On the Distribution of Molecular Crystals of Organic and Elementoorganic Compounds over Symmetry Space Groups

2021 ◽  
Vol 66 (3) ◽  
pp. 361-366
Author(s):  
N. V. Somov ◽  
E. V. Chuprunov
Keyword(s):  
Molecular Crystals ◽  
Space Groups ◽  
Symmetry Space

Space groups of the diamond polytypes

1993 ◽  
Vol 8 (11) ◽  
pp. 2835-2839 ◽  
Author(s):  
A.W. Phelps ◽  
W. Howard ◽  
D.K. Smith
Keyword(s):  
Systematic Method ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Space ◽  
Atomic Coordinates ◽  
Symmetry Space Group

Space groups and atomic coordinates for the 4H, 6H, 8H, 10H, 15R, and 21R polytypes of diamond are presented. The systematic method used to determine the highest symmetry space group for diamond polytypes is described.

Über die Kristallstrukturen der Tellurate Pb3Fe2Te2O12 und Pb2CoTeO6 / On the Crystal Structures of the Tellurates Pb3Fe2Te2O12 and Pb2CoTeO6

1997 ◽  
Vol 52 (1) ◽  
pp. 35-39 ◽  
Author(s):  
B. Wedel ◽  
Hk. Müller-Buschbaum
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Crystal Structures ◽  
Negative Charge ◽  
X Ray ◽  
Space Groups ◽  
Lattice Constants ◽  
Coulomb Term ◽  
Lone Pairs ◽  
Symmetry Space

Pb3Fe2Te2O12 (I) and Pb2CoTeO6 (II) have been prepared by crystallization from melts. Single crystal X-ray investigations led to monoclinic (I) and tetragonal (II) symmetry, space groups C4s-Cc and D174h-14/mmm. Lattice constants I: a = 9.866(3), b = 15.332(4), c = 7.172(2) Å, β = 111.34(3)°, Z = 4. II: a = 5.661(5), c = 8.004(7) Å, Z = 2. (I) represents a new crystal structure, characterized by a network of octahedra occupied by Fe3+ and Te6+ in a disordered manner. The centres of negative charge of the lone pairs of Pb2+ in I are estimated by Coulomb term calculations. II belongs to the elpasolithe type

Toward fully fledged high-pressure macromolecular crystallography

2007 ◽  
Vol 40 (5) ◽  
pp. 912-918 ◽  
Author(s):  
Eric Girard ◽  
Anne-Claire Dhaussy ◽  
Bernard Couzinet ◽  
Jean-Claude Chervin ◽  
Mohamed Mezouar ◽  
...  
Keyword(s):  
High Pressure ◽  
Urate Oxidase ◽  
Macromolecular Crystallography ◽  
Space Groups ◽  
Diamond Anvil ◽  
New Generation ◽  
Multiple Samples ◽  
Hexagonal Crystals ◽  
Symmetry Space ◽  
Low Symmetry

Pressure allows one to explore the energy landscape and the various conformations of macromolecules. This might be one of the most interesting prospects of combining macromolecular crystallography (MX) with pressure perturbation. This paper presents innovations in high-pressure macromolecular crystallography (HPMX). A new-generation diamond anvil cell extends the technical feasibility of HPMX experiments up to about 2.5 GPa (depending on the sample). Thanks to the large useful aperture (82°) provided by this cell and special loading techniques (use of splinter and/or multiple samples), HPMX can now be more readily applied to crystals with very anisotropic habits and/or low-symmetry space groups, as demonstrated by analysis of diffraction data collected at 140 MPa from orthorhombic urate oxidase crystals. The behaviour of hexagonal crystals of an octanucleotide was investigated up to 2 GPa.

Group actions as applied to symmetry breaking in hexagonal crystals with space group P63/m

1984 ◽  
Vol 62 (11) ◽  
pp. 1152-1173
Author(s):  
Rose M. Morra ◽  
Robin L. Armstrong
Keyword(s):  
Phase Transition ◽  
Structural Phase ◽  
Group Actions ◽  
Order Parameters ◽  
High Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Space ◽  
Low Symmetry ◽  
Symmetry Space Group

A procedure is outlined that allows one to predict the possible low-symmetry space groups for a commensurate phase transition associated with a broken symmetry. By considering each irreducible representation of the high-symmetry space group and using a subduction procedure involving the theory of group actions, one may determine a complete set of representative order parameters and their little groups. Each little group can be identified as a possible space group for the low-symmetry phase. The method is used to deduce all possible broken symmetries of space group P63/m that can result from a phase transition associated with one of the symmetry points in the Brillouin zone. As a specific application of the resulting tables of possible order parameters and associated low-symmetry space groups, changes in the X nuclear quadrupole resonance spectrum due to structural phase transitions in hexagonal AX3 crystals with the high-symmetry space group P63/m are considered.

