Fitting EXAFS data phase shifts

Such a function exhibits peaks (Fig. 9C) that correspond to interatomic distances but are shifted to smaller values (recall the distance correction mentioned above). This finding was a major breakthrough in the analysis of EXAFS data since it allowed ready visualization. However, because of the shift to shorter distances and the effects of truncation, such an approach is generally not employed for accurate distance determination. This approach, however, allows for the use of Fourier filtering techniques which make possible the isolation of individual coordination shells (the dashed line in Fig. 9C represents a Fourier filtering window that isolates the first coordination shell). After Fourier filtering, the data is back-transformed to k space (Fig. 9D), where it is fitted for amplitude and phase. The basic principle behind the curve-fitting analysis is to employ a parameterized function that will model the... 

Figure 2. Normalized, -weighted As-EXAFS spectra (a) and Fourier transforms (FT), b) of natural arsenian pyrite sample Clio-2 and model arsenopyrite (modified from Savage et ai, 2000). Solid line is experimental data, dashed line is least squares fit. The coordination environment of in the two phases is quite different, as indicated by the magnitude and position of oscillations in the As-EXAFS spectra and by the magnitude and position of peaks in the FTs. Peak positions in FTs are not corrected for phase-shift effects, and are therefore approximately 0.5 A shorter than the true distance. Reprinted with permission.

The approach adopted amounts to a trial and error procedure in which a series of values is chosen for OsCu and CuOs subject to the constraint of Eq. 4.12. For each set of trial phase shift functions, Eqs. 4.10 and 4.11 for the function Xi(XT, incorporating expressions of the form of Eq. 4.9 for the various x/MO terms, are fit to the corresponding functions derived from the osmium and copper EXAFS data on the osmium-copper catalyst. The fitting exercise yields values of various structural parameters, including the distance between an osmium atom and a copper atom (nearest neighbor atoms). For a given set of phase shift functions for OsCu and CuOs, limited only by the constraint of Eq. 4.12, this distance as derived from the osmium EXAFS will not in general be equal to the distance derived from the copper EXAFS. 

In Figures 4.16 and 4.17 the uppermost fields (labeled a) illustrate the quality of fit of values of the function KnX](K), represented by the points, to the corresponding function (solid line) derived from the EXAFS data (32). The points were calculated for values of structural parameters corresponding to Af o = —4 eV in Figure 4.15. For the osmium EXAFS in Figure 4.16 the function fitted was K2x K), while for the copper EXAFS in Figure 4.17 it was K3x U0- The fits are excellent except at very low K values. The fits can be improved at the very low K values by modification of the details of the phase shift functions, but there is very little effect of such a modification on the values of the structural parameters obtained. 

In order to determine the nearest neighbor interatomic distance and the Debye-Waller factor, the classical EXAFS fitting procedure was used. Since at ambiant pressure and room temperature krypton is a gas, the backscattering amplitude and the phase shift have been obtained from the data at 15.7 GPa where the lattice parameter was known from X-ray diffraction [32]. Only the variation of the Debye-Waller factor can be measured. 

Fig. 6. Backtransformed CoK edge EXAFS data of the first coordination shell of Co in CoAPO-20 (dashed line) fitted using backscattering amplitude and phase-shift functions determined on cobalt acetate hydrate (solid line). Two different sub-shells of oxygen neighbors are necessary in order to obtain a satisfactory fit. Their individual EXAFS functions are shown by dotted lines [42]...

The results from analysis of the EXAFS data (Fig. 8a) indieate that Pb is associated mainly with two phases Pb-carbonate (45%) and Pb bound to an Fe phase (55%). However, the discrepancy in the XANES fit (Fig. 8b) and the large energy shift in the XANES data for the standard of Pb adsorbed on goethite (Fig. 8c) provide ambiguous data regarding the actual presence of a Pb species associated to Fe-oxyhydroxides in this dust sample and warrant further investigation. A combination of /rXRF and xXRD was used for additional sample characterization, specifically to confirm the presence or absence of a Pb-Fe oxyhydroxide phase. 

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