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From Quasicrystals to More Complex Systems pp 115–143Cite as

Random Tiling Models for Quasicrystals

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Part of the book series: Centre de Physique des Houches ((LHWINTER,volume 13))

Abstract

Random tiling models for quasicrystals were introduced in 1985 [1] in the context of discussing the possible role of tiling entropy in stabilizing the thenrecently-discovered quasicrystalline phase [2]. In fact, provided that certain conditions hold, entropic stabilization of a quasicrystalline tiling in three dimensions (3D) will produce a structure whose diffraction pattern contains Bragg peaks. An excellent and thorough overview of random tiling theory can be found in Henley’s 1991 review article [3]. The aim of this lecture is to give a pedagogical review of the most important ideas and results in random tiling theory, including more recent developments.

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Author information

Authors and Affiliations

  1. Department of Applied Physics, Yale University, P.O. Box 208284, New Haven, Connecticut, 06520-8284, USA

    E. Cockayne

  2. Ceramics Division, Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland, 20899-8520, USA

    E. Cockayne

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  1. E. Cockayne
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Editors and Affiliations

  1. Physique des Solides, Bât. 510, F-91405, Orsay Cedex, France

    Françoise Axel  & Françoise Dénoyer  & 

  2. LPTMC, Univ. Paris 7 — Denis Diderot, F-75251, Paris Cedex 05, France

    Jean-Pierre Gazeau

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Cockayne, E. (2000). Random Tiling Models for Quasicrystals. In: Axel, F., Dénoyer, F., Gazeau, JP. (eds) From Quasicrystals to More Complex Systems. Centre de Physique des Houches, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04253-3_5

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  • DOI: https://doi.org/10.1007/978-3-662-04253-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67464-1

  • Online ISBN: 978-3-662-04253-3

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