Chapter

Crystal structure factors and symmetry

Xiaodong Zou, Sven Hovmöller and Peter Oleynikov

in Electron Crystallography

Published in print August 2011 | ISBN: 9780199580200
Published online January 2012 | e-ISBN: 9780191731211 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199580200.003.0003

Series: International Union of Crystallography Texts on Crystallography

Crystal structure factors and symmetry

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The structure factors, with their hkl indices, amplitudes and phases are dealt with in great detail. With figures, text and formulas the physical meaning of amplitudes and phases is explained. Rotation matrices and translation vectors are described mathematically as well as in figures. Plane group and space group determination from HRTEM images and ED patterns are explained. The relation between electrostatic potential and structure factors (Fourier terms, i.e. reflections) is described with formulas, structure model, EM image, ED pattern and a table of numerical values of amplitudes and phases for the structure Zr2Se.

Keywords: Structure factors; symmetry; amplitudes; phases; Fourier synthesis; rotation matrices; translation vectors; equivalent positions; phase restrictions; systematic absences; space-group determination

Chapter.  14105 words.  Illustrated.

Subjects: Crystallography

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