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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.

DOI: 10.1524/zkri.2012.1533 DOI Help

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