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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.
Authors:
Oxana
Magdysyuk
(Max Planck Institute for Solid State Research, Stuttgart, Diamond Light Source)
,
Robert
Dinnebier
(Max Planck Institute for Solid State Research, Stuttgart)
,
Sander
Van Smaalen
(University of Bayreuth, Laboratory of Crystallography)
,
Mikhail
Zykin
(Moscow State University, Department of Materials Science, Moscow)
,
Pavel
Kazin
(Moscow State University, Department of Chemistry, Moscow)
,
Martin
Jansen
(Max Planck Institute for Solid State Research)
Co-authored by industrial partner:
No
Type:
Journal Paper
Journal:
Zeitschrift Fur Kristallographie - Crystalline Materials
, VOL 227 (6)
, PAGES 321-333
State:
Published (Approved)
Published:
June 2012
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.
Journal Keywords: X-Ray Powder Diffraction; Maximum Entropy Method; Electron Density Distribution; Intercalated Apatite
Subject Areas:
Physics,
Materials,
Chemistry
Instruments:
I11-High Resolution Powder Diffraction