scholarly journals TakeTwo: an indexing algorithm suited to still images with known crystal parameters

2016 ◽  
Vol 72 (8) ◽  
pp. 956-965 ◽  
Author(s):  
Helen Mary Ginn ◽  
Philip Roedig ◽  
Anling Kuo ◽  
Gwyndaf Evans ◽  
Nicholas K. Sauter ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Image Data ◽  
Group Efficacy ◽  
Still Images ◽  
Still Image ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Ewald Sphere ◽  
Unit Cell Dimensions

The indexing methods currently used for serial femtosecond crystallography were originally developed for experiments in which crystals are rotated in the X-ray beam, providing significant three-dimensional information. On the other hand, shots from both X-ray free-electron lasers and serial synchrotron crystallography experiments are still images, in which the few three-dimensional data available arise only from the curvature of the Ewald sphere. Traditional synchrotron crystallography methods are thus less well suited to still image data processing. Here, a new indexing method is presented with the aim of maximizing information use from a still image given the known unit-cell dimensions and space group. Efficacy for cubic, hexagonal and orthorhombic space groups is shown, and for those showing some evidence of diffraction the indexing rate ranged from 90% (hexagonal space group) to 151% (cubic space group). Here, the indexing rate refers to the number of lattices indexed per image.

Synthesis and crystal structure of Na3.5Cr1.5Co0.5(PO4)3 phosphate

2006 ◽  
Vol 21 (3) ◽  
pp. 210-213 ◽  
Author(s):  
Mohamed Chakir ◽  
Abdelaziz El Jazouli ◽  
Jean-Pierre Chaminade
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Synthesis And Crystal Structure ◽  
Space Group ◽  
X Ray ◽  
Hexagonal Unit Cell ◽  
Cell Dimensions ◽  
Unit Cell Dimensions

A new Nasicon phosphates series [Na3+xCr2−xCox(PO4)3(0⩽x⩽1)] was synthesized by a coprecipitation method and structurally characterized by powder X-ray diffraction. The selected compound Na3.5Cr1.5Co0.5(PO4)3 (x=0.5) crystallizes in the R3c space group with the following hexagonal unit-cell dimensions: ah=8.7285(3) Å, ch=21.580(2) Å, V=1423.8(1) Å3, and Z=6. This three-dimensional framework is built of PO4 tetrahedra and Cr∕CoO6 octahedra sharing corners. Na atoms occupy totally M(1) sites and partially M(2) sites.

Intergrowth polytypoids as modulated structures: a superspace description of the Sr n (Nb,Ti) n O3n + 2 compound series

2001 ◽  
Vol 57 (4) ◽  
pp. 471-484 ◽  
Author(s):  
L. Elcoro ◽  
J. M. Perez-Mato ◽  
R. L. Withers
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Separation Distance ◽  
Space Group ◽  
Space Groups ◽  
Cell Parameters ◽  
Average Structure ◽  
Layer Stacking ◽  
Compound Series ◽  
Three Dimensional Space

A new, unified superspace approach to the structural characterization of the perovskite-related Sr n (Nb,Ti) n O3n + 2 compound series, strontium niobium/titanium oxide, is presented. To a first approximation, the structure of any member of this compound series can be described in terms of the stacking of (110)-bounded perovskite slabs, the number of atomic layers in a single perovskite slab varying systematically with composition. The various composition-dependent layer-stacking sequences can be interpreted in terms of the structural modulation of a common underlying average structure. The average interlayer separation distance is directly related to the average structure periodicity along the layer stacking direction, while an inherent modulation thereof is produced by the presence of different types of layers (particularly vacant layers) along this stacking direction. The fundamental atomic modulation is therefore occupational and can be described by means of crenel (step-like) functions which define occupational atomic domains in the superspace, similarly to what occurs for quasicrystals. While in a standard crystallographic approach, one must describe each structure (in particular the space group and cell parameters) separately for each composition, the proposed superspace model is essentially common to the whole compound series. The superspace symmetry group is unique, while the primary modulation wavevector and the width of some occupation domains vary linearly with composition. For each rational composition, the corresponding conventional three-dimensional space group can be derived from the common superspace group. The resultant possible three-dimensional space groups are in agreement with all the symmetries reported for members of the series. The symmetry-breaking phase transitions with temperature observed in many compounds can be explained in terms of a change in superspace group, again in common for the whole compound series. Inclusion of the incommensurate phases, present in many compounds of the series, lifts the analysis into a five-dimensional superspace. The various four-dimensional superspace groups reported for this incommensurate phase at different compositions are shown to be predictable from a proposed five-dimensional superspace group apparently common to the whole compound series. A comparison with the scarce number of refined structures in this system and the homologous (Nb,Ca)6Ti6O20 compound demonstrates the suitability of the proposed formalism.

