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Incommensurate Crystallography$
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Sander van Smaalen

Print publication date: 2007

Print ISBN-13: 9780198570820

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198570820.001.0001

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Incommensurate Crystallography

Sander Van Smaalen

Oxford University Press

This chapter gives an overview of compounds with incommensurate crystal structures. Superspace is an excellent tool for crystal chemical considerations, as it is demonstrated for selected classes of compounds with incommensurate crystal structures as well as for compounds with periodic structures. The relations between individual compounds of a homologous series can be better understood by employing a unified superspace group and a unified structure model for all compounds in such a series. Relations between commensurately and incommensurately modulated structures of the different phases of A2BX4 type compounds are made explicit by the superspace approach. So-called t-plots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals. They are used to analyse the stability of the incommensurate structures of the chemical elements, and to compute the atomic valences in aperiodic crystals.

Keywords:   composite crystal, element, homologous series, incommensurate, superspace, superspace group, t-plots, valence

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