Reconstructions of electron density by the Maximum Entropy Method from X-ray powder diffraction data based on incomplete and complete crystal structure models: a case study of apatites with different intercalated metal atoms

Oxana V. Magdysyuk; Robert E. Dinnebier; Sander van Smaalen; Mikhail A. Zykin; Pavel E. Kazin; Martin Jansen

doi:10.1524/zkri.2012.1533

Published by De Gruyter (O) June 6, 2012

Reconstructions of electron density by the Maximum Entropy Method from X-ray powder diffraction data based on incomplete and complete crystal structure models: a case study of apatites with different intercalated metal atoms

Oxana V. Magdysyuk , Robert E. Dinnebier , Sander van Smaalen , Mikhail A. Zykin , Pavel E. Kazin and Martin Jansen

From the journal Zeitschrift für Kristallographie

https://doi.org/10.1524/zkri.2012.1533

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Abstract

In a systematic approach, the ability of the Maximum Entropy Method (MEM) for localization of missing atoms with low occupancies in the crystal structure from X-ray powder diffraction data and for reconstruction of the most probable electron density distribution of these atoms was evaluated. As a case study, the ambient-temperature crystal structures of Sr- and Ca-apatites with different intercalated metal atoms in the hexagonal channels were investigated in detail. Different combinations of F-constraints (based on the observed structure factors) and G-constraints (based on the structure factors amplitudes of overlapping reflections) were used in the MEM calculations. In particular, a combination of amplitudes of structure factors from a Le Bail fit with phases from Rietveld refinement of the incomplete structure was successfully applied for the localization of missing atoms in centrosymmetric crystal structures.

Keywords: X-ray powder diffraction; Maximum Entropy Method; Electron density distribution; Intercalated apatite

^* Correspondence address: Max-Planck-Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Deutschland, r.dinnebier@fkf.mpg.de

Published Online: 2012-06-06

Published in Print: 2012-06

Reconstructions of electron density by the Maximum Entropy Method from X-ray powder diffraction data based on incomplete and complete crystal structure models: a case study of apatites with different intercalated metal atoms

Abstract

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