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The symmetry of quasiperiodic crystals

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  • Lifshitz, R.

Abstract

Experimentally observed crystals range from periodic crystals, through incommensurately modulated crystals and composite crystals, to quasicrystals and even modulated quasicrystals. How does one characterize in a unified manner the symmetry of all these types of crystals? How does one classify all crystals according to their symmetry? These questions are answered through a review of the Fourier-space approach to crystal symmetry of Rokhsar, Wright, and Mermin. The notion of indistinguishability, which is central to the approach, is introduced and used as the basis for a generalization of the traditional space-group classification scheme, applicable to all types of crystals known to date.

Suggested Citation

  • Lifshitz, R., 1996. "The symmetry of quasiperiodic crystals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 232(3), pages 633-647.
    • Handle: RePEc:eee:phsmap:v:232:y:1996:i:3:p:633-647
    DOI: 10.1016/0378-4371(96)00173-2
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