Phase fitting, EXAFS analysis

The EXAFS analysis followed standard procedures as described in ref. [11]. The weighted spectra were Fourier transformed within the limits k=4 to k=16. EXAFS of the first Rh-Rh shell was fitted using phase shift and amplitude functions obtained from a Rh foil under the assumption... 

The methods of preparation of solid samples as XAS standards are also of interest. In the early days of EXAFS analysis the eolleetion of data from structurally characterized model compounds was an essential prerequisite for the determination of empirical phase and amplitude functions that were used to conduct curve-fitting analysis of unknown samples. While modern EXAFS analysis relies upon theoretical phases and amplitudes, as discussed above, standard compounds are still important for eliminating other uncertainties, such as that regarding AEq, as discussed in Seetion 4.2.4. Moreover, our understanding of near-edge spectra is vitally dependent upon standard... 

However the determination of the exact distances and the number of ligands was obtained from a fit of the backtransformation of the contribution of each of the shells of Mn.ATP to those of the unknown compounds. In these fits the previously determined (9) backscattering amplitudes the phase shift and the Debey - Waller (SS) factors obtained from the EXAFS analysis of Mn.ATP complex were used. Similar procedures were used for the other compounds. 

Figure 7. Imaginary part and magnitude of Fourier transform (solid lines weighted without phase correction) of a the CoA12 standard compound and b sample E. The results of EXAFS analysis obtained with the best calculated coordination parameters are shown with trian es. The fits were performed over the [1.2-3.2] r range.

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... 

By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

Furthermore, quantitative structural phase analysis, for instance, is important for investigations of solid catalysts, because one frequently has to deal with more than one phase in the active or precursor state of the catalyst. Principal component analysis (PCA) permits a quantitative determination of the number of primary components in a set of experimental XANES or EXAFS spectra. Primary components are those that are sufficient to reconstruct each experimental spectrum by suitable linear combination. Secondary components are those that contain only the noise. The objective of a PCA of a set of experimental spectra is to determine how many "components" (i.e., reference spectra) are required to reconstruct the spectra within the experimental error. Provided that, first, the number of "references" and, second, potential references have been identified, a linear combination fit can be attempted to quantify the amount of each reference in each experimental spectrum. If a PCA is performed prior to XANES data fitting, no assumptions have to be made as to the number of references and the type of reference compounds used, and the fits can be performed with considerably less ambiguity than otherwise. Details of PCA are available in the literature (Malinowski and Flowery, 1980 Ressler et al., 2000). Recently, this approach has been successfully extended to the analysis of EXAFS data measured for mixtures containing various phases (Frenkel et al., 2002). 

The phenomenon of EXAFS has been known for a considerable time (see ref. 126) but it has been applied to obtain structural information within the last decade only. From equation (2) it is seen that neighbour separation depends on the phase of the EXAFS oscillations, while the co-ordination number Nj and thermal correlation factor (Tj depend on the signal amplitude. In 1971 it was shown by Sayers, Stern, and Lytle that an appropriate Fourier analysis of the data gives a radial structure factor (j) R) from which one can locate the positions of the atoms surrounding the atom which absorbs the X-ray photon (for detailed discussion see refs. 123, 128—130). A second method of data analysis, involving curve fitting techniques, has been used also. ... 

One of the serious limitations of EXAFS technique is with regard to phase parameters. These are quite generally obtained from analysis of EXAFS of crystalline compounds of known structure. In order that such phase information be transferable, the structure around the given atom should be very similar. This admittedly is a weakness because the structure of the glass is clearly unknown. Further use of these phase parameters in fitting the experimental EXAFS of a glass imposes a genetic influence on the structure in the sense that it tries to fit the EXAFS of unknown with as many subshells of atoms (as many sets of phase parameters) as there are in the model crystalline compound. 

Analysis of the Pb EXAFS data from the Fe-plaque revealed a Pb-0 interatomic distance of 2.4 A, which is inconsistent with published data for Pb sorbed to Fe-oxides (-2.27 A). Furthermore, optimized fitting of the second shell EXAFS function was obtained for C or N at a distance of 3.4 A, which is longer than previous reports for Pb bound humic material (Hansel et al. 2001). Based on fits that included a sample where Pb was bound to microbial biofilm it was concluded that the Pb was bound to a microbial biofilm-like material apparently intimately associated with the Fe-plaque. This finding demonstrates the important role of microorganisms in rhizosphere processes and the preferential binding of Pb to extracellular polymeric substances even in the presence of a highly reactive high surface area Fe-oxide phase. 

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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