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Easy and Uneasy Superspace Groups for Incommensurate Crystals

  • P. M. de Wolff

Abstract

The symmetry of an incommensurate crystal structure is usually expressed by its superspace group G. Alternatively one may examine the symmetry G’ of the n-fold superstructure which results when a free coefficient of the modulation vector is replaced by a rational number p/n. It turns out that G’ accounts for all symmetry elements of G only in certain cases: ‘easy’ superspace groups G. Even for them, this may depend on the parity of n. For many superspace groups, G’ never accounts for all symmetry elements, no matter whether n is odd or even: ‘uneasy’ superspace groups G. The symmetry groups which so far have been reliably shown to occur point to a strong and perhaps even exclusive preference for easy groups.

Keywords

Point Group Modulation Vector Symmetry Operation Symmetry Element Symmetry Direction 
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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References

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    P. M. de Wolff, T. Janssen, and A. Janner, The superspace groups for incommensurate crystal structures with a one-dimensional modulation, Acta Cryst. A37:625 (1981).Google Scholar
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    P. M. de Wolff, Dualistic interpretation of the symmetry of incommensurate structures, Acta Cryst. A40:34 (1984).Google Scholar
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    A. C. R. Hogervorst, “Comparative study of the modulated structures in Rb2ZnBr4 and in related compounds”. Thesis Technical University Delft (1986).Google Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • P. M. de Wolff
    • 1
  1. 1.Lab. voor Technische NatuurkundeDelftThe Netherlands

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