆₆), (С₁₃ + 2С₅₅), (С₂₃ + 2С₄₄), (С₁₄ + 2С₅₆), (С₂₅ + 2С₄₆), and (С₃₆ + 2С₄₅) can be calculated most accurately for the general case of anisotropic media with elastic properties of arbitrary symmetry. Since the determining system of equations is illconditioned, the values of elastic constants entering these combinations depend on the choosed initial approximation.     

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.     

Structural investigation of cooperite (PtS) crystals

The single-crystal structure of cooperite, a natural platinum sulfide PtS, is studied by X-ray diffraction supported by high-resolution scanning transmission electron microscopy and X-ray spectrum microanalysis. It is found that, in addition to the main reflections corresponding to the known tetragonal cell (a = 3.47 and c = 6.11 Å; space group P4₂/mmc), many weak reflections with intensities I ≤ 60σ(I) are clearly observed. These reflections fit the tetragonal cell (space group I4/mmm) with doubled parameters. In structures with small (P4₂/mmc) and large (I4/mmm) cells, the S atoms occupy statistically two special positions. It is shown that the chemical composition of the cooperite crystals deviates from the stoichiometric composition: sulfur-deficient specimens predominate.     

Crystal structure of <Emphasis Type="Italic">p</Emphasis>-carboxyphenylhydrazone benzoylacetone

The crystal structure of p-carboxyphenylhydrazone benzoylacetone is determined. The crystals are monoclinic, a = 13.614(4) Å, b = 11.388(2) Å, c = 20.029(6) Å, β = 104.82(2)°, V = 2339(9) ų, Z = 8, space group C2/c, and R = 0.038 for 1622 reflections with I > 2σ(I). The crystal is built of C₁₇H₁₄N₂O₄ neutral molecules that are linked by O-H?O hydrogen bonds between the carboxyl groups into centrosymmetric pseudodimers. The effect of carboxylation of the phenylhydrazone fragment and the position of the carboxyl group on the molecular packing in the crystal is determined. The N(1)-H(1N)?O(1) intramolecular hydrogen bond (N-H, 0.94 Å; H?O, 1.87 Å; N?O, 2.59 Å; and the N-H?O angle, 133°) is formed in the molecule.     

A necessary condition for the formation of a bisystem molecular crystal

A hypothesis is formulated which states that the necessary condition for the existence of a bisystem molecular crystal is the approximate equality of the total energies of the interactions of two symmetrically independent molecules N and N′ with their environment in the crystal structure (U_Σ). The hypothesis was tested on four crystalline organic compounds of the structure class P2₁/c, Z = 8(1, 1). The computations in the atom-atom approximation demonstrated that the energies U_Σ(N) and U_Σ(N′) have very close values despite the different coordination numbers of the molecules and a difference in the structures of the molecular agglomerates that include the molecules N and N′.     

X-ray crystallography of cholest-3,5-diene-7-one

The molecular structure of cholest-3,5-diene-7-one (C₂₇H₄₂O) is determined by X-ray diffraction. The compound crystallizes in the orthorhombic crystal system (space group P2₁2₁2₁) with unit cell parameters a = 11.281(5) Å, b = 11.350(5) Å, c= 18.518(5) Å, and Z = 4. The structure is solved by direct methods and refined to an R-value of 0.054 for 1070 observed reflections [F_o > 4σ(F_o)]. Ring A adopts a distorted half-chair conformation, ring B exists in sofa conformation, ring C acquires a chair conformation, and the five-membered ring D occurs in distorted half-chair conformation. The crystal structure is stabilized by van der Waals forces.