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

作者：Magdysyuk Oxana V; Dinnebier Robert E^*; van Smaalen Sander; Zykin Mikhail A; Kazin Pavel E; Jansen Martin

来源：Zeitschrift fur Kristallographie-Crystalline Materials, 2012, 227(6): 321-333.

DOI：10.1524/zkri.2012.1533

• Powder crystal structure analysis
• X-ray diffraction
• Maximum Entropy Method
• Electron density distribution
• Intercalated apatite

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.

• 出版日期2012