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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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SUPERSTRUCTURES AND THE COMMENSURATE APPROXIMATION

SUPERSTRUCTURES AND THE COMMENSURATE APPROXIMATION

Chapter:
(p.113) 5 SUPERSTRUCTURES AND THE COMMENSURATE APPROXIMATION
Source:
Incommensurate Crystallography
Author(s):

Sander Van Smaalen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570820.003.0005

This chapter develops the relation between crystal structures of aperiodic crystals and superstructures. Superstructures are described as commensurately modulated structures, and it is shown that superspace methods can be applied to this particular kind of periodic crystals. Alternatively, superstructures are obtained as the commensurate approximation to incommensurately modulated crystals and composite crystals. Relations are derived between modulation functions and superspace groups of the modulated-structure description, and atomic coordinates and supercell space groups of the superstructure description.

Keywords:   commensurately modulated structure, modulation function, space group, superspace, superspace group

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