Experimental EXAFS

One of the basic physical inputs to the SEXAFS analysis is a set of phase shifts for electron scattering off surface atoms. The uncertainty in these is one of the limiting factors in the accuracy of the method. However, in some cases comparison with experimental EXAFS data from bulk material can help in circumventing the phase shift uncertainty essentially the bulk and surface phase shifts are assumed equal and these then divide out in the ratio of the surface to bulk data. 

Calcination temperature (°C) of zeolite support Calculated Experimental (EXAFS) ... 

The DFT optimised cluster FSl is found to have the most energetically favourable free-space structure compared to other clusters investigated and is closest in morphology to silica-bound cluster Bl. Cluster B1 is also found to be the best representative silica-bound cluster with respect to the experimental data found thus far and is compared favourably with the experimental EXAFS data for both coordinations and bond-lengths in ref. 54. Conversely cluster Bl is not found to be the lowest energy cluster structure compared with other possible clusters bound to a silica four-ring in the same manner. 

In addition to conventional shell fitting, authors have used Monte Carlo simulation. During MC calculation, the Cm atom was positioned at random position in the 10 A diameter sphere formed by three coordinating BTP molecules, and the corresponding theoretical EXAFS spectra were calculated and compared with the experimental spectrum. From the best agreement between the theoretical and experimental EXAFS spectra, the Cm-N distances equal to 2.52 A and 2.57, 2.59 A for nitrogen atoms of pyridine and triazine rings, respectively, were obtained. 

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. 

Figure 4.16 Contributions of nearest neighbor copper and osmium backscattering atoms (points in fields b and c, respectively) to the EXAFS associated with the osmium Lm absorption edge of a silica-supported osmium-copper catalyst containing 2 wt% Os and 0.66 wt% Cu (32). (Points in field a show how the individual contributions combine to describe the experimental EXAFS represented by the solid line.) (Reprinted with permission from the American Institute of Physics.)...

Comparison between calculated interatomic distances (in pm) and frequencies (in cm" ) for the model rhodium dicarbonyl T4 complex and experimental EXAFS parameters and IR spectra of supported Rh (CO)2 on zeolite DAY. 

After a successful conversion of the raw data in (he filial x(k) function, the last step of daia analysis consists of the determination of the struc dual parameters rJ% N - and a,. To do (his, one dies by variation of these parameters according to equation (10.4), to describe (he experimental y(A) function optimally with a minimal basis set. i.e. preferably few baekscatierers. Frequently, the experimental EXaFS function is. however, first dismantled by means of the Fourier filtering ... 

Figure 15 Experimental EXAFS data obtainedfor the 0.3% PdlH-ZSM-5 catalyst exposed to the SCR reaction at 500 °C for 15 min, compared with the fitted theoretical model (After ref. 122)...

Fig. 2. Schematic diagram of the EXAFS process. The central atom (filled circle) absorbs an X-ray photon. Scattering of the outgoing wave is induced by the neighboring sites (open circles) (left) Schematic presentation of the experimental EXAFS-signal obtained from Ar 2p-excited argon clusters (right).

Fig. 16. Experimental EXAFS signals obtained from the raw spectra shown in Pig. 15 (of. Ref. 73).

Figure 13 Representation of the Sn-beta structure as derived from EXAFS data, viewed along the b-axis (for clarity the oxygen atoms are not shown). The only Sn distribution consistent with the experimental EXAFS data is one where pairs of Sn atoms occupy opposite vertices of the six-member rings. A pair of T5 sites (red), with the required 5.1 A separation is shown, representing one possible tin pair within the beta structure. This tin pair distorts two of the 12-membered ring channels as viewed from the [100] direction and all four 12-membered ring channels as viewed from the [010] direction. This distortion is either direct by the replacement of silicon by tin or by the expansion of the neighboring Si04 tetrahedra. Reproduced with permission from Ref (152) Copyright 2005, The American Chemicai Society.

Figure 3. Fourier transform of experimental EXAFS (solid line). The best fit is obtained by parameters given in Table 1. The Fourier transform corresponding to these parameters is not shown the dotted line shows a theoretical Fourier transform, calculated for one shell of low-Z atoms at 1.85A.

The theoretically based method [9] suffers from the use of a large number of adjustable parameters in the data analysis. However, an alternate theoretical model has recently been proposed which addresses some of the deficiencies [104]. Specifically, the multiple-scattering method incorporates interactions that occur between the absorbing metal and groups of backscattering atoms, enabling simulation of unfiltered experimental EXAFS data [103-105]. 

In experimental EXAFS studies one measures the x-ray absorption the extraction of the EXAFS spectrum from the absorption spectrum is straightforward. In the further data evaluation the Fourier transformation of the measured EXAFS weighted by a factor X" is performed in practice, = 1 and n = 3 are used routinely. The Fourier transform, which is a function of the length R, peaks approximately at those distances that correspond to the positions of the scattering atoms (Figure 22). EXAFS measurements make it possible to determine distances between neighboring atoms with an accuracy of up to 0.01-0.03 A, if calibration... 

Experimentally, EXAFS involves measuring the absorption coefficient of the investigated material or of a parameter correlated with it, depending on the energy of the incident photon X. 

Figure 2-10. Radial Distribution Functions of O ions around in the PrV04 crystal,xerogel and glass. From Rocca (1998). Note the asymmetry at high R, well evident in the two latter cases. The curve was reconstructed from the experimental EXAFS data, using the EDA code (Kuzmin, 1997).

Experimental EXAFS measurements presented in this paper were performed in transmission geometry at the zirconium K-edge and thorium Llll-edge on DIFFABS beamUne of the SOLEIL synchrotron in Gif-Sur-Yvette (France) and on BL27B beamline of the Photon Factory (PF), KEK in Tsukuba (Japan), respectively. 

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