Fitting EXAFS data

After treatment at 373 K in helium flow, the coordination numbers of Mo-0, Mo-S and Mo-Mo were not largely different from those in the cluster 1 and the distances of Mo-0, Mo-S and Mo-Mo were hardly changed. After treatment at 573 K in He flow, however, the color of NaY changed from brown to black and the curve fitting results of the EXAFS data exhibited lower coordination numbers of all interactions than those of the cluster 1. The decrease in the coordination number seems to be not due to the decrease in sulfur amount in the catalyst but to the disordering of each interaction since the S/Mo ratio hardly decreased after thermal treatment. These results show that the structure of the cluster 1 loaded on NaY was maintained at 373 K, but lost at 573 K. 

Figure 9. Data reduction and data analysis in EXAFS spectroscopy. (A) EXAFS spectrum x(k) versus k after background removal. (B) The solid curve is the weighted EXAFS spectrum k3x(k) versus k (after multiplying (k) by k3). The dashed curve represents an attempt to fit the data with a two-distance model by the curve-fitting (CF) technique. (C) Fourier transformation (FT) of the weighted EXAFS spectrum in momentum (k) space into the radial distribution function p3(r ) versus r in distance space. The dashed curve is the window function used to filter the major peak in Fourier filtering (FF). (D) Fourier-filtered EXAFS spectrum k3x (k) versus k (solid curve) of the major peak in (C) after back-transforming into k space. The dashed curve attempts to fit the filtered data with a single-distance model. (From Ref. 25, with permission.)...

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... 

Another noteworthy example is x-ray absorption fine structure (EXAFS). EXAFS data contain information on such parameters as coordination number, bond distances, and mean-square displacements for atoms that comprise the first few coordination spheres surrounding an absorbing element of interest. This information is extracted from the EXAFS oscillations, previously isolated from the background and atomic portion of the absorption, using nonlinear least-square fit procedures. It is important in such analyses to compare metrical parameters obtained from experiments on model or reference compounds to those for samples of unknown structure, in order to avoid ambiguity in the interpretation of results and to establish error limits. 

EXAFS data reduction and fitting were carried out using the WinXAS,18 Atoms,19 FEFF,20 and FEFFIT20 programs. The k- and r-ranges were chosen to be 3-15 A-1 and 1.0-3.0 A, respectively. XANES spectra were compared qualitatively after normalization. 

The data collected are subjected to Fourier transformation yielding a peak at the frequency of each sine wave component in the EXAFS. The sine wave frequencies are proportional to the absorber-scatterer (a-s) distance /7IS. Each peak in the display represents a particular shell of atoms. To answer the question of how many of what kind of atom, one must do curve fitting. This requires a reliance on chemical intuition, experience, and adherence to reasonable chemical bond distances expected for the molecule under study. In practice, two methods are used to determine what the back-scattered EXAFS data for a given system should look like. The first, an empirical method, compares the unknown system to known models the second, a theoretical method, calculates the expected behavior of the a-s pair. The empirical method depends on having information on a suitable model, whereas the theoretical method is dependent on having good wave function descriptions of both absorber and scatterer. 

Fourier transformation of Cu EXAFS data gathered on the Cu(MPG) complex reveals two separate peaks representing shells at distances of 1.9 and 2.3 A. When tested for Ns (coordination number), metal-ligand distance (R as), and Debye-Waller parameter difference (Aa2as) followed by comparison to known model compounds, results show that the presence of both a Cu-(N, O) and Cu-S shell is necessary to obtain an adequate fit to the EXAFS data. Therefore it was concluded that a Cu-S bond is present in the compound. 

In order to obtain data with reduced temperature smearing, experiments were also carried out at 77 K. However, such experiments could not be carried out in. situ and the catalysts were thus exposed to air before the measurements. EXAFS data of three catalysts with Co/Mo atomic ratios of 0.0., 0.25, and 0.50 were obtained. The results show many similarities with the data recorded in situ and were fitted in a similar fashion using phase and amplitude functions of the well-crystallized model compound M0S2 recorded at 77 K. The results, which are given in Table III, show that the bond lengths for the first and second coordination shell are the same for all the catalysts and identical to the values obtained for the catalyst recorded in situ (Table II). The coordination numbers for both shells appear, however, to be somewhat smaller. Although coordination numbers determined by EXAFS cannot be expected to be determined with an accuracy better than + 20, the observed reduction... 

The Co/Mo = 0.125 catalyst has all the cobalt atoms present as Co-Mo-S and, therefore, the EXAFS studies of this catalyst can give information about the molybdenum atoms in the Co-Mo-S structure. The Fourier transform (Figure 2c) of the Mo EXAFS of the above catalyst shows the presence of two distinct backscatterer peaks. A fit of the Fourier filtered EXAFS data using the phase and amplitude functions obtained for well-crystallized MoS2 shows (Table II) that the Mo-S and Mo-Mo bond lengths in the catalyst are identical (within 0.01 A) to those present in MoS2 (R =... 

The fit error is defined as [2(Xexp Xcaic) / Xexp where x is the EXAFS data point. The... 

The effects of particle size on the EXAFS region of the XAS spectra are reflected in the coordination numbers obtained in the fits to the EXAFS data. Figure 15 shows the EXAFS or xi ) data and corresponding Fourier transforms for a Pt foil, a Pt02... 

The effect of the applied potential on the XANES region of the XAS spectra for Pt/C catalysts has been briefly introduced above and is related to both the adsorption of H at negative potentials and the formation of the oxide at more positive potentials. The adsorption of H and the formation of oxides are also apparent in the EXAFS and corresponding Fourier transforms, as seen in the work by Herron et al. shown in Figure 15. As the potential is increased from 0.1 to 1.2 V vs SCE, the amplitude of the peak in the Fourier transform at 2.8 A decreases and that at 1.8 A increases. The effect on the EXAFS, (A), data is less easily observed the amplitude of the oscillations at A > 8 A decreases as the potential is increased, with the greatest change seen between 0.8 and 1.0 V. The results of fitting these data are shown in Table 2. Note that a value for the inner potential... 

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