scholarly journals Double crystallographic groups and their representations on the Bilbao Crystallographic Server

2017 ◽  
Vol 50 (5) ◽  
pp. 1457-1477 ◽  
Author(s):  
Luis Elcoro ◽  
Barry Bradlyn ◽  
Zhijun Wang ◽  
Maia G. Vergniory ◽  
Jennifer Cano ◽  
...  
Keyword(s):  
Irreducible Representations ◽  
Site Symmetry ◽  
Crystallographic Groups ◽  
Space Groups ◽  
Symmetry Approach ◽  
Wyckoff Position ◽  
Double Space ◽  
Elementary Band ◽  
Symmetry Relations ◽  
Symmetry Operations

A new section of databases and programs devoted to double crystallographic groups (point and space groups) has been implemented in the Bilbao Crystallographic Server (http://www.cryst.ehu.es). The double crystallographic groups are required in the study of physical systems whose Hamiltonian includes spin-dependent terms. In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups. The new section includes databases of symmetry operations (DGENPOS) and of irreducible representations of the double (point and space) groups (REPRESENTATIONS DPGandREPRESENTATIONS DSG). The toolDCOMPRELprovides compatibility relations between the irreducible representations of double space groups at differentkvectors of the Brillouin zone when there is a group–subgroup relation between the corresponding little groups. The programDSITESYMimplements the so-called site-symmetry approach, which establishes symmetry relations between localized and extended crystal states, using representations of the double groups. As an application of this approach, the programBANDREPcalculates the band representations and the elementary band representations induced from any Wyckoff position of any of the 230 double space groups, giving information about the properties of these bands. Recently, the results ofBANDREPhave been extensively applied in the description of and the search for topological insulators.

scholarly journals The site-symmetry induced representations of layer groups on the Bilbao Crystallographic Server

2019 ◽  
Vol 52 (5) ◽  
pp. 1214-1221 ◽  
Author(s):  
Gemma de la Flor ◽  
Danel Orobengoa ◽  
Robert A. Evarestov ◽  
Yuri E. Kitaev ◽  
Emre Tasci ◽  
...  
Keyword(s):  
Van Der Waals ◽  
Site Symmetry ◽  
Induced Representations ◽  
Symmetry Approach ◽  
Layered Crystals ◽  
Symmetry Relations ◽  
Layer Groups

The section of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) dedicated to subperiodic groups includes a new tool called LSITESYM for the study of materials with layer and multilayer symmetry. This new program, based on the site-symmetry approach, establishes the symmetry relations between localized and extended crystal states using representations of layer groups. The efficiency and utility of the program LSITESYM is demonstrated by illustrative examples, which include the analysis of phonon symmetry in Aurivillius compounds and in van der Waals layered crystals MoS2 and WS2.

Ray representations of point groups and the irreducible representations of space groups and double space groups

1966 ◽  
Vol 260 (1108) ◽  
pp. 1-36 ◽  
Keyword(s):  
Finite Group ◽  
Irreducible Representations ◽  
High Symmetry ◽  
Full Matrix ◽  
Space Groups ◽  
Double Space ◽  
Point Groups ◽  
A Finite Group ◽  
Representations Of Space ◽  
Complex Cases

The theory of the ray representations of a finite group is summarized and full matrix ray representations are derived and tabulated for all thirty-two point groups. It is shown that any irreducible representation of any of the 230 space groups and of the corresponding double groups may be obtained quickly and easily from these ray representations of the point groups. The most complex cases which arise, namely points of high symmetry on the surface of the Brillouin zone for the regular holohedric space groups, 01 ... OJ°, are treated explicitly. The relation of the present work to the recent treatments of Slater and Kovalev is discussed.

Single oxygen vacancy in BaCoO3: Hybrid DFT calculations and local site symmetry approach

2022 ◽  
Vol 375 ◽  
pp. 115835
Author(s):  
Davis Zavickis ◽  
Guntars Zvejnieks ◽  
Andrei Chesnokov ◽  
Denis Gryaznov
Keyword(s):  
Oxygen Vacancy ◽  
Dft Calculations ◽  
Site Symmetry ◽  
Symmetry Approach ◽  
Local Site ◽  
Single Oxygen

scholarly journals First-principles calculations of oxygen interstitials in corundum: a site symmetry approach

2017 ◽  
Vol 19 (37) ◽  
pp. 25245-25251 ◽  
Author(s):  
Robert A. Evarestov ◽  
Alexander Platonenko ◽  
Denis Gryaznov ◽  
Yuri F. Zhukovskii ◽  
Eugene A. Kotomin
Keyword(s):  
First Principles ◽  
Symmetry Analysis ◽  
Crystalline Lattice ◽  
Site Symmetry ◽  
First Principles Calculations ◽  
Symmetry Approach ◽  
Spatial Configurations ◽  
A Site

Site symmetry analysis allows one to define four possible spatial configurations for inserting O atoms into the α-Al2O3 crystalline lattice.

scholarly journals Open Meeting of the Commission on International Tables for Crystallography

2014 ◽  
Vol 70 (a1) ◽  
pp. C1782-C1782
Author(s):  
Carolyn Brock
Keyword(s):  
Reciprocal Space ◽  
Group Symmetry ◽  
Biological Macromolecules ◽  
Planning Stage ◽  
Space Groups ◽  
3 Dimensional ◽  
Magnetic Structures ◽  
Open Meeting ◽  
Symmetry Relations ◽  
Physical And Chemical

The development of the seriesInternational Tables for Crystallographysince the 2011 Congress in Madrid will be discussed. The series includes eight published volumes with a ninth expected before the end of 2014 and definite plans for a tenth. A new edition of Volume A (Space-group symmetry, Editor Mois Aroyo) is nearly ready. A great deal of work has been done on the associated onlineSymmetry Database. Volume A1 (Symmetry relations between space groups, 2011, editors Hans Wondratschek and Ulrich Müller) is the companion volume. Work on a revision of theBrief Teaching Editionwill begin once the new Volume A is finished. Volume B (Reciprocal space, 2010; Editor Gervais Chapuis, who succeeded Uri Shmueli in 2011) and Volume C (Mathematical, physical and chemical tables, 2006, Editor Richard Welberry) are undergoing revisions, which will be major. The volumes will be reorganized with those topics connected to reciprocal space in B and those connected to direct space in C. A new edition of Volume D (Physical properties of crystals, Editor André Authier) was completed in 2013. A new edition of Volume F (Crystallography of biological macromolecules, Editors Eddy Arnold, Daniel Himmel, and Michael Rossmann) appeared in 2012. A new Volume H onPowder diffraction(Editors Chris Gilmore, Jim Kaduk, and Henk Schenk) is nearing completion. A new Volume I onXAFS(Editors Chris Chantler, Federico Boscherini, and Bruce Bunker) is in the planning stage. The Commission on Magnetic Structures is developing plans for a volume. In the meantime Danny Litvin's compilation of 1-, 2-, and 3-dimensional magnetic subperiodic groups and space groups was published as an e-book by the IUCr in 2013. Ideas for future developments will be welcome.

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