Easy and Uneasy Superspace Groups for Incommensurate Crystals

  • P. M. de Wolff


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.


Point Group Modulation Vector Symmetry Operation Symmetry Element Symmetry Direction 
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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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