Commission on Aperiodic Crystals

Commission web page


  • U. Grimm (Chair, UK)
  • G. Borgstahl (USA)
  • M. Dusek (Czech Republic)
  • A. Goldman (USA)
  • J. Hadermann (Belgium)
  • N.K. Mukhopadhyay (India)
  • O. Perez (France)
  • H. Takakura (Japan)
  • J. Wolny (Poland)


  • C. Basilio Pinheiro (Brazil)
  • L. Bindi (Italy)
  • M. de Boissieu (France)
  • R. Lifshitz (Israel)
  • S. van Smaalen (Germany)

Annual Reports

Triennial Reports

Terms of Reference

In the following, by "crystal" is meant any solid having an essentially discrete diffraction diagram, and by "aperiodic crystal" is meant any crystal in which three dimensional lattice periodicity can be considered to be absent. As an extension, the latter term will also include those crystals in which three dimensional periodicity is too weak to describe significant correlations in the atomic configuration, but which can be properly described by crystallographic methods developed for actual aperiodic crystals.

  • To promote the development of common methods and nomenclature for the crystallographic investigation of aperiodic crystals, including modulated structures, polytypes, incommensurate misfit or composite crystals, and quasicrystals.
  • To promote and coordinate scientific interchange among groups working in the field of incommensurate structures, quasicrystals, polytypes and aperiodic crystals in general. In particular, to promote the dissemination of the existing methods for structural analysis, and support the development of new ones.
  • To promote the exchange of adequate samples and / or experimental data sets of these crystals, so that they can be made available to a larger number of groups.
  • To cooperate with the Commission on Crystallographic Nomenclature and other interested groups in the development of a standard nomenclature for dealing with higher dimensional descriptions of aperiodic crystals.
  • To promote cooperation between crystallographers working on aperiodic crystals and mathematicians working in the field of high-dimensional symmetry groups and/or aperiodic systems, and to stimulate the development ot mathematical crystallography.
  • To promote knowledge among crystallographers of superspace or high- dimensional space methods as tools which can also be used to advantage investigation of certain periodic crystal structures.
  • To cooperate with other Commissions of the IUCr in establishing adequate guidelines and standards for articles to be published in IUCr journals reporting structurals investigations of aperiodic crystals and theoretical investigations of aperiodic patterns.
  • To promote and coordinate scientific meetings dealing with aperiodic crystals; in particular to continue the triennial series of meetings begun by the preceding Commision.
  • To advise the IUCr on organizing or sponsoring sessions on aperiodic crystals and/or high-dimensional crystallography at Congresses.