VRML general position diagrams of magnetic space groups

2006 ◽  
Vol 39 (4) ◽  
pp. 620-620
Author(s):  
J. S. Burke ◽  
N. R. Cordisco ◽  
D. B. Litvin
Keyword(s):  
General Position ◽  
Magnetic Moments ◽  
Three Dimensional ◽  
Space Groups

Three-dimensional general position diagrams of the superfamilies of all non-cubic magnetic space groups have been developed. The diagrams can be rotated and zoomed to aid in the visualization of the general position diagrams and include both the general positions of the atoms and the general orientations of the associated magnetic moments.

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.

scholarly journals Na3Co2(As0.52P0.48)O4(As0.95P0.05)2O7

2013 ◽  
Vol 69 (12) ◽  
pp. i85-i86 ◽  
Author(s):  
Youssef Ben Smida ◽  
Abderrahmen Guesmi ◽  
Mohamed Faouzi Zid ◽  
Ahmed Driss
Keyword(s):  
Solid State ◽  
Solid State Reaction ◽  
Title Compound ◽  
General Position ◽  
Structural Model ◽  
Three Dimensional ◽  
The Other ◽  
Coordination Polyhedra ◽  
Bond Valence Sum ◽  
Full Occupancy

The title compound, trisodium dicobalt(II) (arsenate/phosphate) (diarsenate/diphosphate), was prepared by a solid-state reaction. It is isostructural with Na3Co2AsO4As2O7. The framework shows the presence of CoX22O12(X2 is statistically disordered with As0.95P0.05) units formed by sharing corners between Co1O6octahedra andX22O7groups. These units form layers perpendicular to [010]. Co2O6octahedra andX1O4(X1 = As0.54P0.46) tetrahedra form Co2X1O8chains parallel to [001]. Cohesion between layers and chains is ensured by theX22O7groups, giving rise to a three-dimensional framework with broad tunnels, running along thea- andc-axis directions, in which the Na+ions reside. The two Co2+cations, theX1 site and three of the seven O atoms lie on special positions, with site symmetries 2 andmfor the Co,mfor theX1, and 2 andm(× 2) for the O sites. One of two Na atoms is disordered over three special positions [occupancy ratios 0.877 (10):0.110 (13):0.066 (9)] and the other is in a general position with full occupancy. A comparison between structures such as K2CdP2O7, α-NaTiP2O7and K2MoO2P2O7is made. The proposed structural model is supported by charge-distribution (CHARDI) analysis and bond-valence-sum (BVS) calculations. The distortion of the coordination polyhedra is analyzed by means of the effective coordination number.

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.

scholarly journals Bis[tris(propane-1,3-diamine-κ2N,N′)nickel(II)] diaquabis(propane-1,3-diamine-κ2N,N′)nickel(II) hexabromide dihydrate

2014 ◽  
Vol 70 (6) ◽  
pp. m227-m228 ◽  
Author(s):  
Aymen Yangui ◽  
Walid Rekik ◽  
Slim Elleuch ◽  
Younes Abid
Keyword(s):  
Hydrogen Bonds ◽  
Title Compound ◽  
General Position ◽  
Three Dimensional ◽  
The Other ◽  
Octahedral Coordination ◽  
Water Molecules ◽  
Coordination Environment ◽  
Lattice Water ◽  
Dimensional Network

In the title compound, [Ni(C3H10N2)3]2[Ni(C3H10N2)2(H2O)2]Br6·2H2O, one Ni2+cation, located on an inversion centre, is coordinated by four N atoms from two ligands and by two water O atoms. The other Ni2+cation, located in a general position, is coordinated by six N atoms from three ligands. In both cases, the Ni2+cation has an octahedral coordination environment. The overall structural cohesion is ensured by three types of hydrogen bonds, N—H...Br, O—H...Br and O—H...O, which connect the two types of complex cations, the bromide counter-anions and the lattice water molecules into a three-dimensional network.

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.

scholarly journals Stochastic dynamics of planar magnetic moments in a three-dimensional environment

2018 ◽  
Vol 510 ◽  
pp. 98-109 ◽  
Author(s):  
Zochil González Arenas ◽  
Daniel G. Barci ◽  
Miguel Vera Moreno
Keyword(s):  
Stochastic Dynamics ◽  
Magnetic Moments ◽  
Three Dimensional

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.

Poly[deca-μ2-cyanido-dicyanidobis(μ2-ethylenediamine)bis(ethylenediamine)tricadmium(II)dicobalt(III)]: a two-dimensional coordination polymer

2009 ◽  
Vol 65 (3) ◽  
pp. m118-m120
Author(s):  
Olha Sereda ◽  
Helen Stoeckli-Evans
Keyword(s):  
Coordination Polymer ◽  
Network Structure ◽  
General Position ◽  
Rotation Axis ◽  
Three Dimensional ◽  
The Other ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Asymmetric Unit ◽  
Dimensional Network

