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Maximum entropy method and charge flipping, a powerful combination to visualize the true nature of structural disorder from in situ X-ray powder diffraction data

Title data

Samy, Ali ; Dinnebier, Robert E. ; van Smaalen, Sander ; Jansen, Martin:
Maximum entropy method and charge flipping, a powerful combination to visualize the true nature of structural disorder from in situ X-ray powder diffraction data.
In: Acta Crystallographica Section B. Vol. 66 (April 2010) Issue 2 . - pp. 184-195.
ISSN 2052-5206
DOI: https://doi.org/10.1107/S0108768109052616

Official URL: Volltext

Abstract in another language

In a systematic approach, the ability of the Maximum Entropy Method (MEM) to reconstruct the most probable electron density of highly disordered crystal structures from X-ray powder diffraction data was evaluated. As a case study, the ambient temperature crystal structures of disordered α-Rb₂[C₂O₄] and α-Rb₂[CO₃] and ordered δ-K₂[C₂O₄] were investigated in detail with the aim of revealing the `true' nature of the apparent disorder. Different combinations of F (based on phased structure factors) and G constraints (based on structure-factor amplitudes) from different sources were applied in MEM calculations. In particular, a new combination of the MEM with the recently developed charge-flipping algorithm with histogram matching for powder diffraction data (pCF) was successfully introduced to avoid the inevitable bias of the phases of the structure-factor amplitudes by the Rietveld model. Completely ab initio electron-density distributions have been obtained with the MEM applied to a combination of structure-factor amplitudes from Le Bail fits with phases derived from pCF. All features of the crystal structures, in particular the disorder of the oxalate and carbonate anions, and the displacements of the cations, are clearly obtained. This approach bears the potential of a fast method of electron-density determination, even for highly disordered materials. All the MEM maps obtained in this work were compared with the MEM map derived from the best Rietveld refined model. In general, the phased observed structure factors obtained from Rietveld refinement (applying F and G constraints) were found to give the closest description of the experimental data and thus lead to the most accurate image of the actual disorder.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: charge flipping; maximum entropy method; disorder; X-ray powder diffraction
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences > Chair Crystallography
Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences > Chair Crystallography > Chair Crystallography - Univ.-Prof. Dr. Sander van Smaalen
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Group Material Sciences
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 530 Physics
Date Deposited: 07 Aug 2015 08:27
Last Modified: 07 Aug 2015 08:40
URI: https://eref.uni-bayreuth.de/id/eprint/17601