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Common Vertex (common + vertex)

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Chemistry66%

Selected Abstracts

The stability of stars of triangular equilibrium plate elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009
E. A. W. Maunder
Abstract Equilibrium models for finite element analyses are becoming increasingly important in complementary roles to those from conventional conforming models, but when formulating equilibrium models questions of stability, or admissibility of loads, are of major concern. This paper addresses these questions in the context of flat plates modelled with triangular hybrid elements involving membrane and/or flexural actions. Patches of elements that share a common vertex are considered, and such patches are termed stars. Stars may be used in global analyses as assemblies of elements forming macro-elements, or in local analyses. The conditions for stability, or the existence and number of spurious kinematic modes, are determined in a general algebraic procedure for any degree of the interpolation polynomials and for any geometric configuration. The procedure involves the determination of the rank of a compatibility matrix by its transformation to row echelon form. Examples are presented to illustrate some of the characteristics of spurious kinematic modes when they exist in stars with open or closed links. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Automatic construction of non-obtuse boundary and/or interface Delaunay triangulations for control volume methods

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2002
Nancy Hitschfeld
Abstract A Delaunay mesh without triangles having obtuse angles opposite to boundary and interface edges (obtuse boundary/interface triangles) is the basic requirement for problems solved using the control volume method. In this paper we discuss postprocess algorithms that allow the elimination of obtuse boundary/interface triangles of any constrained Delaunay triangulation with minimum angle ,. This is performed by the Delaunay insertion of a finite number of boundary and/or interface points. Techniques for the elimination of two kinds of obtuse boundary/interface triangles are discussed in detail: 1-edge obtuse triangles, which have a boundary/interface (constrained) longest edge; and 2-edge obtuse triangles, which have both their longest and second longest edge over the boundary/interface. More complex patterns of obtuse boundary/interface triangles, namely chains of 2-edge constrained triangles forming a saw diagram and clusters of triangles that have constrained edges sharing a common vertex are managed by using a generalization of the above techniques. Examples of the use of these techniques for semiconductor device applications and a discussion on their generalization to 3-dimensions (3D) are also included. Copyright © 2002 John Wiley & Sons, Ltd. [source]

In1.06Ho0.94Ge2O7: a thortveitite-type compound

ACTA CRYSTALLOGRAPHICA SECTION C, Issue 2 2004
Erick A. Juarez-Arellano
A new indium holmium digermanate, In1.06Ho0.94Ge2O7, with a thortveitite-type structure, has been prepared as a polycrystalline powder material by high-temperature solid-state reaction. This new compound crystallizes in the monoclinic system (space group C2/c, No. 15). The structure was characterized by Rietveld refinement of powder laboratory X-ray diffraction data. The In3+ and Ho3+ cations occupy the same octahedral site, forming a hexagonal arrangement on the ab plane. In their turn, the hexagonal arrangements of (In/Ho)O6 octahedral layers are held together by sheets of isolated diortho groups comprised of double tetrahedra sharing a common vertex. In this compound, the Ge2O7 diortho groups lose the ideal D3d point symmetry and also the C2h point symmetry present in the thortveitite diortho groups. The Ge,O,Ge angle bridging the diortho groups is 160.2,(3)°, compared with 180.0° for Si,O,Si in thortveitite (Sc2Si2O7). The characteristic mirror plane in the thortveitite space group (C2/m, No. 12) is not present in this new thortveitite-type compound and the diortho groups lose the C2h point symmetry, reducing to C2. [source]

In1.08Gd0.92Ge2O7: a new member of the thortveitite family

ACTA CRYSTALLOGRAPHICA SECTION C, Issue 10 2002
Erick-Adrian Juarez-Arellano
Indium gadolinium digermanium heptaoxide, In1.08Gd0.92Ge2­O7, with a thortveitite-type structure, has been prepared as a polycrystalline powder material by a high-temperature solid-state reaction. As in the mineral thortveitite, the crystal structure belongs to the monoclinic system, with space group C2/m (No. 12). The precise structural parameters were obtained by applying the Rietveld method of refinement to the X-ray powder diffraction data. This layered structure presents, on one side, a honeycomb-like arrangement of the unique octahedral site, which is occupied randomly by In and Gd atoms, and, on the other side, sheets of isolated Ge2O7 diortho-groups made up of double tetrahedra sharing a common vertex and displaying C2h point symmetry. This compound showed a remarkable photoluminescence effect when it was irradiated with the X-ray beam during the X-ray diffraction measurements, and with the , beam during the Rutherford back-scattering spectrometry experiments employed to analyze the chemical stoichiometry. [source]

Bis­(tetra­methyl­ammonium) hexa­molyb­date hydrate, [(CH3)4N]2[Mo6O19]·H2O

ACTA CRYSTALLOGRAPHICA SECTION C, Issue 7 2000
Neven Strukan
The crystal and molecular structure of the title compound, (C4H12N)2[Mo6O19]·H2O, has been determined from X-ray diffraction data. The poly­oxo­anion [Mo6O19]2, is built up from six distorted MoO6 octa­hedra sharing common edges and one common vertex at the central O atom, and has crystallographic m3m (Oh) symmetry. The cation has crystallographic 3m symmetry. [source]

Zn[BPO4(OH)2]: A Zinc Borophosphate with the Rare Moganite-Type Topology

CHEMISTRY - A EUROPEAN JOURNAL, Issue 6 2008
Ya-Xi Huang Dr.
Abstract A novel zinc borophosphate Zn[BPO4(OH)2] with moganite-type topology (a rare polymorph of silica) has been prepared from a mixture of ZnO, B2O3, and P2O5 by hydrothermal treatment at 443,K. The crystal structure was determined from single-crystal X-ray data (orthorhombic, Pbcn (no. 60), a=915.07(3), b=897.22(3), c=1059.19(3),pm, V=869.62(5)×106,pm3, Z=8, R1=0.028, wR2=0.075). The crystal structure comprises unbranched vierer -single borophosphate chains running along [010] and interconnected via ZnO2(OH)2 -tetrahedra by sharing common vertices. The resulting topology of the three-dimensional tetrahedral framework structure is described by the Schläfli symbol (42.62.82)(4.64.8)2. Although showing Zn in a tetrahedral coordination, the title compound does not belong to the group of zincoborophosphates but is a special case of a borophosphate containing vierer single rings of tetrahedra with the sequence Zn-B-Zn-P. [source]