scholarly journals Symmetry Relations Between Space Groups in Layered Germanate Structures: Modeling Crystal Structures

2014 ◽  
Vol 70 (a1) ◽  
pp. C1763-C1763
Author(s):  
Nelly Flores-Sanchez ◽  
Ivonne Rosales ◽  
Lauro Bucio
Keyword(s):  
Crystal Structures ◽  
Rietveld Refinement ◽  
Structural Model ◽  
Structural Data ◽  
X Rays ◽  
Monoclinic System ◽  
Space Group ◽  
Space Groups ◽  
Group Type ◽  
Symmetry Relations

Structural models for the new layered germanates ScInGe2O7 and ScFeGe2O7 were analyzed within the framework of symmetry relations between space groups. These compounds were supposed to be hettotypes of the thortveitite mineral, (Sc,Y)2Si2O7, which was considered as the aristotype. Thortveitite crystallizes in the monoclinic system, and the symmetry is described by the space group type C2/m. Other monoclinic hettotypes for the thortveitite are FeInGe2O7 (PDF 01-070-8447, ICSD - 94487), space group C2/m (No. 12); TbInGe2O7 (PDF 01-072-6515, ICSD - 96360), space group C2/c (No. 15); and FeYGe2O7 (PDF 01-072-6099, ICSD - 95935), space group P21/m (No. 11). All these space groups are related by symmetry. By the use of these relations, we proposed starting models for the crystal structures of ScInGe2O7 and ScFeGe2O7. For ScInGe2O7 this was found to be isostructural to FeInGe2O7 reported by our laboratory [1]. The structural data for this compound were obtained by conventional Rietveld refinement of the powder diffraction data of X-rays, using the GSAS program and EXPGUI [2, 3] interface. For ScFeGe2O7 the symmetry related structural model was found in the triclinic system by symmetry reduction from the space group C2/m (unique axis b) to the triclinic space group P1 (figure 1). Rietveld refinement was performed reaching to the following results: lattice parameters a = 5.3434 (8), b = 5.3145 (8), c = 4.8732 (7 ) Å, α = 99 468 (2), β = 97 257 (2), γ = 104 609 (2)0, V = 130.03 (5) A3, Z = 1; WRp = 0.047, Rp = 0.04 and reduced χ2 of 2.176 for 64 variables. This study was sponsored by CONACyT project CB-2011/167624.

scholarly journals VI. Tabulated data for the examination of the 230 space-groups by homogeneous X-rays

1924 ◽  
Vol 224 (616-625) ◽  
pp. 221-257 ◽  
Keyword(s):  
Crystal Structures ◽  
Chemical Society ◽  
Unit Cell ◽  
X Rays ◽  
Screw Axis ◽  
Monoclinic System ◽  
Space Group ◽  
X Ray ◽  
Space Groups ◽  
Relative Arrangement

The object of the present paper is to express the conclusions of mathematical crystallography in a form which shall be immediately useful to workers using homogeneous X-rays for the analysis of crystal structures. The results are directly applicable to such methods as the Bragg ionisation method, the powder method, the rotating crystal method, etc., and summarise in as compact a form as possible what inferences may be made from the experimental observations, whichever one of the 230 possible space-groups may happen to be under examination. It is only in certain cases that the spacings of crystal planes as determined by the aid of homogeneous X-rays agree with the values of those spacings which would be expected from ordinary crystallographic calculations. In the majority of cases the relative arrangement of the molecules in the unit cell leads to apparent anomalies in the experimental results, the observed spacings of certain planes or sets of planes being sub-multiples of the calculated spacings. The simplest case (fig. 8) of such an apparent anomaly is found in the space-group C 2 2 of the monoclinic system, where the presence of a two-fold screw-axis, because it interleaves halfway the (010) planes by molecules which are exactly like those lying in the (010) planes, except that they have been rotated through 180°, leads to an observed periodicity which is half the periodicity to be inferred from the dimensions of the unit cell, that is, leads to an observed spacing for (010) which is half the calculated. All screw-axes produce similar results, and, in general, a p -fold screw-axis leads to an observed spacing for the plane perpendicular to it which is 1/ p th that to be inferred from the dimensions of the cell. Besides those produced by the screw-axes, other abnormalities arise out of the presence of glide-planes. The simplest case of this is shown by the space-group C s 2 (fig. 4) of the monoclinic system, in which the second molecule is obtained from the first by a reflection in a plane parallel to (010) and half a primitive translation parallel to that plane. If we look along a direction perpendicular to this glide-plane, the projections of the two molecules on the (010) plane are indistinguishable except in position, which is equivalent to saying that, for the purposes of X-ray interference, certain planes perpendicular to this plane of projection are interleaved by an identical molecular distribution. Furthermore, since the translation associated with the glide-plane must always be half a primitive translation parallel to the glide-plane, we know that the interleaving is always a submultiple of the full spacing and the periodicity is again reduced in a corresponding manner. The use of this method for discriminating between the various space-groups of the monoclinic system was described by Sir Wm. Bragg in a lecture to the Chemical Society. In the present paper the method has been extended to the whole of the 230 space-groups possible to crystalline structures. In general, it may be said that if a crystal possesses a certain glide-plane, a certain set of planes lying in the zone whose axis is perpendicular to that glide-plane will have their periodicity reduced by one-half.

