Indexing approximants of icosahedral quasicrystals

1999 ◽  
Vol 55 (6) ◽  
pp. 975-983 ◽  
Author(s):  
M. Quiquandon ◽  
A. Katz ◽  
F. Puyraimond ◽  
D. Gratias
Keyword(s):  
Unit Cell ◽  
Dimensional Lattice ◽  
Geometrical Properties ◽  
Actual Model ◽  
Icosahedral Quasicrystals ◽  
Low Dimensional

It is well known that the crystallography of approximants is directly related to that of the parent quasicrystal, once its unit-cell vectors are identified as parallel projections of certain N-dimensional lattice nodes {\bf A}^{i}. Derived here are explicit simple relations for calculating the shear matrices {\boldvarepsilon} and the related crystallographic properties of the corresponding approximants, including diffraction indexing and the determination of the lattice in perpendicular space. Applied to low-dimensional approximants, the derivation shows that the systematic `accidental' extinction rules observed in the pentagonal phases are generic extinctions that are due to the geometrical properties of the projected 1D lattice and are independent of the actual model of the quasicrystal.

Determination of the structure of bis(propyldithiocarbamate)nickel(II)

1990 ◽  
Vol 55 (4) ◽  
pp. 1010-1014 ◽  
Author(s):  
Jiří Kameníček ◽  
Richard Pastorek ◽  
František Březina ◽  
Bohumil Kratochvíl ◽  
Zdeněk Trávníček
Keyword(s):  
Molecular Structure ◽  
Title Compound ◽  
Crystal And Molecular Structure ◽  
Heavy Atom ◽  
Unit Cell ◽  
Monoclinic Space Group ◽  
Planar Configuration ◽  
Compound C ◽  
Heavy Atom Method

The crystal and molecular structure of the title compound (C8H16N2NiS4) was solved by the heavy atom method and the structure was refined anisotropically to a final R factor of R = 0.029 (wR = 0.037) for 715 observed reflections. The crystal is monoclinic, space group P21/c with a = 948.3(2), b = 776.9(2), c = 1 167.4(2) pm, β = 125.14(2)°, Z = 2. The molecule contains two four-membered NiSCS rings of approximately planar configuration with the Ni atom situated at a centre of symmetry. The molecules are arranged in chains along the c-axis of the unit cell.

Unit cell constants of zeolites stabilized by dealumination determination of Al content from lattice parameters

1984 ◽  
Vol 19 (1) ◽  
pp. K1-K3 ◽  
Author(s):  
H. Fichtner-Schmittler ◽  
U. Lohse ◽  
G. Engelhardt ◽  
V. Patzelová
Keyword(s):  
Unit Cell ◽  
Lattice Parameters ◽  
Al Content

Low-dimensional lattices. VI. Voronoi reduction of three-dimensional lattices

1992 ◽  
Vol 436 (1896) ◽  
pp. 55-68 ◽  
Keyword(s):  
Simple Formula ◽  
Three Dimensional ◽  
Voronoi Cell ◽  
Dimensional Lattice ◽  
Usual Treatment ◽  
Low Dimensional

The aim of this paper is to describe how the Voronoi cell of a lattice changes as that lattice is continuously varied. The usual treatment is simplified by the introduction of new parameters called the vonorms and conorms of the lattice. The present paper deals with dimensions n ≼ 3; a sequel will treat four-dimensional lattices. An elegant algorithm is given for the Voronoi reduction of a three-dimensional lattice, leading to a new proof of Voronoi’s theorem that every lattice of dimension n ≼ 3 is of the first kind, and of Fedorov’s classification of the three-dimensional lattices into five types. There is a very simple formula for the determinant of a three-dimensional lattice in terms of its conorms.

scholarly journals Combining solution wide-angle X-ray scattering and crystallography: determination of molecular envelope and heavy-atom sites

2009 ◽  
Vol 42 (2) ◽  
pp. 259-264 ◽  
Author(s):  
Xinguo Hong ◽  
Quan Hao
Keyword(s):  
Structure Determination ◽  
Heavy Atom ◽  
Unit Cell ◽  
Wide Angle ◽  
X Ray ◽  
X Ray Scattering ◽  
Molecular Envelope ◽  
Waxs Data ◽  
Ray Scattering

Solving the phase problem remains central to crystallographic structure determination. A six-dimensional search method of molecular replacement (FSEARCH) can be used to locate a low-resolution molecular envelope determined from small-angle X-ray scattering (SAXS) within the crystallographic unit cell. This method has now been applied using the higher-resolution envelope provided by combining SAXS and WAXS (wide-angle X-ray scattering) data. The method was tested on horse hemoglobin, using the most probable model selected from a set of a dozen bead models constructed from SAXS/WAXS data using the programGASBORat 5 Å resolution (qmax= 1.25 Å−1) to phase a set of single-crystal diffraction data. It was found that inclusion of WAXS data is essential for correctly locating the molecular envelope in the crystal unit cell, as well as for locating heavy-atom sites. An anomalous difference map was calculated using phases out to 8 Å resolution from the correctly positioned envelope; four distinct peaks at the 3.2σ level were identified, which agree well with the four iron sites of the known structure (Protein Data Bank code 1ns9). In contrast, no peaks could be found close to the iron sites if the molecular envelope was constructed using the data from SAXS alone (qmax= 0.25 Å−1). The initial phases can be used as a starting point for a variety of phase-extension techniques, successful application of which will result in complete phasing of a crystallographic data set and determination of the internal structure of a macromolecule to atomic resolution. It is anticipated that the combination ofFSEARCHand WAXS techniques will facilitate the initial structure determination of proteins and provide a good foundation for further structure refinement.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

Über neue monocyclische Acyloxyfluoroborane 2.2.6.6-Tetrafluoro-1.4-dialkyl-1.3.5-trioxa-1.6-diboracyclohexene: Darstellung, Molekül- und Kristallstruktur/ New Monocyclic Acyloxyfluoroboranes 2,2,6,6-Tetrafluoro-1,4-dialkyl-1,3,5-trioxa-2,6-diboracyclohexenes: Synthesis, Molecular and Crystal Structure

1983 ◽  
Vol 38 (5) ◽  
pp. 554-558 ◽  
Author(s):  
Herbert Binder ◽  
Walter Matheis ◽  
Hans-Jörg Deiseroth ◽  
Han Fu-Son
Keyword(s):  
Crystal Structure ◽  
Organic Acid ◽  
Structure Determination ◽  
Unit Cell ◽  
Ring Conformation ◽  
X Ray ◽  
Conformational Isomers ◽  
Ring Group ◽  
Acid Anhydrides

Abstract Acyloxyfluoroboranes Trimeric alkoxydifluoroboranes (F2BOR)3 (2) react with organic acid anhydrides by substitution of a ring group OR forming monocyclic acyloxyfluoroboranes of the type 2,2,6,6-tetrafluoro-l,4-dialkyl-l,3,5-trioxa-2,6-diboracyclohexene (3). The X-ray crystal structure determination of 3a shows two conformational isomers: two planar and two non-planar six-membered rings are present in the unit cell. The ring conformation is influenced by weak intermolecular H — F interactions.

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