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

Development of Symmetry Concepts for Aperiodic Crystals

email
Received: 21 February 2014; in revised form: 18 March 2014 / Accepted: 26 March 2014 / Published: 31 March 2014
(This article belongs to the Special Issue Crystal Symmetry and Structure)
View Full-Text   |   Download PDF [493 KB, uploaded 31 March 2014]
Abstract: 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.
Keywords: symmetry; aperiodic crystals; superspace
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Export to BibTeX |
EndNote


MDPI and ACS Style

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

AMA Style

Janssen T. Development of Symmetry Concepts for Aperiodic Crystals. Symmetry. 2014; 6(2):171-188.

Chicago/Turabian Style

Janssen, Ted. 2014. "Development of Symmetry Concepts for Aperiodic Crystals." Symmetry 6, no. 2: 171-188.


Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert