Theoretical crystal chemistry of M x (TO4)y sulfates and selenates: Topological analysis and classification of suprapolyhedral invariants

A geometric topological analysis of orthotetrahedral phases M _x (TO₄)_y (T = S or Se) is performed for 46 sulfates and 17 selenates with the TOPOS 3.2 software package. The values of coordination sequences {N _k } of T atoms are used as classification parameters of topologically different MTO nets. The crystal structures are analyzed within 12 coordination spheres of T sites and assigned to 26 topological types. It is established that only 7 types are common for the structures of sulfates and selenates, 16 types include only sulfates, and 3 types include only selenates. The average values of the bond lengths are determined: 〈R(S-O)〉 = 1.48(2) Å and 〈R(Se-O)〉 = 1.63(2) Å. The hierarchical ordering of the crystal structure is performed using the concept of a polyhedral microensemble of the structure.     

Basis functions of the backprojection operator

The problem of reconstruction of an unknown object by backprojection in a space of arbitrary dimension p ≥ 2 is considered. Expressions are obtained to solve the problem in the form of series in multidimensional spherical harmonics. Bases of functions applicable to the expansion of radial components of the series in spherical harmonics are found.     

The Differential Constraints Method: Application to Analysis of the Shearless Turbulence Mixing Layer. Stable and Unstable Stratifications

In this article we study dynamics of the shearless stratified turbulence flows. Using the method of differential constraints we find a class of explicit solutions to the problem and establish that the obtained differential constraint coincides with the well‐known Zeman‐Lumley model for stratified flows (see [1]).     

Crystal chemistry of germanates: Characteristic structural features of Li,Ge-germanates

Crystallochemical classification of eleven compounds from the Li-germanate family is suggested. Depending on the set of the primary building units (PBU) (M-octahedra of the composition [GeO₆] and T-tetrahedra of the composition [GeO₄]) and the type of their “condensation,” these germanates are divided into three crystallochemical groups: framework MT-structures (four phases), condensed MT-structures (two phases), and tetrahedral T-condensed structures (five phases). The structural characteristics of the framework Li,Ge-germanates are considered, i.e., their symmetry, crystallographically independent sets of the primary building units, framework architecture, and the types of chains and layers of the (Ge,O)-radicals.     

Numerical simulation of axisymmetric turbulent jets

The flow in axisymmetric turbulent jets is numerically simulated with the use of a semi-empirical second-order turbulence model including differential transport equations for the normal Reynolds stresses. Calculated results are demonstrated to agree with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 55–60, September–October, 2008.     

Complex Energetic Perchlorates of Cobalt(III) Amminates,with Cyclopentamethylenetetrazole as Ligand

Energetic metal complexes, pentammine(cyclopentamethylenetetrazole)cobalt(III) perchlorate and tetraammine-bis(cyclopentamethylenetetrazole)cobalt(III) perchlorate, were obtained by reaction of aquapentaamminecobalt(III) and diaquatetraamminecobalt(III) ions with cyclopentamethylenetetrazole. Microwave heating was used, together with the conventional convective heating, for thermal activation of the process. The thermal decomposition of the compounds synthesized was studied. The explosive characteristics and toxicity of the metal complexes were determined.__________Translated from Zhurnal Prikladnoi Khimii, Vol. 78, No. 2, 2005, pp. 195–199.Original Russian Text Copyright © 2005 by Zhilin, Ilyushin, Tselinskii, Nikitina, Kozlov, Shugalei.     

Millimeter-Wave Spectrum of CF(2)Cl(2), Taking into Account the Hyperfine Structure

A new investigation of the CF(2)(35)Cl(2) ground state rotational spectrum in the 50-100 GHz frequency range gave an opportunity to improve the accuracy of rotational and quartic distortion parameters by an order of magnitude and to determine values of six sextic centrifugal distortion parameters. A special technique was used to process line profiles of unresolved or partially resolved hyperfine structures of rotational transitions. It allowed us to improve significantly values for the diagonal parameters of quadrupole coupling chi(aa), (chi(bb)-chi(cc)) and to determine the off-diagonal parameter chi(ab). Copyright 2000 Academic Press.     

Cluster self-organization of germanate systems: Suprapolyhedral precursor nanoclusters and self-assembly of CAN-Na8(Al6Ge6O24)Ge(OH)6(H2O)2 and CAN-Cs2Na6(Al6Ge6O24)Ge(OH)6) zeolite crystal structures re]20100419

Geometrical and topological analysis of zeolite crystal structures having a tetrahedral framework of the cancrinite (CAN) type, namely, (CAN) Na₈(Al₆Ge₆O₂₄)Ge(OH)₆(H₂O)₂ (acentric space group P6₃, hP64, Na-CAN) and Cs₂Na₆(Al₆Ge₆O₂₄)Ge(OH)₆ (P6₃, hP52, CsNa-CAN), is carried out with the use of computer techniques (the TOPOS 4.0 program package). An AT ₆ hexapolyhedral precursor nanocluster centered with a template cation A (Na, Cs) is identified. The topological type of a two-dimensional (2D) crystalforming T-net 4.6.12, which corresponds to a uninodal semiregular Shubnikov net, is recognized. The full 3D reconstruction of crystal structure self-assembly is performed as follows: precursor nanocluster → primary chain → microlayer → microframework → … framework. The symmetry of an AT6 precursor nanocluster is described by point group 3; the symmetry axis passes through the center of the nanocluster and cation A. The coordination number (CN) of a precursor nanocluster, which characterizes the nanocluster stacking in the macrostructure, is six. In both structures, six Na atoms and a Ge(OH)₆ polyhedral species are spacers filling the voids between AT ₆ precursor nanoclusters. The Ge(OH)₆ polyhedral species is characterized by four and two orientationally allowed positions in Na-CAN and CsNa-CAN, respectively. The minimal number of suprapolyhedral AT ₆ precursor nanoclusters required for the 3D microframework to form is 16; that is, 96 tetrahedra are involved in microframework self-assembly.     

Geometrical and topological model of formation, selection, and evolution of precursor nanoclusters in the convergent matrix self-assembly mechanism of crystal formation

Combinatorial-topological analysis algorithms have been developed to reconstruct the code of convergent matrix self-assembly in the form of a sequence of significant elementary events e _i proceeding from structure data in a crystal-forming system that contains diverse structural units (atoms, molecules, and polyheral clusters). Mechanisms of selection of suprastructural units with maximal values of their connectivity indices to form chains from precursor clusters are considered. Two special cluster formation mechanisms are recognized. One is a linear mechanism where the number of particles is constantly increasing. The other is a discrete mechanism with an obligatory transiton of the evolving system to the matrix (complementary) selfassembly mode. Structure self-assembly follows the principle of the maximal filling of the crystal space and, accordingly, obeys the requirement for the maximal degree of complementary connectivity of precursor nanoclusters at all evolution steps. The model developed in this way has been used to interpret the formation and structural-topology specifics of carbon allotropes (fullerenes C60 and C70) and polymorphs of metals, H₂O (ice), silica, hydrido- and chlorosiloxanes, MEP clathrate family, some aluminosilicates (feldspar and zeolites), and C₂₀₄H₇₅₆Cl₃₆Mn₈₄O₄₆₂ (V = 20992 ?).