Using the P-symmetry space groups of crystals to investigate 6D symmetry groups

2009 ◽  
Vol 54 (4) ◽  
pp. 539-547 ◽  
Author(s):  
A. F. Palistrant
Keyword(s):  
Symmetry Groups ◽  
Space Groups ◽  
Symmetry Space

3D Braided Geometry Structures Based on Space Group

2010 ◽  
Vol 152-153 ◽  
pp. 1156-1161 ◽  
Author(s):  
Wen Suo Ma ◽  
Bin Qian Yang ◽  
Xiao Zhong Ren
Keyword(s):  
Group Theory ◽  
Symmetry Groups ◽  
The Novel ◽  
Geometrical Structures ◽  
Braided Group ◽  
Space Group ◽  
Space Groups ◽  
Geometry Structure ◽  
Point Groups ◽  
Space Point

3D braided group theory is dissertated. The analysis procedure is described from the existing braided geometry structure to the braided space group; 3D braided geometrical structures are finally described by means of group theory. Some of novel 3D braided structures are deduced from the braided space groups. By describing the 3D braided materials with braided space point and braided space groups, the braided space groups are not always the same as symmetry groups of crystallographic because novel lattices can be produced and the reflection operation cannot exist in braided space point groups. Braided point and space groups are theoretical basis for deriving the novel braided geometry structure.

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

Ferroelectric space groups

1986 ◽  
Vol 42 (1) ◽  
pp. 44-47 ◽  
Author(s):  
D. B. Litvin
Keyword(s):  
Electric Dipole ◽  
Space Time ◽  
Discrete Space ◽  
Symmetry Groups ◽  
Space Groups ◽  
Point Groups

The 440 ferroelectric space groups, viz the Heesch-Shubnikov (magnetic) space groups, which are symmetry groups of ferroelectric electric-dipole arrangements in crystals, are derived and tabulated. By considering automorphisms induced by the automorphisms of the discrete space-time group, we show that although ferroelectric, ferromagnetic and ferrocurrent point groups all number 31, the number of ferroelectric space groups differs from 275, which is that of both ferromagnetic and ferrocurrent space groups.

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.

Two-dimensional space groups with sevenfold symmetry

1986 ◽  
Vol 42 (1) ◽  
pp. 55-56 ◽  
Author(s):  
A. L. Mackay
Keyword(s):  
Dimensional Space ◽  
Symmetry Groups ◽  
Two Dimensional ◽  
Space Groups ◽  
Symmetry Operations

Fivefold and sevenfold symmetry operations are, of course, incompatible with repetition by a lattice but, with the appearance of structures involving curved sheets, they and other non-crystallographic operations must now be taken into consideration as possibilities of non-Euclidean crystallography develop. Here are described the symmetry groups which might be called 732 and 73m and which may be found in two-dimensional manifolds.

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¯.

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