Jump to ContentJump to Main Navigation
Aperiodic CrystalsFrom Modulated Phases to Quasicrystals:  Structure and Properties$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 06 March 2021

Origin and stability

Origin and stability

Chapter:
(p.405) 6 Origin and stability
Source:
Aperiodic Crystals
Author(s):

Ted Janssen

Gervais Chapuis

Marc de Boissieu

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198824442.003.0006

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .