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

Print publication date: 2018

Print ISBN-13: 9780198824442

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198824442.001.0001

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Origin and stability

Origin and stability

(p.405) 6 Origin and stability
Aperiodic Crystals

Ted Janssen

Gervais Chapuis

Marc de Boissieu

Oxford University Press

The origin of the stability of aperiodic systems is very difficult to answer. Often the terms ‘competitive forces’ or ‘frustration’ have been proposed as the origin of stability. The role of Fermi surfaces and Brillouin zone boundary have also been invoked. This chapter deals with the numerous attempts which have been proposed for a better understanding. First, the Landau theory of phase transition, which has often been applied to understand the stability of incommensurate and composite systems, is presented here. Various semi-microscopic models are also proposed, in particular the Frenkel–Kontorova and Frank–Van der Merwe models, as well as spin models. Phase diagrams have been calculated with some success with the ANNI and DIFFOUR models. For quasicrystals, only the simplest general features are found in model systems. For a better understanding, more complex calculations are required, using, for example, ab initio methods. The chapter also discusses electronic instabilities, charge-density systems, Hume–Rothery compounds, and the growth of quasicrystals.

Keywords:   Landau theory, semi-microscopic model, spin model, electronic instability, charge-density system, Hume–Rothery compound, growth of quasicrystals

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