Modulation functions of incommensurately modulated Cr₂P₂O₇ studied by the maximum entropy method (MEM)

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Li, Liang ; Schönleber, Andreas ; van Smaalen, Sander:
Modulation functions of incommensurately modulated Cr₂P₂O₇ studied by the maximum entropy method (MEM).
In: Acta Crystallographica Section B. Bd. 66 (2010) Heft 2 . - S. 130-140.
ISSN 2052-5206
DOI: https://doi.org/10.1107/S0108768110003393

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Abstract

The maximum entropy method (MEM) has been used to determine electron density in superspace of incommensurately modulated chromium pyrophosphate from X-ray diffraction data measured by Palatinus et al. (2006), Acta Cryst. B 62, 556-566. Chromium pyrophosphate, Cr₂P₂O₇, contains ordered regions (83% of the volume) and regions with disorder. Analysis of the MEM density has allowed the determination of the displacive modulation functions within ordered regions. The disordered regions can be described as the alternate occupation of two conformations of the pyrophosphate group and two positions of the chromium atom, with occupational probabilities that depend continuously on the phase of modulation t. A structure model based on the interpretation of the MEM density provides a fit to the diffraction data of the same quality as the model given by Palatinus et al. (2006). The failure to find a model that better fits the data is attributed to the intrinsic inaccuracy of ∼ 0.01 Å for positions derived from the MEM and to the difficulties in constructing an appropriate model for the anharmonic ADPs and their modulation functions from electron densities.