Computer program for the derivation of symmetry operations from the space-group symbols

1982 ◽  
Vol 15 (4) ◽  
pp. 464-467 ◽  
Author(s):  
H. Burzlaff ◽  
A. Hountas
Keyword(s):  
Computer Program ◽  
Space Group ◽  
Symmetry Operations

Matching selenium-atom peak positions with a different hand or origin

2002 ◽  
Vol 35 (3) ◽  
pp. 368-370 ◽  
Author(s):  
G. David Smith
Keyword(s):  
Computer Program ◽  
Iterative Procedure ◽  
Polar Axis ◽  
Polar Space ◽  
Selenium Atom ◽  
Space Group ◽  
Space Groups ◽  
Fortran 90 ◽  
Symmetry Operations

An algorithm is described for matching and correlating two or more sets of peaks or atoms. The procedure is particularly useful for matching putative selenium atoms from a selenium-atom substructure as obtained fromEmaps from two or more random-atom trials. The algorithm will work for any space group exceptP1. For non-polar space groups, the procedure is relatively straightforward. For polar space groups, the calculation is performed in projection along the polar axis in order to identify potential matching peaks, and an iterative procedure is used to eliminate incorrect peaks and to calculate the displacement along the polar axis. The algorithm has been incorporated into a computer program,NANTMRF, written in Fortran 90. Less than 0.5 s are required to match 27 peaks in space groupP21, and the output lists the correct origin, enantiomorph, symmetry operations, and provides the relative displacements between pairs of matching peaks.

A computer program to derive (3+1)-dimensional symmetry operations from two-line symbols

1997 ◽  
Vol 30 (1) ◽  
pp. 73-78 ◽  
Author(s):  
Z.-Q. Fu ◽  
H.-F. Fan
Keyword(s):  
Computer Program ◽  
Crystal Structures ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Direct Methods ◽  
Basic Space ◽  
Space Group ◽  
Symmetry Operations ◽  
Three Dimensional Space

A computer program has been written for the derivation of (3 + 1)-dimensional symmetry operations from the two-line symbols. The derivation is based on the concept of generators {[Γ(Rv E ), ∊v , s v , τv , q)|v = 1, NG}, in which {[Γ(Rv E ), s v )|v = 1, NG} denotes the set of generators of the basic space group represented by the upper line. The program, called SPGR4D, is written in Fortran77 and based on the program by Burzlaff & Hountas (1982). [J. Appl. Cryst. (1982), 15, 464–467] for the derivation of symmetry operations in three-dimensional space. SPGR4D has been incorporated into a new version of the direct-methods program DIMS for solving incommensurate modulated crystal structures.

TABLES, a program to display space-group symmetry information in three dimensions

1987 ◽  
Vol 20 (6) ◽  
pp. 532-535 ◽  
Author(s):  
C. Abad-Zapatero ◽  
T. J. O'Donnell
Keyword(s):  
Computer Graphics ◽  
Computer Program ◽  
Three Dimensional ◽  
Spatial Location ◽  
Three Dimensions ◽  
Group Symmetry ◽  
Space Group ◽  
Interactive Display ◽  
Symmetry Operators ◽  
Group Information

TABLES is a computer program developed to display the crystal symmetry and the spatial location of the different symmetry operators for a given space group using interactive computer graphics. It allows the three-dimensional interactive display of the space-group information contained in International Tables for Crystallography [(1983), Vol. A. Dordrecht: Reidel]. Such a program is useful as a teaching aid in crystallography and is valuable for exploring molecular packing arrangements.

SECTION– a computer program for the graphic display of cross sections through a unit cell

1999 ◽  
Vol 32 (2) ◽  
pp. 353-354 ◽  
Author(s):  
Leonard J. Barbour
Keyword(s):  
Crystal Structure ◽  
Computer Program ◽  
Cross Sections ◽  
Unit Cell ◽  
Graphic Display ◽  
Cross Sectional ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Microsoft Windows ◽  
Symmetry Operations

SECTIONis a 32-bit Microsoft Windows-based program that displays cross-sectional slices through a packed crystal structure. Unit-cell dimensions as well as the unique atomic positions and symmetry operations are read fromSHELXinstruction files.

LAZY PULVERIX, a computer program, for calculating X-ray and neutron diffraction powder patterns

1977 ◽  
Vol 10 (1) ◽  
pp. 73-74 ◽  
Author(s):  
K. Yvon ◽  
W. Jeitschko ◽  
E. Parthé
Keyword(s):  
Neutron Diffraction ◽  
Computer Program ◽  
Input Data ◽  
Anomalous Dispersion ◽  
Dispersion Correction ◽  
Space Group ◽  
X Ray ◽  
Limited Knowledge ◽  
Scattering Factor ◽  
Correction Terms

A computer program has been written with the aim of calculating powder patterns without the use of crystallographic tables. This has been achieved by deriving all symmetry information such as general equivalent positions from the Hermann-Mauguin space-group symbols, by calculating automatically the multiplicities of special positions and by storing the necessary constants, such as scattering factor tables, anomalous dispersion correction terms and X-ray wavelengths in the program. Owing to the very restricted amount of input data this program is especially suited for users with a limited knowledge of crystallography.

