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.

scholarly journals From patterns to space groups and the eigensymmetry of crystallographic orbits: a reinterpretation of some symmetry diagrams in IUCr Teaching Pamphlet No. 14

2012 ◽  
Vol 45 (4) ◽  
pp. 834-837
Author(s):  
Leopoldo Suescun ◽  
Massimo Nespolo
Keyword(s):  
Alternative Interpretation ◽  
Polar Space ◽  
Space Group ◽  
Space Groups ◽  
General Orbit

The space group of a crystal pattern is the intersection group of the eigensymmetries of the crystallographic orbits corresponding to the occupied Wyckoff positions. Polar space groups without symmetry elements with glide or screw components smaller than 1/2 do not contain characteristic orbits and cannot be realized in patterns (structures) made by only one crystallographic type of object (atom). The space-group diagram of the general orbit for this type of group has an eigensymmetry that corresponds to a special orbit in a centrosymmetric supergroup of the generating group. This fact is often overlooked, as shown in the proposed solution for Plates (i)–(vi) of IUCr Teaching Pamphlet No. 14, and an alternative interpretation is given.

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.

Extension of three-dimensional space-group generators to the (3+1) case

1999 ◽  
Vol 32 (3) ◽  
pp. 452-455
Author(s):  
Kazimierz Stróż
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Group ◽  
Space Groups ◽  
Symmetry Operations ◽  
Three Dimensional Space

A method of building up the generators of 775 (3+1)-dimensional superspace groups is proposed. The generators are based on the conventional space-group generators selected by Wondratschek and applied in theInternational Tables for Crystallography(1995, Vol. A). By the method, the generation of (3+1) space groups is found to be easier, the description of symmetry operations is closer to that used for the conventional space groups, and ambiguities in the (3+1) group notation are avoided.

SPGGEN: a computer program for retrieval of space-group information in several settings and generator-containing space-group symbols

2016 ◽  
Vol 49 (4) ◽  
pp. 1370-1376 ◽  
Author(s):  
Uri Shmueli
Keyword(s):  
Computer Program ◽  
Dimensional Space ◽  
Three Dimensional ◽  
General Setting ◽  
Detailed Comparison ◽  
Space Group ◽  
Space Groups ◽  
Group Number ◽  
Group Information ◽  
Three Dimensional Space

A brief outline of the algorithm for the derivation of a space group is followed by a detailed description of the explicit space-group symbols here employed. These space-group symbols are unique insofar as they contain explicitly the generators of the space group dealt with. Next, the implementation of the above in a computer program,SPGGEN, is briefly discussed and the options presented by the program are outlined. Briefly, these options are (i) conventional derivation of the space group from an explicit symbol, including a user-defined one; (ii) such derivation from the conventional space-group number only; (iii) introduction of a general setting into the derivation; (iv) introduction of a Cartesian setting into the derivation; and (v) treatment of some non-conventional settings of orthorhombic space groups. This is followed by a detailed comparison withInternational Tables for Crystallography, Vol. A, and by examples of the output ofSPGGEN. A complete tabulation of the explicit three-dimensional space-group symbols is readily accessed.

Symmetry and space Groups

2010 ◽  
Author(s):  
Jenny Pickworth Glusker ◽  
Kenneth N. Trueblood
Keyword(s):  
Fundamental Property ◽  
Natural World ◽  
Symmetry Operation ◽  
Bravais Lattice ◽  
High Symmetry ◽  
Space Group ◽  
Space Groups ◽  
The Difference ◽  
Symmetry Operations ◽  
The Way

A certain degree of symmetry is apparent in much of the natural world, as well as in many of our creations in art, architecture, and technology. Objects with high symmetry are generally regarded with pleasure. Symmetry is perhaps the most fundamental property of the crystalline state and is a reason that gemstones have been so appreciated throughout the ages. This chapter introduces some of the fundamental concepts of symmetry—symmetry operations, symmetry elements, and the combinations of these characteristics of finite objects (point symmetry) and infinite objects (space symmetry)—as well as the way these concepts are applied in the study of crystals. An object is said to be symmetrical if after some movement, real or imagined, it is or would be indistinguishable (in appearance and other discernible properties) from the way it was initially. The movement, which might be, for example, a rotation about some fixed axis or a mirror-like reflection through some plane or a translation of the entire object in a given direction, is called a symmetry operation. The geometrical entity with respect to which the symmetry operation is performed, an axis or a plane in the examples cited, is called a symmetry element. Symmetry operations are actions that can be carried out, while symmetry elements are descriptions of possible symmetry operations. The difference between these two symmetry terms is important. It is possible not only to determine the crystal system of a given crystalline specimen by analysis of the intensities of the Bragg reflections in the diffraction pattern of the crystal, but also to learn much more about its symmetry, including its Bravais lattice and the probable space group. As indicated in Chapter 2, the 230 space groups represent the distinct ways of arranging identical objects on one of the 14 Bravais lattices by the use of certain symmetry operations to be described below. The determination of the space group of a crystal is important because it may reveal some symmetry within the contents of the unit cell.