Die Röntgenstrukturanalyse von (CO)9Co3CΟΒΒr2Ν(C5)3. X-ray Structure Analysis of (CO)9Co3COBBr2N(C2H5)3

1976 ◽  
Vol 31 (3) ◽  
pp. 342-344 ◽  
Author(s):  
Volker Bätzel
Keyword(s):  
Least Squares ◽  
Structure Analysis ◽  
Reliability Index ◽  
Three Dimensional ◽  
Diagonal Matrix ◽  
Crystal Data ◽  
Block Diagonal Matrix ◽  
Fourier Methods ◽  
Space Group ◽  
X Ray

Using three dimensional X-ray data collected on a four circle diffractometer, the structure of (CO)9Co3COBBr2N(C2H5)3 was solved by Patterson and Fourier methods. Least squares refinement with a block-diagonal matrix leads to a reliability index of R = 10.7%. Crystal data: α = 13.277(6) Å, b = 10.17(1) Å, c = 9.22(2) Å; α = 91.12(6)°, β = 87.61(4)°, γ = 98.79(2)°; space group P1̅; Z = 2; V = 1229,7 Å3; Dx = 1.97 gcm-3.

Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces

2017 ◽  
Vol 73 (5) ◽  
pp. 387-402 ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Sajdeh Sajjadi ◽  
Bernard Shiffman ◽  
Steven M. Zucker
Keyword(s):  
General Theory ◽  
Rigid Body ◽  
Three Dimensional ◽  
Molecular Replacement ◽  
Translation Group ◽  
Common Occurrence ◽  
Space Group ◽  
Space Groups ◽  
Relevant Case ◽  
The Subject

In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.

Crystal data and X-ray powder diffraction data of 2,4-diiodo-4-nitrophenol (disophenol), C6H3I2NO3. More precise X-ray powder diffraction data of p-nitrophenol, C6H5NO3

1996 ◽  
Vol 11 (4) ◽  
pp. 301-304
Author(s):  
Héctor Novoa de Armas ◽  
Rolando González Hernández ◽  
José Antonio Henao Martínez ◽  
Ramón Poméz Hernández
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Unit Cell ◽  
Crystal Data ◽  
Powder Diffraction Data ◽  
Space Group ◽  
X Ray ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Monoclinic Cell

p-nitrophenol, C6H5NO3, and disophenol, C6H3I2NO3, have been investigated by means of X-ray powder diffraction. The unit cell dimensions were determined from diffractometer methods, using monochromatic CuKα1 radiation, and evaluated by indexing programs. The monoclinic cell found for p-nitrophenol was a=6.159(2) Å, b=8.890(2) Å, c=11.770(2) Å, β=103.04(2)°, Z=4, space group P21 or P2l/m, Dx=1.469 Mg/m3. The monoclinic cell found for disophenol has the dimensions a=8.886(1) Å, b=14.088(2) Å, c=8.521(1) Å, β=91.11(1)°, Z=4, space group P2, P2, Pm or P2/m, Dx=2.438 Mg/m3.

Powder X-Ray Diffraction Data for Ca2Bi2O5and C4Bi6O13

1992 ◽  
Vol 7 (2) ◽  
pp. 109-111 ◽  
Author(s):  
C.J. Rawn ◽  
R.S. Roth ◽  
H.F. McMurdie
Keyword(s):  
Powder Diffraction ◽  
Diffraction Data ◽  
Neutron Powder Diffraction ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Cell Dimensions ◽  
Powder Samples ◽  
Orthorhombic Cell ◽  
Unit Cell Dimensions

AbstractSingle crystals and powder samples of Ca2Bi5O5and Ca4Bi6O13have been synthesized and studied using single crystal X-ray diffraction as well as X-ray and neutron powder diffraction. Unit cell dimensions were calculated using a least squares analysis that refined to a δ2θof no more than 0.03°. A triclinic cell was found with space group , a = 10.1222(7), b = 10.1466(6), c = 10.4833(7) Å. α= 116.912(5), β= 107.135(6) and γ= 92.939(6)°, Z = 6 for the Ca2Bi2O5compound. An orthorhombic cell was found with space group C2mm, a = 17.3795(5), b = 5.9419(2) and c = 7.2306(2) Å, Z = 2 for the Ca4Bi6O13compound.

scholarly journals From space to superspace and back: Superspace Group Finder

2008 ◽  
Vol 41 (6) ◽  
pp. 1182-1186 ◽  
Author(s):  
Ivan Orlov ◽  
Lukas Palatinus ◽  
Gervais Chapuis
Keyword(s):  
Crystal Structure ◽  
Dimensional Space ◽  
Flexible Structures ◽  
Three Dimensional ◽  
Real Space ◽  
Space Group ◽  
Space Groups ◽  
Group A ◽  
Modular Composition ◽  
Three Dimensional Space

The symmetry of a commensurately modulated crystal structure can be described in two different ways: in terms of a conventional three-dimensional space group or using the superspace concept in (3 +d) dimensions. The three-dimensional space group is obtained as a real-space section of the (3 +d) superspace group. A complete network was constructed linking (3 + 1) superspace groups and the corresponding three-dimensional space groups derived from rational sections. A database has been established and is available at http://superspace.epfl.ch/finder/. It is particularly useful for finding common superspace groups for various series of modular (`composition-flexible') structures and phase transitions. The use of the database is illustrated with examples from various fields of crystal chemistry.

