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

  • Václav Petříček EMAIL logo , Václav Eigner , Michal Dušek and Antonín Čejchan
Published/Copyright: March 16, 2016
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 231 Issue 5

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.

Keywords: crystal structure analysis; Jana2006; modulated structures
Corresponding author: Václav Petříček, Institute of Physics of the Czech Academy of Sciences, Na Slovance 2, 182 21 Praha 8, Czech Republic, E-mail:

Acknowledgments

We acknowledge support of project No. LO1603 under the Ministry of Education, Youth and Sports National sustainability program I of Czech Republic. We would like thank to both referees for a stimulating discussions and valuable comments.

References

[1] S. van Smaalen, Incommensurate Crystallography, Oxford University Press, Oxford, 2007.10.1093/acprof:oso/9780198570820.001.0001Search in Google Scholar

[2] T. Janssen, G. Chapuis, M. de Boissieu, Aperiodic Crystals, Oxford University Press, Oxford, 2007.10.1093/acprof:oso/9780198567776.001.0001Search in Google Scholar

[3] P. M. de Wollf, T. Janssen, A. Janner, The superspaee groups for incommensurate crystal structures with a one-dimensional modulation. Acta Crystallogr.1981,A37, 625.10.1107/S0567739481001447Search in Google Scholar

[4] V. Petříček, P. Becker, P. Coppens, Structure analysis of displacively modulated molecular crystals. Acta Crystallogr.1985, A41, 478.10.1107/S0108767385001027Search in Google Scholar

[5] V. Petříček, Y. Gao, P. Lee, P. Coppens, The incommensurate modulation in the Bi2Sr2-xCaxCuO6 superconductor and its relation to the modulation in Bi2Sr2–xCaxCu2O8. Phys. Rev. B1990, 42, 387.Search in Google Scholar

[6] V. Petříček, A. van der Lee, M. Evain, On the use of crenel functions for occupationally modulated structures. Acta Crystallogr.1995, A51, 529.10.1107/S0108767395000365Search in Google Scholar

[7] M. Evain, F. Boucher, O. Gourdon, V. Petříček, M. Dušek, P. Bezdíčka, Incommensurate versus commensurate description of the AxBX3 hexagonal perovskite-type structure. Chem. Matter.1998, 14, 3068.10.1021/cm9801800Search in Google Scholar

[8] J. M. Peréz-Mato, M. Zakhour-Nakhl, F. Weill, J. Darriet, Structure of composites A1+x(A′xB1–x)O3 related to the 2H hexagonal perovskite: relation between composition and modulation. J. Mater. Chem.1999, 9, 2795.10.1039/a903723cSearch in Google Scholar

[9] H. Leligny, D. Grebille, O. Pérez, A. C. Masset, Herviue, B. Raveau, A five-dimensional structural investigation of the misfit layer compound [Bi0.87SrO2]2[CoO2]1.82. Acta Crystallogr.2000, B56, 173.10.1107/S0108768199012586Search in Google Scholar

[10] P. M. De Wolff, The pseudo-symmetry of modulated crystal structures. Acta Crystallogr.1974, A30, 777.10.1107/S0567739474010710Search in Google Scholar

[11] L. Palatinus, G. Chapuis, SUPERFLIP – a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions. J. Appl. Cryst.2007, 41, 786.10.1107/S0021889807029238Search in Google Scholar

[12] J. M. Peréz-Mato, G. Madariaga, M. J. Tello, Diffraction symmetry of incommensurate structures. J. Phys. C1986, 19, 2613.10.1088/0022-3719/19/15/008Search in Google Scholar

[13] V. Petříček, P. Coppens, P. Becker, Structure analysis of displacively modulated molecular crystals. Acta Crystallogr.1985, A41, 478.10.1107/S0108767385001027Search in Google Scholar

[14] A. Yamamoto, Structure factor of modulated crystal structures. Acta Crystallogr.1982, A38, 87.10.1107/S0567739482000163Search in Google Scholar

[15] M. Dušek, V. Petříček, L. Palatinus, Advances in solution of modulated structures reflected by Jana system. J. Phys. C2010, 226, 012014.10.1088/1742-6596/226/1/012014Search in Google Scholar

[16] M. Abramowitz, I. A. Stegun, Handbook of mathematical functions, Dover publications, inc., New York, 1972.Search in Google Scholar

[17] V. Petříček, M. Dušek, J. Černák, Modulated one-dimensional structure of [Cd(NH3)3Ni(CN)4]. Acta Cryst. B2005, 61, 280.10.1107/S0108768105012632Search in Google Scholar PubMed

[18] V. Petříček, M. Dušek, L. Palatinus, Crystallographic computing system JANA2006 – general features. Z. Kristallogr.2014, 229, 345.10.1515/zkri-2014-1737Search in Google Scholar

[19] S. van Smaalen, L. Palatinus, Schneider: the maximum-entropy method in superspace. Acta Cryst. A2003,61, 459.10.1107/S010876730301434XSearch in Google Scholar PubMed

Supplemental Material:

The online version of this article (DOI: 10.1515/zkri-2015-1913) offers supplementary material, available to authorized users.

Received: 2015-11-7
Accepted: 2016-2-9
Published Online: 2016-3-16
Published in Print: 2016-5-1

©2016 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Graphical Synopsis
  3. Inorganic Crystal Structures
  4. β-K2Se2 and K2Se4: missing links in the binary system K-Se
  5. Debye function analysis of nanocrystalline gallium oxide γ-Ga2O3
  6. Crystal structure of the alluaudite Ag2Mn3(VO4)3
  7. Organic and Metalorganic Crystal Structures
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  12. Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
  13. Corrigendum
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https://doi.org/10.1515/zkri-2015-1913
Keywords for this article
crystal structure analysis; Jana2006; modulated structures

Articles in the same Issue

  1. Frontmatter
  2. Graphical Synopsis
  3. Inorganic Crystal Structures
  4. β-K2Se2 and K2Se4: missing links in the binary system K-Se
  5. Debye function analysis of nanocrystalline gallium oxide γ-Ga2O3
  6. Crystal structure of the alluaudite Ag2Mn3(VO4)3
  7. Organic and Metalorganic Crystal Structures
  8. Crystal structures of (E)-2-((2-((pyridin-2-yl)hydrazonyl)methyl)phenolic compounds: different sets of classical hydrogen bonds, X–H···Y (X, Y = O, N)
  9. Syntheses, crystal structures and thermal properties of two novel isostructural Co(III) complexes with salophen ligand
  10. Crystal structures and vibrational spectra of biuret co-crystals with cyanuric and glutaric acids, discussion of hydrogen bonding involving carbonyl groups
  11. Crystallographic Computing
  12. Discontinuous modulation functions and their application for analysis of modulated structures with the computing system JANA2006
  13. Corrigendum
  14. Corrigendum to: Disorder, pseudo symmetry and photoluminescence properties of a new diphosphate K2Ba3(P2O7)2
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