Octahedral tilting in the tungsten bronzes

2015 ◽  
Vol 71 (3) ◽  
pp. 342-348 ◽  
Author(s):  
Thomas A. Whittle ◽  
Siegbert Schmid ◽  
Christopher J. Howard
Keyword(s):  
Group Theory ◽  
Computer Program ◽  
Unit Cell ◽  
Group Symmetry ◽  
Space Group Symmetry ◽  
Space Group ◽  
X Ray ◽  
Unit Cells ◽  
Octahedral Tilting ◽  
Special Points

Possibilities for `simple' octahedral tilting in the hexagonal and tetragonal tungsten bronzes (HTB and TTB) have been examined, making use of group theory as implemented in the computer programISOTROPY. For HTB, there is one obvious tilting pattern, leading to a structure in space groupP63/mmc. This differs from the space groupP63/mcmfrequently quoted from X-ray studies – these studies have in effect detected only displacements of the W cations from the centres of the WO6octahedra. The correct space group, taking account of both W ion displacement and the octahedral tilting, isP6322 – structures in this space group and matching this description have been reported. A second acceptable tilting pattern has been found, leading to a structure inP6/mmmbut on a larger `2 × 2 × 2' unit cell – however, no observations of this structure have been reported. For TTB, a search at the special points of the Brillouin zones revealed only one comparable tilting pattern, in a structure with space-group symmetryI4/mon a `21/2 × 21/2by 2' unit cell. Given several literature reports of larger unit cells for TTB, we conducted a limited search along the lines of symmetry and found structures with acceptable tilt patterns inBbmmon a `21/22 × 21/2 × 2' unit cell. A non-centrosymmetric version has been reported in niobates, inBbm2 on the same unit cell.

The crystallographic chameleon: when space groups change skin

2016 ◽  
Vol 72 (5) ◽  
pp. 523-538 ◽  
Author(s):  
Massimo Nespolo ◽  
Mois I. Aroyo
Keyword(s):  
Space Group ◽  
Practical Applications ◽  
Space Groups ◽  
Common Substructure ◽  
Group Information ◽  
Alternative Setting ◽  
The Common ◽  
Alternative Settings ◽  
Unnecessary Complication ◽  
Symmetry Operations

VolumeAofInternational Tables for Crystallographyis the reference for space-group information. However, the content is not exhaustive because for many space groups a variety of settings may be chosen but not all of them are described in detail or even fully listed. The use of alternative settings may seem an unnecessary complication when the purpose is just to describe a crystal structure; however, these are of the utmost importance for a number of tasks, such as the investigation of structure relations between polymorphs or derivative structures, the study of pseudo-symmetry and its potential consequences, and the analysis of the common substructure of twins. The aim of the article is twofold: (i) to present a guide to expressing the symmetry operations, the Hermann–Mauguin symbols and the Wyckoff positions of a space group in an alternative setting, and (ii) to point to alternative settings of space groups of possible practical applications and not listed in VolumeAofInternational Tables for Crystallography.

Space-group and origin ambiguity in macromolecular structures with pseudo-symmetry and its treatment with the programZanuda

2014 ◽  
Vol 70 (9) ◽  
pp. 2430-2443 ◽  
Author(s):  
Andrey A. Lebedev ◽  
Michail N. Isupov
Keyword(s):  
Unit Cell ◽  
Unit Cell Parameters ◽  
Incorrect Choice ◽  
Space Group ◽  
Cell Parameters ◽  
Crystallographic Symmetry ◽  
Symmetry Operations

The presence of pseudo-symmetry in a macromolecular crystal and its interplay with twinning may lead to an incorrect space-group (SG) assignment. Moreover, if the pseudo-symmetry is very close to an exact crystallographic symmetry, the structure can be solved and partially refined in the wrong SG. Typically, in such incorrectly determined structures all or some of the pseudo-symmetry operations are, in effect, taken for crystallographic symmetry operations andvice versa. A mistake only becomes apparent when theRfreeceases to decrease below 0.39 and further model rebuilding and refinement cannot improve the refinement statistics. If pseudo-symmetry includes pseudo-translation, the uncertainty in SG assignment may be associated with an incorrect choice of origin, as demonstrated by the series of examples provided here. The programZanudapresented in this article was developed for the automation of SG validation.Zanudaruns a series of refinements in SGs compatible with the observed unit-cell parameters and chooses the model with the highest symmetry SG from a subset of models that have the best refinement statistics.

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