Backscattering amplitude functions

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-... 

Figure 6 shows the backscattering amplitude functions for the first coordination shells of Fe in Na,K(Fe) chabazite and H(Fe) chabazite. The shape of this function, with the singularity at k = 0, is indicative of backscattering by first row elements and... 

Backscattering amplitude functions for first coordination shells In Na,K(Fe) chabazlte and H(Fe) chabazite. 

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). 

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...

Figure 10. Backscattering amplitude as a function of wave vector for C, Si, Ge, Sn, and Pb. (Adapted from Ref. 50.)...

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 ... 

Because of the similarity rn the amplitude functions of platinum and iridium, we do not separate the backscattering contributions of platinum and iridium atoms in the analysis of EXAFS data on platinum-iridium clusters or alloys. In our quantitative treatment of EXAFS arising from nearest neighbor atoms of platinum and iridium, the EXAFS function of Eq. 4.3 consists of only one term, as will be seen in the following discussion. 

The theoretical form of the EXAFS as described by Eq. (11) is a sum of damped sinusoidal functions, with frequencies related to the distance of the absorber atom from the backscattering atoms, and an amplitude function which contains information about the number of backscatterers at that distance. This structural information can be best extracted by the Fourier transform technique, which converts data from k or momentum space into R or distance space. The following Fourier transformation of... 

Equation (11) contains the polarization dependent factor cos Gij, the distance R between the absorber shell j and the backscatterer shell i, Fi(k) is the backscattering amplitude, which forms with both exponential terms the amplitude function js the loss factor, and is the Debye-... 

With regard to the determination of the structural parameters Nj,Rj and Oj, the knowledge of the scattering amplitude function jEj (which depends only on the type of backscattering atoms) and of the phase shin function (which depends... 

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]...

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