Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006

Discontinuous modulation functions and their application for analysis of modulated structures... Abstract Discontinuous modulation functions called crenel and saw-tooth have been developed for description and refinement of strongly modulated crystal structures with abrupt changes of modulation parameters. Although used for refinement of many modulated structures and mentioned in books on aperiodic crystals, technical details of such refinements have never been published and remained hidden in the source code of the refinement program Jana2006. In this article we explain how to recognize discontinuous modulations in a Fourier map and how to refine structures where crenel or saw-tooth functions are combined with additional secondary modulation. Three sets of functions suitable for such combination are presented: the traditional ortho-harmonics, and newly developed sets of Legendre polynomials and x-harmonics. Tiny differences between refinements based on particular function sets are demonstrated using simulated as well as existing modulated structures. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für Kristallographie - Crystalline Materials de Gruyter

Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006

Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006


Discontinuous modulation functions called crenel and saw-tooth have been developed for description and refinement of strongly modulated crystal structures with abrupt changes of modulation parameters. Although used for refinement of many modulated structures and mentioned in books on aperiodic crystals, technical details of such refinements have never been published and remained hidden in the source code of the refinement program Jana2006. In this article we explain how to recognize discontinuous modulations in a Fourier map and how to refine structures where crenel or saw-tooth functions are combined with additional secondary modulation. Three sets of functions suitable for such combination are presented: the traditional ortho-harmonics, and newly developed sets of Legendre polynomials and x-harmonics. Tiny differences between refinements based on particular function sets are demonstrated using simulated as well as existing modulated structures. Keywords: crystal structure analysis; Jana2006; modulated structures. Introduction Structure analysis of modulated structures has become well established field of crystallography [1, 2]. The superspace theory as formulated by de Wollf et al. [3] has proven to be the best tool to generalize methods originally developed for solution and refinement of regular structures, and to apply them for calculation of modulated and composite structures. In these systems any structural parameter *Corresponding author: Václav Petícek, Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic, E-mail: petricek@fzu.cz Václav Eigner, Michal Dusek and Antonín Cejchan: Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic (2) The modulated structure is fully described if the set of coefficients p0, psn, pcn is determined for each structural parameter being affected by modulation. The number of summation terms (also called...
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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
2194-4946
eISSN
2196-7105
DOI
10.1515/zkri-2015-1913
Publisher site
See Article on Publisher Site

Abstract

Abstract Discontinuous modulation functions called crenel and saw-tooth have been developed for description and refinement of strongly modulated crystal structures with abrupt changes of modulation parameters. Although used for refinement of many modulated structures and mentioned in books on aperiodic crystals, technical details of such refinements have never been published and remained hidden in the source code of the refinement program Jana2006. In this article we explain how to recognize discontinuous modulations in a Fourier map and how to refine structures where crenel or saw-tooth functions are combined with additional secondary modulation. Three sets of functions suitable for such combination are presented: the traditional ortho-harmonics, and newly developed sets of Legendre polynomials and x-harmonics. Tiny differences between refinements based on particular function sets are demonstrated using simulated as well as existing modulated structures.

Journal

Zeitschrift für Kristallographie - Crystalline Materialsde Gruyter

Published: May 1, 2016

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