Reciprocal Space and Irreducible Representations of Space Groups

1986 ◽  
pp. 78-87
Author(s):  
Hugo Friedrich Franzen
Keyword(s):  
Reciprocal Space ◽  
Irreducible Representations ◽  
Space Groups ◽  
Representations Of Space

Irreducible representations of space groups and superspace symmetry

1984 ◽  
Vol 53 (1) ◽  
pp. 293-296 ◽  
Author(s):  
J. M. Perez Mato ◽  
G. Madariaga ◽  
M. J. Tello
Keyword(s):  
Irreducible Representations ◽  
Space Groups ◽  
Representations Of Space

Brillouin-zone database on theBilbao Crystallographic Server

2014 ◽  
Vol 70 (2) ◽  
pp. 126-137 ◽  
Author(s):  
Mois I. Aroyo ◽  
Danel Orobengoa ◽  
Gemma de la Flor ◽  
Emre S. Tasci ◽  
J. Manuel Perez-Mato ◽  
...  
Keyword(s):  
New York ◽  
Brillouin Zone ◽  
Irreducible Representations ◽  
Group Representations ◽  
General Introduction ◽  
Space Groups ◽  
Symmetry Properties ◽  
Parameter Ranges ◽  
Representations Of Space

The Brillouin-zone database of theBilbao Crystallographic Server(http://www.cryst.ehu.es) offersk-vector tables and figures which form the background of a classification of the irreducible representations of all 230 space groups. The symmetry properties of the wavevectors are described by the so-called reciprocal-space groups and this classification scheme is compared with the classification of Cracknellet al.[Kronecker Product Tables, Vol. 1,General Introduction and Tables of Irreducible Representations of Space Groups(1979). New York: IFI/Plenum]. The compilation provides a solution to the problems of uniqueness and completeness of space-group representations by specifying the independent parameter ranges of general and specialkvectors. Guides to thek-vector tables and figures explain the content and arrangement of the data. Recent improvements and modifications of the Brillouin-zone database, including new tables and figures for the trigonal, hexagonal and monoclinic space groups, are discussed in detail and illustrated by several examples.

Decomposition of Plane Waves into Irreducible Representations of Space Groups

1995 ◽  
Vol 50 (6) ◽  
pp. 577-583
Author(s):  
H. Teuscher ◽  
P. Kramer
Keyword(s):  
Dirichlet Problem ◽  
Representation Theory ◽  
Boundary Problem ◽  
Plane Waves ◽  
Neumann Boundary ◽  
Basis Functions ◽  
Irreducible Representations ◽  
Space Groups ◽  
Crystallographic Space Groups ◽  
Representations Of Space

Abstract Using a relation between representation theory of crystallographic space groups and a Dirichlet type of boundary problem for the Laplacian, we derive the solutions for the Dirichlet problem, as well as for a similar Neumann boundary problem, by a complete decomposition of plane waves into irreducible representations of a particular space group. This decomposition corresponds to a basis transformation in L2(Ω) and yields a new set of basis functions adapted to the symmetry of the lattice considered.

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