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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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MODULATED CRYSTALS IN SUPERSPACE

MODULATED CRYSTALS IN SUPERSPACE

Chapter:
(p.26) 2 MODULATED CRYSTALS IN SUPERSPACE
Source:
Incommensurate Crystallography
Author(s):

Sander Van Smaalen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570820.003.0002

This chapter introduces the superspace theory for the description of the crystal structures of incommensurately modulated crystals. Two alternative constructions of superspace are presented. In reciprocal space the observed scattering vectors of Bragg reflections are considered to be the projections of reciprocal lattice points in (3+1)-dimensional superspace. Lattice translations in superspace applied to the atomic positions in three-dimensional, physical space generate the structure model in superspace. Thus, the latter is a periodic structure in superspace by definition. Structure factors of Bragg reflections are shown to be the Fourier transform of the electron density on one unit cell of the superspace lattice. t-Plots are defined, and their use in structural chemistry is demonstrated by the application to the incommensurately modulated structure of Sr2Nb2O7.

Keywords:   Bragg reflection, electron density, incommensurately modulated crystal, reciprocal space, physical space, structure factor, t-plot

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