EXAFS backscattering amplitude

Figure 4.11. Left Simulated EXAFS spectrum of a dimer such as Cu2, showing that the EXAFS signal is the product of a sine function and a backscattering amplitude F(k) divided by k, as expressed by Eq. (6). Note that F k)/k remains visible as the envelope around the EXAFS signal xW- Right The Cu EXAFS spectrum of a cluster such as CU2O is the sum of a Cu-Cu and a Cu-O contribution. Fourier analysis is the mathematical tool used to...

Final detennination of the structure was made by proposing a structural model with Cu sitting in threefold hollow sites and O atoms on atop sites with respect to the Cu atoms (Fig. 27.16). A program, FEFFIT, was used to analyze the data (Stem et al., 1995). This calculates the phase and amplitude parameters for the various backscatters. The EXAFS for the parallel polarization could be fitted six Cu-Cu interactions at a bond distance of 2.67 A and three Cu-Pt interactions at 2.6 A. For the perpendicular polarization, the data could be fitted one Cu-0 interaction at 1.96 A and three Cu-Pt interactions at 2.6 A. The Cu-Pt bond length is shorter than the sum of the metallic radii of Cu and Pt, which is 2.66 A. This indicates a Cu oxidation state different from zero, which agrees with the XANES results. 

A straightforward Fourier transform of the EXAFS signal does not yield the true radial distribution function. First, the phase shift causes each coordination shell to peak at the incorrect distance second, due to the element-specific backscattering amplitude, the intensity may not be correct. The appropriate corrections can be made, however, when phase shift and amplitude functions are derived from reference samples or from theoretical calculations. The phase- and amplitude-corrected Fourier transform becomes ... 

The reason for multiplying with a k weighting factor is to compensate for the decrease of the EXAFS amplitudes at high k values due to the Debye-Waller factor, the backscattering amplitude, and the k 1 dependence of the EXAFS (see, e.g., Ref. (21)). 

In order to interpret an EXAFS spectrum quantitatively, the phase shifts for the absorber and backscatterer and the backscattering amplitude function must be known. Empirical phase shifts and amplitude functions can be obtained from studies of known structures which are chemically similar to that under investigati-... 

The backscattering amplitude, F)(A), and phase shift, dj k), for the absorber—neighbor pair may be extracted from the EXAFS of reference compounds or calculated theoretically using widely available... 

Because the R term, and the mean-free path of backscattered photoelectrons is small (usually < 25 A), typically the total number of shells rarely exceeds 7. The backscattering amplitude, Fj(k), and phase shift, dj(k), for the absorber-neighbor pair may either be extracted from the EXAFS of reference materials or calculated theoretically using widely available codes such as the FEFF developed by John Rehr s group at the University of Washington. ... 

EXAFS measurements were performed at the MRCAT undulator beam-line equipped with a double-crystal Si (111) monochromator with resolution of better than 4 eV at 11.5 keV (Pt L3 edge). Spectra of the metal solutions contained in plastic cuvettes were taken in fluorescence mode and those of solids as pressed powders in transmission mode. Phase-shift and backscattering amplitudes were obtained from various solid reference compounds. Details of the experimental and fitting procedures can be found in [6]. 

The intensity of the FT peak increases showing that the atoms of the first shell either have a larger backscattering amplitude or are in increasing number. At the end of the process, the characteristic FT of metallic copper is obtained. Figure 11 (a, b, c, d) shows the filtered back-transformed spectra of the first shell. These curves exhibit a continuous decrease of the amplitude of the oscillations with the appearance of a beat node at about 250 eV (Fig. 11c) directly related to the splitting of the Fourier transform. This beat node evidences that two different atoms with a k difference in their phase shifts contribute to the EXAFS oscillations. A direct explanation involves the O and S atoms in the first shell. This is consistent with the EXAFS characteristics drawn from two samples used as standards the... 

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. 

Standard procedures based on WINXAS97 software [10] were used to extract the EXAFS data. Phase shifts and backscattering amplitudes were obtained from EXAFS data for reference compounds Na2Pt(OH)e for Pt-0, H2PtCl6 for Pt-Cl, and Pt foil for Pt-Pt. 

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]...

In both backtransformed EXAFS functions, it can be seen that the envelope of the EXAFS does not drop continuously with k, as was observed with backscat-terers of small atomic number (as oxygen, see Fig.4j, k). Here, we have elements with higher atomic numbers as backscatterers, where Ramsauer-Townsend resonances introduce non-monotonic behavior into the backscattering amplitude functions (see Sect 3.1). 

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. 

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