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Symmetry 2014, 6(2), 171-188; doi:10.3390/sym6020171

Development of Symmetry Concepts for Aperiodic Crystals

Theoretical Physics, University of Nijmegen, Nijmegen 6525 ED, The Netherlands
Received: 21 February 2014 / Revised: 18 March 2014 / Accepted: 26 March 2014 / Published: 31 March 2014
(This article belongs to the Special Issue Crystal Symmetry and Structure)
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An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. Further extensions use time reversal and time translation operations on magnetic and electrodynamic systems. An alternative description of magnetic structures to that with symmetry groups, the Shubnikov groups, is using representations of space groups. The same can be done for aperiodic crystals. A discussion of the relation between the two approaches is given. Representations of space groups and superspace groups play a role in the study of physical properties. These, and generalizations of them, are discussed for aperiodic crystals. They are used, in particular, for the characterization of phase transitions between aperiodic crystal phases. View Full-Text
Keywords: symmetry; aperiodic crystals; superspace symmetry; aperiodic crystals; superspace

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Janssen, T. Development of Symmetry Concepts for Aperiodic Crystals. Symmetry 2014, 6, 171-188.

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