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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Cockayne, E. (2000). Random Tiling Models for Quasicrystals. In: Axel, F., DĂ©noyer, 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
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