The title coordination polymer, [Cd3Co2(CN)12(C2H8N2)4]n, has an infinite two-dimensional network structure. The asymmetric unit is composed of two crystallographically independent CdIIatoms, one of which is located on a twofold rotation axis. There are two independent ethylenediamine (en) ligands, one of which bis-chelates to the Cd atom that sits in a general position, while the other bridges this Cd atom to that sitting on the twofold axis. The Cd atom located on the twofold rotation axis is linked to four equivalent CoIIIatomsviacyanide bridges, while the Cd atom that sits in a general position is connected to three equivalent CoIIIatomsviacyanide bridges. In this way, a series of trinuclear, tetranuclear and pentanuclear macrocycles are linked to form a two-dimensional network structure lying parallel to thebcplane. In the crystal structure, these two-dimensional networks are linkedviaN—H...N hydrogen bonds involving an en NH2H atom and a cyanide N atom, leading to the formation of a three-dimensional structure. This coordination polymer is only the second example involving a cyanometallate where the en ligand is present in both chelating and bridging coordination modes.

scholarly journals The CCP13FibreFixprogram suite: semi-automated analysis of diffraction patterns from non-crystalline materials

2007 ◽  
Vol 40 (1) ◽  
pp. 178-184 ◽  
Author(s):  
Ganeshalingam Rajkumar ◽  
Hind A. AL-Khayat ◽  
Felicity Eakins ◽  
Carlo Knupp ◽  
John M. Squire
Keyword(s):  
Structural Information ◽  
Protein Crystallography ◽  
Three Dimensional ◽  
Automated Analysis ◽  
Crystalline Materials ◽  
Space Groups ◽  
Naturally Occurring ◽  
Single User ◽  
Diffraction Patterns ◽  
User Friendly

The extraction of useful information from recorded diffraction patterns from non-crystalline materials is non-trivial and is not a well defined operation. Unlike protein crystallography where one expects to see well behaved diffraction spots in predictable positions defined by standard space groups, the diffraction patterns from non-crystalline materials are very diverse. They can range from uniaxially oriented fibre patterns which are completely sampled as Bragg peaks, but rotationally averaged around the fibre axis, to fibre patterns that are completely unsampled, to either kind of pattern with considerable axial misalignment (disorientation), to liquid-like order and even to mixtures of these various structure types. In the case of protein crystallography, the specimen is generated artificially and only used if the degree of order is sufficient to yield a three-dimensional density map of high enough resolution to be interpreted sensibly. However, with non-crystalline diffraction, many of the specimens of interest are naturally occurring (e.g.cellulose, rubber, collagen, muscle, hair, silk) and to elucidate their structure it is necessary to extract structural information from the materials as they actually are and to whatever resolution is available. Even when synthetic fibres are generated from purified components (e.g.nylon, polyethylene, DNA, polysaccharides, amyloidsetc.) and diffraction occurs to high resolution, it is rarely possible to obtain perfect uniaxial alignment. The CCP13 project was established in the 1990s to generate software which will be generally useful for analysis of non-crystalline diffraction patterns. Various individual programs were written which allowed separate steps in the analysis procedure to be carried out. Many of these programs have now been integrated into a single user-friendly package known asFibreFix, which is freely downloadable from http://www.ccp13.ac.uk. Here the main features ofFibreFixare outlined and some of its applications are illustrated.

Ternary Indides REMgIn (RE = Y, La–Nd, Sm, Gd–Tm, Lu). Synthesis, Structure and Magnetic Properties

2004 ◽  
Vol 59 (5) ◽  
pp. 513-518 ◽  
Author(s):  
Rainer Kraft ◽  
Martin Valldor ◽  
Daniel Kurowski ◽  
Rolf-Dieter Hoffmann ◽  
Rainer Pöttgen
Keyword(s):  
Magnetic Moments ◽  
Three Dimensional ◽  
Temperature Dependent ◽  
Variable Parameters ◽  
Magnetic Susceptibility Data ◽  
X Ray ◽  
Susceptibility Data ◽  
Sample Chamber ◽  
Trigonal Prismatic Coordination ◽  
Trigonal Prismatic

Abstract The equiatomic rare earth-magnesium-indium compounds REMgIn (RE = Y, La-Nd, Sm, Gd- Tm, Lu) were prepared from the elements in sealed tantalum tubes inside a water-cooled sample chamber of an induction furnace. All compounds were characterized through their X-ray powder patterns. They crystallize with the hexagonal ZrNiAl type structure, space group P6̄̄2m, with three formula units per cell. The structure of SmMgIn was refined from X-ray single crystal diffractometer data: a = 761.3(2), c = 470.3(1) pm, wR2 = 0.0429, 380 F2 values and 14 variable parameters. The DyMgIn, HoMgIn, and TmMgIn structures have been analyzed using the Rietveld technique. The REMgIn structures contain two cystallographically independent indium sites, both with tri-capped trigonal prismatic coordination: In1Sm6Mg3 and In2Mg6Sm3. Together the magnesium and indium atoms form a three-dimensional [MgIn] network with Mg-Mg distances of 320 and Mg-In distances in the range 294 - 299 pm. Temperature dependent magnetic susceptibility data show Curie-Weiss behavior for DyMgIn, HoMgIn, and TmMgIn with experimental magnetic moments of 11.0(1) μB/Dy atom, 10.9(1) μB/Ho atom, and 7.5(1) μB/Tm atom. The three compounds order antiferromagnetically at TN = 22(2) K (DyMgIn), 12(1) K (HoMgIn), and 3(1) K (TmMgIn).

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