Statistics of Crystallographic Sites of Central Monatomic Entities

  • Fedor Valach
  • Jan Ondráček
  • Milan Melník
Part of the Inorganic Chemistry Concepts book series (INORGANIC, volume 12)


Nonrigid properties of monatomic entities manifest themselves in the whole geometry of their environs. Until now we studied the statistics of these geometries using radial distributions of interatomic vectors. The classification of surroundings of a certain central monatomic entity MZ+ can be based also on their symmetry. It has group — theoretical properties and it can be described by means of non — crystallographic symmetry point groups, of which there are infinitely many. There is, however, a finite amount of crystallographic point groups, viz. 2 one-dimensional, 10 two-dimensional and 32 three-dimensional point groups. The latest of them also describe the site symmetry of monatomic entity in the crystal structure and thus also the symmetry of its surroundings. Surroundings of monatomic entity means here, however, not only the near surroundings usually consisting of coordinating ligands, but the complete surroundings containing all other non coordinating entities of the structure. The symmetry of an ideal crystal structure — of discontinuum, is described by one of 230 space groups. The site symmetry of each monatomic entity of the structure thus has a certain connection with the relative positions of entities which may be classified based on the conception of lattice complexes.


Irreducible Representation Point Group Standard Representation Symmetry Operation Symmetry Point Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Fedor Valach
    • 1
  • Jan Ondráček
    • 2
  • Milan Melník
    • 3
  1. 1.Department of Chemical Physics and Nuclear TechniqueSlovak Technical UniversityBratislavaČSSR
  2. 2.Institute of Chemical TechnologyComputing CentrePrague-6ČSSR
  3. 3.Department of Inorganic ChemistrySlovak Technical UniversityBratislavaČSSR

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