Solving crystal structures inP1: an automated procedure for finding an allowed origin in the correct space group

2000 ◽  
Vol 33 (2) ◽  
pp. 307-311 ◽  
Author(s):  
Maria Cristina Burla ◽  
Benedetta Carrozzini ◽  
Giovanni Luca Cascarano ◽  
Carmelo Giacovazzo ◽  
Giampiero Polidori
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Structural Model ◽  
Structure Refinement ◽  
Human Intervention ◽  
Space Group ◽  
Space Groups ◽  
Structure Solution ◽  
Actual Space ◽  
Complex Crystal

Crystal structure solution inP1 may be particularly suitable for complex crystal structures crystallizing in other space groups. However, additional efforts and human intervention are often necessary to locate correctly the structural model so obtained with respect to an allowed origin of the actual space group. An automatic procedure is described which is able to perform such a task, allowing the routine passage to the correct space group and the subsequent structure refinement. Some tests are presented proving the effectiveness of the procedure.

scholarly journals FIDEL: A new method for SDPD of nanocrystalline organic compounds

2014 ◽  
Vol 70 (a1) ◽  
pp. C134-C134
Author(s):  
Martin Schmidt ◽  
Stefan Habermehl ◽  
Philipp Moerschel ◽  
Pierre Eisenbrandt
Keyword(s):  
Crystal Structures ◽  
Rietveld Refinement ◽  
Organic Compounds ◽  
Structure Data ◽  
Structural Model ◽  
Lattice Energy ◽  
Lattice Parameters ◽  
Low Energy ◽  
Powder Pattern ◽  
Field Methods

Rietveld refinements generally fail, if the lattice parameters of the structural model differ more than slightly from the correct lattice parameters and the simulated reflections do not overlap with the experimental ones. For molecular crystals, we have developed a more robust fitting algorithm, which uses the cross-correlation function of calculated and experimental powder patterns, and allows a FIt with DEviating Lattice parameters (FIDEL). The method is also successful for nanocrystalline organic compounds showing only 10-20 peaks in their powder diagrams. The FIDEL method has proven to be useful for various applications, including refinements starting from (1) structure data of an isostructural chemical derivative; (2) structure data of an isostructural hydrate or solvate; (3) structure data from measurements at another temperature (e.g. for fitting a room-temperature powder diagram starting with a structure determined from a single-crystal measurement at 100K). FIDEL is also used for determining crystal structures from non-indexed powder diagrams of nanocrystalline organic compounds. Three steps are performed: (1) Prediction of possible crystal structures in various space groups using global lattice-energy minimizations by force-field methods. (2) FIDEL fit of 100 to 600 low-energy structures to the experimental powder pattern. The structure candidate leading to the correct structure results in a significantly better fit than all other structures. (3) Rietveld refinement. The FIDEL method was used to determine the hitherto unknown crystal structure of the nanocrystalline alpha-phase of 2,9-dichloroquinacridone (C20H10Cl2N2O2). The upper part of the figure shows the experimental powder pattern and the simulated powder diagram of one of the predicted low-energy structures before any fitting. The lower part displays the result of the FIDEL fit, before the Rietveld refinement.

On the treatment of settings of space-groups and crystal structures by spezialized short Hermann-Mauguin space-group symbols

2002 ◽  
Vol 217 (4) ◽  
Author(s):  
H. Burzlaff ◽  
H. Zimmermann
Keyword(s):  
Crystal Structures ◽  
Shift Vector ◽  
Space Group ◽  
Space Groups ◽  
Matrix Description ◽  
Simple Rules ◽  
The Matrix ◽  
Free Parameters ◽  
Generating Operators

AbstractFrom the short Hermann-Mauguin space-group symbol a set of generating operators can be derived. The matrix description of the operators depends on three free parameters related to the origin of the setting. Simple rules allow the specification of an origin, the origin of the symbol. The use of any other origin is notated by appending a shift vector from the symbol origin to the new one selected.

scholarly journals Crystal Structures of Ethyl 4-(4-Florophenyl)-6-phenyl-2-substituted-3-pyridinecarboxylates

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
ElSayed M. Shalaby ◽  
Aisha M. Moustafa ◽  
Adel S. Girgis ◽  
Aida M. ElShaabiny
Keyword(s):  
Crystal Structures ◽  
Piperidine Ring ◽  
Monoclinic System ◽  
Orthorhombic System ◽  
Space Group ◽  
Morpholine Ring

