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Advances in theoretical crystallography. Color symmetry of defect crystals
Author(s) -
Koptsik V. A.
Publication year - 1975
Publication title -
kristall und technik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0023-4753
DOI - 10.1002/crat.19750100302
Subject(s) - symmetry operation , symmetry (geometry) , point group , symmetry group , crystal (programming language) , space group , rotational symmetry , reciprocal lattice , theoretical physics , physics , crystallography , mathematics , geometry , quantum mechanics , chemistry , x ray crystallography , computer science , diffraction , programming language
The compound (color) groups of symmetry of defect crystals are defined for the first time as subgroups of the wreath product, G ( W ) = WG ⊆ PsG = ( P g 1 ⊗ … ⊗ P gn ) (S) G of two groups, G and P , acting in geometrical and physical subspaces of the matter space, respectively. This definition encloses all the cases of color symmetry that have so far been considered by Heesch; Shubnikov; Belov et al.; Zamorzayev; nan der Waerden et al.; Niggli; Wittke ans other authors. It opens wide new possibilities in the field of physical applications of the group theory. The methods of constructing compound groups and their correspondence to the symmetry of real crystals are discussed in detail. Among the physical applications of the generalized theory there are considered the magnetic symmetry of crystals, the complex symmetry of reciprocal (or Fourier) space, the Mössbauer symmetry of crystals with hyperfine structure of nuclei, the color symmetry of crystal lattices with point defects and the symmetry of crystal growth forms.