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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.

zeitschrift für kristallographie

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