The crystal structure of gersdorffite (III), a distorted and disordered pyrite structure

1968 ◽  
Vol 36 (283) ◽  
pp. 940-947 ◽  
Author(s):  
P. Bayliss ◽  
N. C. Stephenson
Keyword(s):  
Crystal Structure ◽  
Metal Atom ◽  
Diffraction Data ◽  
Three Dimensional ◽  
Unit Cell ◽  
X Ray Diffraction ◽  
Space Group ◽  
X Ray ◽  
Partially Ordered ◽  
The Ideal

SummaryThe crystal structure of gersdorffite (III) has been examined with three-dimensional Weissenberg X-ray diffraction data. The unit cell is isometric with a 5·6849 ± 0·0003 Å, space group PI, and four formula units per cell. This structure has the sulphur and arsenic atoms equally distributed over the non-metal atom sites of pyrite. All atoms show significant random displacements from the ideal pyrite positions to produce triclinic symmetry, which serves to distinguish this mineral from a disordered cubic gersdorffite (II) and a partially ordered cubic gersdorffite (I). Factors responsible for the atomic distortions are discussed.

CaPtIn4 – an intergrowth variant of CaPtIn2 and indium slabs

2019 ◽  
Vol 74 (9) ◽  
pp. 693-698 ◽  
Author(s):  
Birgit Heying ◽  
Jutta Kösters ◽  
Rainer Pöttgen
Keyword(s):  
Intermetallic Compound ◽  
Single Crystal ◽  
Peritectic Reaction ◽  
Three Dimensional ◽  
Type Structure ◽  
Space Group ◽  
X Ray ◽  
Structure Space ◽  
Indium Metal

AbstractThe indium-rich intermetallic compound CaPtIn4 is formed in a peritectic reaction of CaPtIn2 and indium metal at T = 670 K (14 days annealing). CaPtIn4 crystallizes with the YNiAl4-type structure, space group Cmcm, which was refined from single crystal X-ray diffractometer data: a = 446.3(5), b = 1659.50(18), c = 756.8(8) pm, wR2 = 0.0646, 640 F2 values and 24 variables. Geometrically one can describe the CaPtIn4 structure as an intergrowth variant of CaPtIn2 (MgCuAl2 type) and indium slabs. The three-dimensional [PtIn4] polyanionic network shows short Pt–In distances of 269–280 pm and a broader range of In–In distances (304–378 pm) within substantially distorted In@In8 cubes.

scholarly journals Isomers and polymorphs of (E,E)-1,4-bis(nitrophenyl)-2,3-diaza-1,3-butadienes

2006 ◽  
Vol 62 (4) ◽  
pp. 666-675 ◽  
Author(s):  
Christopher Glidewell ◽  
John N. Low ◽  
Janet M. S. Skakle ◽  
James L. Wardell
Keyword(s):  
Hydrogen Bond ◽  
Hydrogen Bonds ◽  
Three Dimensional ◽  
Stacking Interactions ◽  
Space Group ◽  
Stacking Interaction ◽  
Space Groups ◽  
Π Stacking ◽  
Π Stacking Interaction ◽  
Polymorphic Forms

The structures of five of the possible six isomers of (E,E)-1,4-bis(nitrophenyl)-2,3-diaza-1,3-butadiene are reported, including two polymorphs of one of the isomers. (E,E)-1,4-Bis(2-nitrophenyl)-2,3-diaza-1,3-butadiene, C14H10N4O4 (I), crystallizes in two polymorphic forms (Ia) and (Ib) in which the molecules lie across centres of inversion in space groups P21/n and P21/c, respectively: the molecules in (Ia) and (Ib) are linked into chains by aromatic π...π stacking interactions and C—H...π(arene) hydrogen bonds, respectively. Molecules of (E,E)-1-(2-nitrophenyl)-4-(3-nitrophenyl)-2,3-diaza-1,3-butadiene (II) are linked into sheets by two independent C—H...O hydrogen bonds. The molecules of (E,E)-1,4-bis(3-nitrophenyl)-2,3-diaza-1,3-butadiene (III) lie across inversion centres in the space group P21/n, and a combination of a C—H...O hydrogen bond and a π...π stacking interaction links the molecules into sheets. A total of four independent C—H...O hydrogen bonds link the molecules of (E,E)-1-(3-nitrophenyl)-4-(4-nitrophenyl)-2,3-diaza-1,3-butadiene (IV) into sheets. In (E,E)-1,4-bis(4-nitrophenyl)-2,3-diaza-1,3-butadiene (V) the molecules, which lie across centres of inversion in the space group P21/n, are linked by just two independent C—H...O hydrogen bonds into a three-dimensional framework.

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