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Aperiodic CrystalsFrom Modulated Phases to Quasicrystals:  Structure and Properties$
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Ted Janssen, Gervais Chapuis, and Marc de Boissieu

Print publication date: 2018

Print ISBN-13: 9780198824442

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198824442.001.0001

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Description and symmetry of aperiodic crystals

Description and symmetry of aperiodic crystals

(p.32) 2 Description and symmetry of aperiodic crystals
Aperiodic Crystals

Ted Janssen

Gervais Chapuis

Marc de Boissieu

Oxford University Press

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

Keywords:   aperiodic function, quasiperiodic function, superspace group, scaling symmetry, magnetic system, approximant

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