Three substituted pyridinecarboxylates were synthesized; (I) ethyl 2-bromo-4-4(fluorophenyl)-6-phenyl-3-pyridinecarboxylate, C20H15BrFNO2, (II) ethyl 4-(4-fluorophenyl)-2-(4-morpholinyl)-6-phenyl-3-pyridinecarboxylate, C24H23FN2O3, and (III) ethyl 4-(4-fluorophenyl)-6-phenyl-2-(1-piperidinyl)-3-pyridinecarboxylate, C25H25FN2O2. It was found that compound (I) belongs to the orthorhombic system with space group P212121, compound (II) to the monoclinic system with space group P21/c, and compound (III) to the monoclinic system with space group C2/c. The morpholine ring in (II) and piperidine ring in (III) have the shape of the distorted chair configuration.

scholarly journals Die Kristallstrukturen von Strontium- und Bariumhexacyanoferrat(III)-Hexamethylentetramin-Hydraten. Strukturmodell für Additionsverbindungen der Alkali- und Erdalkalimetallhexacyanoferrate mit Hexamethylentetramin / The Crystal Structures of Hydrates of Strontium and Barium Hexacyanoferrate(III) with Hexamethylenetetramine. Structural Model for Adducts of the Hexacyanoferrates of Alkaline and Alkaline Earth Metals with Hexamethylenetetramine

1989 ◽  
Vol 44 (5) ◽  
pp. 519-525 ◽  
Author(s):  
Hans-Jürgen Meyer ◽  
Joachim Pickardt
Keyword(s):  
Aqueous Solutions ◽  
Crystal Structures ◽  
General Formula ◽  
Alkaline Earth ◽  
Structural Model ◽  
Earth Metal ◽  
Alkaline Earth Metals ◽  
Alkaline Earth Metal ◽  
Monoclinic Space Group ◽  
Space Group

By reaction of methanolic solutions of hexamethylenetetramine with aqueous solutions of hexacyanoferrates(III) of strontium and barium resp., crystals of the compounds were obtained. Sr3[Fe(CN)6]2 · 3 C6H12N4 · 18 H2O, tetragonal, space group P42/nmc, Z = 4, a = 1931.8(4), c = 1579.9(4) pm, 1358 reflections. R = 0.066. Ba3[Fe(CN)6]2 · 2 C6H12N4 · 11 Η2Ο. monoclinic. space group P21/n, Ζ = 2, a = 1148.0(4), b = 1369.7(4), c = 1584.5(4) pm, γ = 95.79(3)°, 2583 reflections, R = 0.057. The crystal structures of these adducts are compared with those of other hexamethylenetetramine adducts of alkaline and alkaline earth metal hexacyanoferrates of the general formula M,[Fe(CN)6]y · zC6H12N4 · vH2O recently investigated by us. A structural model for the adducts is presented.

scholarly journals Photoreduction and validation of haem–ligand intermediate states in protein crystals byin situsingle-crystal spectroscopy and diffraction

IUCrJ ◽  
2017 ◽  
Vol 4 (3) ◽  
pp. 263-270 ◽  
Author(s):  
Demet Kekilli ◽  
Tadeo Moreno-Chicano ◽  
Amanda K. Chaplin ◽  
Sam Horrell ◽  
Florian S. N. Dworkowski ◽  
...  
Keyword(s):  
Crystal Structures ◽  
Structural Data ◽  
X Rays ◽  
Solvated Electrons ◽  
X Ray ◽  
Redox States ◽  
Density Maps ◽  
Correct Assignment ◽  
Wide Range

Powerful synergies are available from the combination of multiple methods to study proteins in the crystalline form. Spectroscopies which probe the same region of the crystal from which X-ray crystal structures are determined can give insights into redox, ligand and spin states to complement the information gained from the electron-density maps. The correct assignment of crystal structures to the correct protein redox and ligand states is essential to avoid the misinterpretation of structural data. This is a particular concern for haem proteins, which can occupy a wide range of redox states and are exquisitely sensitive to becoming reduced by solvated electrons generated from interactions of X-rays with water molecules in the crystal. Here, single-crystal spectroscopic fingerprinting has been applied to investigate the laser photoreduction of ferric haem in cytochromec′. Furthermore,in situX-ray-driven generation of haem intermediates in crystals of the dye-decolourizing-type peroxidase A (DtpA) fromStreptomyces lividansis described.

