Pair distribution function, Monte Carlo modelling and Factor Analysis: New approaches to EXAFS analysis.

X-ray absorption fine-structure (EXAFS) spectroscopy allows the study of a large number of elements and compounds in different physical and chemical states. The most prominent structural parameters derived from EXAFS are coordination numbers, interatomic distances, static and vibrational disorder expressed by the Debye-Waller factor. These parameters are used in the conventional shell fitting approach to approximate the true radial pair distribution function (PDF). This shell fitting approach has three critical limitations for which we present possible solutions.

a) Due to the approximation of the PDF with Gaussian peak shapes, the conventional shell fitting approaches fails for all systems which show anharmonic contributions to the vibrational or static displacement of atoms, caused for instance by temperature effects or week bonds in adsorbate-adsorbent interactions [1]. To overcome this limitation we present two techniques: (1) a Monte Carlo simulation technique for EXAFS spectra which takes not only the first order scattering, but also higher order scattering into account [2] and (2) a novel application designed for the direct calculation of the PDF from the EXAFS spectrum.

b) Due to the limited resolution in R, the shell fitting approach commonly fails, if the X-ray absorbing atom is present in different chemical environments at the same time, i.e. in case of chemical mixtures. For this case we present a way to isolate the pure spectral components by Iterative Factor Analysis [3] and/or by a mathematical combination of Factor Analysis and Monte Carlo simulation [2].

c) In order to find a unique structural solution, shell fitting tends to be a soft modelling approach, because many structural arrangements may lead to a similar description of the EXAFS signal and have to be tested. Especially for the investigation of the unknown structures of sorption complexes, a hard modelling approach, which can take the complete substrate structure into account, would be much better suited. We show that the Monte Carlo simulation technique can be used as a hard modelling approach to solve the structure of sorption complexes [4].

[1] Crozier, E. D. Impact of the Asymmetric Pair Distribution Function in the Analysis of Xafs. Physica B-Condensed Matter 209, 330-333 (1995).
[2] Rossberg, A. & Scheinost, A. C. Three-dimensional modeling of EXAFS spectral mixtures by combining Monte Carlo Simulations and Target Transformation Factor Analysis. Analytical and Bioanalytical Chemistry 383(1), 56-66 (2005).
[3] Rossberg, A., Reich, T. & Bernhard, G. Complexation of uranium(VI) with protocatechuic acid - application of iterative transformation factor analysis to EXAFS spectroscopy. Analytical and Bioanalytical Chemistry 376, 631-638 (2003).
[4] Ulrich, K.-U., Rossberg, A., Foerstendorf, H., Zänker, H. & Scheinost, A. C. Molecular characterization of uranium(VI) sorption complexes on iron(III)-rich acid mine water colloids. Geochimica Et Cosmochimica Acta 70, 5469-5487 (2006).