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Philosophical Magazine Volume 87, 2007 - Issue 18-21: Proceedings of Aperiodic, 2006
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Original Articles

Mean-field theory of Archimedean and quasicrystalline tilings

T. DoteraKyoto University, Katsura, Kyoto 615-8510, Japan
Pages 3011-3019 | Received 31 Aug 2006, Accepted 24 Oct 2006, Published online: 02 Dec 2010
 
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Abstract

A simple Landau theory of three-component alloy systems under incompressible condition is investigated, which appears to give regions of the phase diagram in which Archimedean tiling phases are stable in two dimensions. Moreover, we find regions where dodecagonal and decagonal quasicrystals appear to be stable. The Alexander–MacTague and Mermin–Troian theories of weak crystallization are revisited.

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