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

Print publication date: 2007

Print ISBN-13: 9780198567776

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198567776.001.0001

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Aperiodic Crystals

Ted Janssen

Gervais Chapuis

Marc de Boissieu

Oxford University Press

This chapter discusses the physical properties of aperiodic crystals. Topics covered include tensorial properties, hydrodynamics, phonons, phasons, non-linear excitations, and electrons. It is shown that phonons and electrons in quasiperiodic crystals behave differently from those in periodic crystals. The most important differences include: (i) phonon eigenvectors and electron states occur as extended, as found in all periodic crystals, but they also occur as localized or as critical; (ii) quasiperiodic crystals show examples of absolute continuous, singular continuous, and point parts in their spectra; and (iii) electron and phonon dispersion curves have an infinite number of gaps, although these may be negligible for modulated phases and composites.

Keywords:   aperiodic crystals, tensorial properties, hydrodynamics, phonons, phasons, non-linear excitations, electrons

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