Distribution of Molecular Centres in Crystallographic Unit Cells

1997 ◽  
Vol 53 (4) ◽  
pp. 726-736 ◽  
Author(s):  
W. D. S. Motherwell
Keyword(s):  
Visual Inspection ◽  
Global Minimum ◽  
Molecular Crystals ◽  
Close Packing ◽  
Interaction Energies ◽  
Space Groups ◽  
Packing Parameter ◽  
Unit Cells ◽  
Structural Database ◽  
The Ideal

A survey has been made of the position of molecular centres in unit cells for the seven most populated space groups in the Cambridge Structural Database. Visual inspection of histograms and scattergrams reveals very clear peaks and clusters, showing preferred locations for molecules. These preferred positions are midway between centres of symmetry or screw axes. Some simple calculations of interaction energies of molecules with neighbours in a molecular coordination sphere suggest reasons for these preferred positions. These diagrams show that simplification of molecules to spheres is helpful in visualizing the prevalence of layers of molecules and tendencies to the ideal close packing of spheres. global minimum, but not always. This observation has been noted both by workers who have exhaustively explored packing parameter space (Williams, 1969; van Eijck, Mooij & Kroon, 1995) or have used Monte Carlo methods plus simulated annealing to take statistical samples of the total space and proceed to a local minimum (Karfunkel & Gdanitz, 1992). What is certain is the importance of the principle of close packing. The present study takes the approach of looking at the total available data on packing of molecular crystals to identify certain tendencies in packing and certain commonly occurring patterns. If such patterns exist then these will have implications as regards the methods of prediction, if only on the basis of probability of occurrence.

The geometry and structural properties of the 4,8,12-trioxa-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrene system in the cationic state. Structures of a planar organic cation with various monovalent and divalent anions

1999 ◽  
Vol 55 (3) ◽  
pp. 410-423 ◽  
Author(s):  
Frederik C. Krebs ◽  
Bo W. Laursen ◽  
Ib Johannsen ◽  
André Faldt ◽  
Klaus Bechgaard ◽  
...  
Keyword(s):  
Structural Properties ◽  
Organic Cation ◽  
Characteristic Pattern ◽  
High Symmetry ◽  
X Ray ◽  
Space Groups ◽  
Temperature Study ◽  
Different Temperatures ◽  
Anions And Cations ◽  
Symmetry Space

The geometry of the 4,8,12-trioxa-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrene system in the cationic state was established by X-ray structural resolution of the salts formed between the cation and various anions. The geometry was found to be planar for the 4,8,12-trioxa-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrenylium and 2,6,10-tri(tert-butyl)-4,8,12-trioxa-4,8,12,12c-tetrahydrodibenzo[cd,mn]pyrenylium cations with the monovalent anions I−, BF_4^-, PF_6^-, AsF_6^-, HNO3.NO_3^- and CF3SO_3^-, and the divalent anions S2O_6^{2-} and Mo6Cl_{14}^{2-}. The salts were found to crystallize in distinct space groups following a characteristic pattern. Mixed cation–anion stacking resulted in space groups with high symmetry: Pbca in three cases and R3¯c in one; a temperature study of the latter was made at ten different temperatures. The formation of dimers of anions and cations resulted in lower-symmetry space groups, mainly monoclinic (P21/n, P21/c and C2/c), but also P1¯.

scholarly journals Use of software to search for higher symmetry: space group C2

2001 ◽  
Vol 57 (6) ◽  
pp. 800-805 ◽  
Author(s):  
Richard E. Marsh ◽  
Anthony L. Spek
Keyword(s):  
Cambridge Structural Database ◽  
Higher Symmetry ◽  
Space Group ◽  
Space Groups ◽  
Bond Lengths ◽  
Structural Database ◽  
Symmetry Space ◽  
Coordinate Data ◽  
Symmetry Space Group

From a search of the October 2000 release of the Cambridge Structural Database we find coordinate data for approximately 1500 entries under space group No. 5: C2 or, occasionally, A2, I2 or B112. Software designed to detect cases of missed higher symmetry identified 144 entries for detailed inspection. Of these, 50 should, we believe, be revised to space groups of higher symmetry. The most common revision is to space group C2/m, which entails adding a center of inversion and usually results in important changes in bond lengths and angles.

Microstructure and crystal symmetry of Pb2Sr2(Y/Ca)Cu3O9−δ

1990 ◽  
Vol 48 (4) ◽  
pp. 64-65
Author(s):  
Y. P. Lin ◽  
J. S. Xue ◽  
J. E. Greedan
Keyword(s):  
Electron Diffraction ◽  
High Temperature Superconductors ◽  
Carbon Film ◽  
Basic Structure ◽  
Crystal Symmetry ◽  
X Ray Diffraction ◽  
X Ray ◽  
Space Groups ◽  
New Family ◽  
Convergent Beam

A new family of high temperature superconductors based on Pb2Sr2YCu3O9−δ has recently been reported. One method of improving Tc has been to replace Y partially with Ca. Although the basic structure of this type of superconductors is known, the detailed structure is still unclear, and various space groups has been proposed. In our work, crystals of Pb2Sr2YCu3O9−δ with dimensions up to 1 × 1 × 0.25.mm and with Tc of 84 K have been grown and their superconducting properties described. The defects and crystal symmetry have been investigated using electron microscopy performed on crushed crystals supported on a holey carbon film.Electron diffraction confirmed x-ray diffraction results which showed that the crystals are primitive orthorhombic with a=0.5383, b=0.5423 and c=1.5765 nm. Convergent Beam Electron Diffraction (CBED) patterns for the and axes are shown in Figs. 1 and 2 respectively.

Symmetry breaking in convergent-beam diffraction

1989 ◽  
Vol 47 ◽  
pp. 480-481
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Space Groups ◽  
Atomic Displacements ◽  
Small Probe ◽  
Phase Sensitive ◽  
Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

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