Rietveld refinement of the crystal structures of hexagonal Y6Cr4+xAl43−x (x=2.57) and tetragonal YCr4−xAl8+x (x=1.22)

1995 ◽  
Vol 10 (2) ◽  
pp. 86-90 ◽  
Author(s):  
R. Černý ◽  
K. Yvon ◽  
T. I. Yanson ◽  
M. B. Manyako ◽  
O. I. Bodak
Keyword(s):  
Crystal Structures ◽  
Rietveld Refinement ◽  
Powder Diffraction ◽  
Diffraction Data ◽  
Structure Refinement ◽  
Powder Diffraction Data ◽  
Space Group ◽  
X Ray

Y6Cr4+xAl43−x (x = 2.57); space group P63/mcm, a = 10.8601(1) Å, c = 17.6783(3) Å, V= 1805.7(1) Å3, Z=2; isostructural to Yb6Cr4+xAl43−x, (x=1.76) with two aluminium sites partially occupied by chromium (44% and 27% Cr). YCr4−xAl8+x (x=1.22); space group I4/mmm, a = 9.0299(2) Å, c = 5.1208(2) Å, V=417.55(3) Å3, Z=2, disordered variant of CeMn4Al8 with one chromium site (8f) partially occupied by aluminium (33% Al); X-ray powder diffraction data were collected on a well-crystallized multiphase sample containing 43 wt.% of Y6Cr4+xAl43−x, 27 wt.% of Y2Cr8−xAl16+x, 16 wt.% of Al, 13 wt.% of YAl3, and traces of Y2O3. Structure refinement converged at Rwp = 2.0% and RB = 3.5, 3.6% resp. for a total of 78 parameters and 1190 reflections.

scholarly journals Partial rotational lattice order–disorder in stefin B crystals

2014 ◽  
Vol 70 (4) ◽  
pp. 1015-1025 ◽  
Author(s):  
Miha Renko ◽  
Ajda Taler-Verčič ◽  
Marko Mihelič ◽  
Eva Žerovnik ◽  
Dušan Turk
Keyword(s):  
Crystal Lattice ◽  
Crystal Structures ◽  
Electron Density ◽  
Rejection Rate ◽  
Lattice Order ◽  
Space Group ◽  
Space Groups ◽  
Additional Layer ◽  
Diffraction Patterns ◽  
Ordered Layers

At present, the determination of crystal structures from data that have been acquired from twinned crystals is routine; however, with the increasing number of crystal structures additional crystal lattice disorders are being discovered. Here, a previously undescribed partial rotational order–disorder that has been observed in crystals of stefin B is described. The diffraction images revealed normal diffraction patterns that result from a regular crystal lattice. The data could be processed in space groupsI4 andI422, yet one crystal exhibited a notable rejection rate in the higher symmetry space group. An explanation for this behaviour was found once the crystal structures had been solved and refined and the electron-density maps had been inspected. The lattice of stefin B crystals is composed of five tetramer layers: four well ordered layers which are followed by an additional layer of alternatively placed tetramers. The presence of alternative positions was revealed by the inspection of electron-density score maps. The well ordered layers correspond to the crystal symmetry of space groupI422. In addition, the positions of the molecules in the additional layer are related by twofold rotational axes which correspond to space groupI422; however, these molecules lie on the twofold axis and can only be related in a statistical manner. When the occupancies of alternate positions and overlapping are equal, the crystal lattice indeed fulfills the criteria of space groupI422; when these occupancies are not equal, the lattice only fulfills the criteria of space groupI4.

New Quaternary Selenoantimonates AHgSbSe3 (A = Rb, Cs): Synthesis, Structures and Optical Properties

1998 ◽  
Vol 547 ◽  
Author(s):  
Zhen Chen ◽  
Ru-Ji Wang ◽  
Jing Li
Keyword(s):  
Optical Properties ◽  
Alkali Metal ◽  
Crystal Structures ◽  
Diffuse Reflectance ◽  
Layered Materials ◽  
Band Gaps ◽  
Alkali Metal Cations ◽  
Monoclinic System ◽  
Orthorhombic System ◽  
Space Group

AbstractSolvothermal reactions in ethylenediamine have resulted in two quaternary mercury containing selenoantimonates: RbHgSbSe3 (I) and CsHgSbSe3 (II). Compound I crystallizes in monoclinic system, space group P2l/c (no. 14) with a = 7.758(2)Å, b = 11.234(2)Å, c = 8.849(2) Å, β = 106.60(3)°, V = 739.1(3)Å3, Z = 4. Compound II crystallizes in orthorhombic system, space group Cmcm (no. 63) with a = 4.444(1)Å, b = 15.514(6)Å, c = 11.261(7) Å, V = 776.4(6) Å3, Z = 4. Both compounds are layered materials and their crystal structures are closely related. Both contain layers of 2[HgSbSe3-] separated by alkali-metal cations A+ (Rb, Cs). Diffuse reflectance experiments show that both compounds are semiconductors with estimated band gaps of 1.7 eV for I and 1.6 eV for II, respectively.

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