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Maximum entropy method: an unconventional approach to explore observables related to the electron density in phengites

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Abstract

The maximum entropy method (MEM) is used here to get an insight into the electron density [ρ(r)] of phengites 2M 1 and 3T, paying special attention to the M1-formally empty site and charge distribution. Room temperature single crystal X-ray diffraction data have been used as experimental input for MEM. The results obtained by MEM have been compared with those from conventional structure refinement which, in turn, has provided the prior-electron density to start the entropy maximization process. MEM reveals a comparatively non-committal approach, able to produce information related to the M1-site fractional occupancy, and yields results consistent with those from the difference Fourier synthesis, but free of the uncertainties due to the abrupt truncation of the series. The charge distribution is investigated by means of the notion of ‘‘site basin’’, i.e., those site-centered volumes delimited by a surface such as ∇ρ·n = 0. In particular, we observe: (1) the overall partitioning of the basin total charge between cation and anion sites, and the interlayer site charge seems to depend on sample composition, and (2) the apical-oxygen plane total basin charge and hydroxyl basin charge are presumably related to the polytype. The MEM-determined electron density does not allow full exploration of the critical points for very complex structures as micas, insofar as conventional room temperature experimental diffraction data are used.

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Acknowledgments

Italian Ministry for University and Research (M.U.R.S.T) and Italian National Research Council (C.N.R) are kindly acknowledged for contributing fund to the present study. The authors are indebted to R Papoular for remarks and suggestions which really enhanced the quality of the manuscript.

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Authors and Affiliations

  1. Dipartimento di Chimica e Fisica della Terra e Applicazioni alle Georisorse e ai Rischi Naturali, Università degli Studi di Palermo, Via Archirafi 36, 90123, Palermo, Italy

    Marcello Merli

  2. Dipartimento Scienze della Terra ‘‘A. Desio’’, Università degli Studi di Milano, Via Botticelli 23, 20133, Milan, Italy

    Alessandro Pavese

  3. Consiglio Nazionale delle Ricerche, CNR-IDPA, Sezione di Milano, Via Mangiagalli 34, 20133, Milan, Italy

    Alessandro Pavese

  4. Dipartimento Scienze Mineralogiche e Petrologiche, Università degli Studi di Torino, Via Valperga Caluso 35, 10100, Turin, Italy

    Nadia Curetti

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  1. Marcello Merli
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  2. Alessandro Pavese
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Correspondence to Alessandro Pavese.

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Merli, M., Pavese, A. & Curetti, N. Maximum entropy method: an unconventional approach to explore observables related to the electron density in phengites. Phys Chem Minerals 36, 19–28 (2009). https://doi.org/10.1007/s00269-008-0255-1

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