Search results for "Point group"
showing 10 items of 18 documents
Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$
2006
Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles
2014
Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodic…
Commensurability classification of a family of right-angled Coxeter groups
2008
We classify the members of an infinite family of right-angled Coxeter groups up to abstract commensurability.
Lattice dynamics of the fluoride scheelite CaZnF4
2000
The lattice dynamics of the fluoride scheelite CaZnF4 have been investigated by means of infrared reflectivity and Raman scattering. The measured phonon modes have been assigned to the various irreducible representations of the point group of the crystal. The phonon dispersion curves, density of states and sound velocities have been calculated within a rigid-ion model based on experimental zone-centre phonons.
Decacyclene as complexation manifold: synthesis, structure and properties of its Fe2 and Fe4 slipped triple-decker complexes.
2006
Reaction of [(eta(5)-Me4EtC5)Fe(II)Cl(tmeda)] (tmeda = N,N,N'N'-tetramethylethylenediamine) with a polyanion solution of decacyclene (1) results in the formation of the triple-deckers [{(eta(5)-Me4EtC5)Fe}2-mu2-(eta(6):eta(6)-decacyclene)] (3) and [{(eta(5)-Me4EtC5)Fe}4-mu4-(eta(6):eta(6):eta(6):eta(6)-decacyclene)] (4). Metal complexation in 3 and 4 occurs on opposite faces of the pi perimeter in an alternating mode. The decacyclene ring adopts a gently twisted molecular propeller geometry with twofold crystallographic symmetry (C2). Complex 4 crystallizes in the chiral space group C222(1); the investigated crystal only contains decacyclene rings with M chirality. The handedness can be ass…
Symmetry and Stability of the Rutile-Based TiO2 Nanowires: Models and Comparative LCAO-Plane Wave DFT Calculations
2012
The rod symmetry groups for monoperiodic (1D) nanostructures have been applied for construction of models for bulk-like titania nanowires (NWs) cut from a rutile-based 3D crystal along the direction of a chosen crystallographic symmetry axis (in this study we consider only Ti atom-centered axes). The most stable [001]-oriented TiO2 NWs with rhombic cross sections are found to display the energetically preferable {110} facets only, while the nanowires with quasi-square sections across the [110] axis are formed by the alternating {110} and {001} facets. For simulations on rutile-based nanowires possessing four different diameters for each NW type, we have performed comparative large-scale ab …
Morphotropic ceramic solid solutions of the Pb(B3+½Nb½)O3- PbTiO3binary system
2000
Abstract The structure, dielectric, ferroelectric and electromechanical properties of lead lutecium niobate-titanate (PLuNT) and lead erbium niobate-titanate (PErNT) binary systems are reported. The data of phase diagram, crystallographic symmetry and morphotropic phase boundaries (MPB) are provided. High values of the electromechanical coupling coefficients kp = 0.66, kt = 0.48, k31 = 0.36 of (1−x)PLuN − xPT ceramics are attained in compositions near the MPB at x≈0.41.
Extension of the MIRS computer package for the modeling of molecular spectra : from effective to full ab initio ro-vibrational hamiltonians in irredu…
2012
The MIRS software for the modeling of ro-vibrational spectra of polyatomic molecules was considerably extended and improved. The original version (Nikitin, et al. JQSRT, 2003, pp. 239--249) was especially designed for separate or simultaneous treatments of complex band systems of polyatomic molecules. It was set up in the frame of effective polyad models by using algorithms based on advanced group theory algebra to take full account of symmetry properties. It has been successfully used for predictions and data fitting (positions and intensities) of numerous spectra of symmetric and spherical top molecules within the vibration extrapolation scheme. The new version offers more advanced possib…
Temperature-dependent polymorphism of N-(4-fluorophenyl)-1,5-dimethyl-1H-imidazole-4-carboxamide 3-oxide: experimental and theoretical studies on int…
2014
X-ray analysis of N-(4-fluorophenyl)-1,5-dimethyl-1H-imidazole-4-carboxamide 3-oxide reveals the temperature-dependent polymorphism associated with the crystallographic symmetry conversion. The observed crystal structure transformation corresponds to a symmetry reduction from I41 /a (I) to P43 (II) space groups. The phase transition mainly concerns the subtle but clearly noticeable reorganization of molecules in the crystal space, with the structure of individual molecules left almost unchanged. The Hirshfeld surface analysis shows that various intermolecular contacts play an important role in the crystal packing, revealing graphically the differences in spatial arrangements of the molecule…
Structure and Physical Properties of Na1/2Bi1/2TiO3-CdTiO3Solid Solutions
2011
Behaviour of ferroelectric properties in Na1/2Bi1/2TiO3-CdTiO3 solid solutions correlates with dependence of lattice symmetry versus concentration of constituents. However, some overlapping is observed in concentration range close to the morphotropic phase boundary. The properties of dielectric permittivity, characteristic for relaxor ferroelectrics, diminish, if concentration of CdTiO3 increases, but it is not influenced by the change of crystallographic symmetry. The electromechanical properties are mostly pronounced in the range of cubic-tetragonal morphotropic phase boundary.