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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 provides a complete account of the method of structure refinement of incommensurately modulated structures and incommensurate composite crystals. Modulation functions for displacive modulation, for occupational modulation, and for modulation of anisotropic displacement parameters (ADPs; temperature parameters) are described by truncated Fourier series, thus providing the Fourier amplitudes as parameters of the structure model. Constraints and restraints on the structural parameters are discussed, including the use of rigid bodies and non-crystallographic site symmetries. The block-wave (crenel) function and the saw-tooth function are presented as special modulation functions that may be alternatives to Fourier series. Next to structure refinements against single-crystal diffraction data, refinements of incommensurate structures against powder diffraction data (Rietveld refinement) are presented.

Keywords:   constraints, crenel function, diffraction, modulation, restraints, Rietveld refinement, rigid body, site symmetry, saw-tooth function

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