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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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QUANTITATIVE DESCRIPTION OF THE DIFFRACTION BY APERIODIC CRYSTALS

QUANTITATIVE DESCRIPTION OF THE DIFFRACTION BY APERIODIC CRYSTALS

Chapter:
(p.125) 6 QUANTITATIVE DESCRIPTION OF THE DIFFRACTION BY APERIODIC CRYSTALS
Source:
Incommensurate Crystallography
Author(s):

Sander Van Smaalen

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570820.003.0006

This chapter presents the quantitative analysis of the intensities of Bragg reflections of incommensurately modulated crystals and composite crystals. The observed structure factor is introduced in analogy with the observed structure factor of periodic crystals. The problems of twinning and overlap of reflections are discussed. The effects of atomic vibrations on diffracted intensities are analysed. Phasons, amplitudons, and the sliding mode do not lead to specific forms of the Debye-Waller factor. Instead, Debye-Waller factors that contain modulated anisotropic displacement parameters (ADPs) must be used. The statistical properties of diffracted intensities of incommensurately modulated crystals closely follow the statistical properties of Bragg intensities of periodic crystals.

Keywords:   amplitudon, anisotropic displacement parameter, Debye-Waller factor, observed structure factor, phason, sliding mode, statistical properties, twinning

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