Ferroelectric–paraelectric phase transitions with no group–supergroup relation between the space groups of both phases?

2001 ◽  
Vol 57 (4) ◽  
pp. 599-601 ◽  
Author(s):  
E. Kroumova ◽  
M. I. Aroyo ◽  
J. M. Pérez-Mato ◽  
R. Hundt
Keyword(s):  
Phase Transitions ◽  
Room Temperature ◽  
Paraelectric Phase ◽  
Polar Space ◽  
Space Group ◽  
Space Groups ◽  
Actual Space

The structures of Sr3(FeF6)2, β-NbO2, TlBO2 and CrOF3, previously reported as possible ferroelectrics with no group–supergroup relation between the ferroelectric and the paraelectric symmetries, have been carefully studied. We could not confirm any structural pseudosymmetry with respect to a space group which is not a supergroup of their room-temperature polar space group. In all cases, pseudosymmetry was indeed detected, but only for non-polar supergroups of the actual space groups of the structures. In this sense, the four compounds are possible ferroelectrics, but fulfilling the usual group–supergroup relation between the phase symmetries.

Algorithms for deriving crystallographic space-group information

1999 ◽  
Vol 55 (2) ◽  
pp. 383-395 ◽  
Author(s):  
R. W. Grosse-Kunstleve
Keyword(s):  
Three Dimensional ◽  
Basis Matrix ◽  
Space Group ◽  
Space Groups ◽  
Group Type ◽  
Group Information ◽  
Commercial Applications ◽  
Crystallographic Space Groups ◽  
Symmetry Operations

Algorithms are presented for three-dimensional crystallographic space groups, handling tasks such as the generation of symmetry operations, the characterization of symmetry operations (determination of rotation-part type, axis direction, sense of rotation, screw or glide part and location part), the determination of space-group type [identified by the space-group number of the International Tables for Crystallography (Dordrecht: Kluwer Academic Publishers)] and the generation of structure-seminvariant vectors and moduli. The latter are an algebraic description of allowed origin shifts, which are important in crystal structure determination methods or for comparing crystal structures. The space-group type determination produces a change-of-basis matrix which transforms a given space-group representation to the standard one according to the International Tables for Crystallography. The algorithms were implemented and tested using the SgInfo library. The source code is free for non-commercial applications.

Magnetic symmetry in the Bilbao Crystallographic Server: a computer program to provide systematic absences of magnetic neutron diffraction

2012 ◽  
Vol 45 (6) ◽  
pp. 1236-1247 ◽  
Author(s):  
Samuel V. Gallego ◽  
Emre S. Tasci ◽  
Gemma de la Flor ◽  
J. Manuel Perez-Mato ◽  
Mois I. Aroyo
Keyword(s):  
Neutron Diffraction ◽  
Computer Program ◽  
Magnetic Moments ◽  
General Information ◽  
Resolving Power ◽  
Space Groups ◽  
Magnetic Structures ◽  
Starting Point ◽  
Magnetic Symmetry ◽  
Symmetry Operations

MAGNEXTis a new computer program available from the Bilbao Crystallographic Server (http://www.cryst.ehu.es) that provides symmetry-forced systematic absences or extinction rules of magnetic nonpolarized neutron diffraction. For any chosen Shubnikov magnetic space group, the program lists all systematic absences, and it can also be used to obtain the list of the magnetic space groups compatible with a particular set of observed systematic absences. Absences corresponding to specific ordering modes can be derived by introducing effective symmetry operations associated with them. Although systematic extinctions in neutron diffraction do not possess the strong symmetry-resolving power of those in nonmagnetic crystallography, they can be important for the determination of some magnetic structures. In addition,MAGNEXTprovides the symmetry-adapted form of the magnetic structure factor for different types of diffraction vectors, which can then be used to predict additional extinctions caused by some prevailing orientation of the atomic magnetic moments. This program, together with a database containing comprehensive general information on the symmetry operations and the Wyckoff positions of the 1651 magnetic space groups, is the starting point of a new section in the Bilbao Crystallographic Server devoted to magnetic symmetry and its applications.

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