EXAFS backscatterers

If the identity of the backscatterer is known, then the interest is in determining the number of near neighbors. In this case, one needs to compare the amplitude of the EXAFS of the material of interest (unknown) to that for a compound of known coordination number and structure. However, unlike transferability of phase, which is generally regarded as an excellent approximation, the transferability of amplitude is not. This is because there are many factors that affect the amplitude and, except for the case of model compounds of very similar structures, these will not necessarily (and often will not) be the same. As a result, determination of coordination numbers (near neighbors) is usually no better than 20%. 

Melroy and co-workers88 recently reported on the EXAFS spectrum of Pb underpotentially deposited on silver (111). In this case, no Pb/Ag scattering was observed and this was ascribed to the large Debye-Waller factor for the lead as well as to the presence of an incommensurate layer. However, data analysis as well as comparison of the edge region of spectra for the underpotentially deposited lead, lead foil, lead acetate, and lead oxide indicated the presence of oxygen from either water or acetate (from electrolyte) as a backscatterer. 

Since the surface atoms are likely to be relatively strong backscatterers the extended fine structure will be dominated by the scattering from the substrate. This relatively weak modulation at higher energy is referred to as the surface EXAFS, or SEXAFS. An analysis of the SEXAFS can give further structural information, most valuably, on the adsorption site (for further details, see Ref. [2]). 

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 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 =... 

Notation N, coordination number R, distance between absorber and backscatterer atom A a2, Debye-Waller factor AEo, inner potential correction. Commonly accepted error bounds on structural parameters obtained by EXAFS spectroscopy are N, 10-15% R, 0.02 A ... 

In Figure 1 (a,b) the Fourier-Transformed (FT) EXAFS spectra of the Co/C and the Co-Mo/C catalyst together with the Co Sg reference compound are plotted. The absolute FT spectrum of Co Sg (Fig. 1 (a)) exhibits two peaks. The first peak is attributed to combined Co-S and Co-Co coordinations, the second one only to a Co-Co coordination (denoted Co-Co(2), to differentiate it from the Co-Co(1) coordination in the first peak). In bulk Co Sg 8/9 of the cobalt atoms are tetrahedrally coordinated and 1/9 are octahedrally coordinated by sulfurs. The Co-S coordination distances are in the range 2.13-2.39 A. The Co-Co coordination distance of Co-Co(1) is 2.50 A, for Co-Co(2) the distance is 3.51 A. From Figure 1 (a) it is apparent that in the catalyst spectra the first peak is shifted to lower r-values compared to that in Co Sg. This shift is larger for Co-Mo/C than for Co/C. It is furthermore clear that a Co-Co(2) coordination is also present in the Co/C catalyst, but not in the promoted catalyst. On the other hand, the latter catalyst shows an additional peak which is not present in COgSg and Co/C and, consequently, might be ascribed to Mo backscatterers. 

Notation N coordination number, R distance between the absorber and backscatterer atoms, short oxygen, Oj long oxygen. EXAFS expected errors N= 10% R = 0.02A... 

Photoionization (and therefore EXAFS) takes place on a time scale that is very short relative to atomic motions, so the experiment samples an average configuration of the neighbors around the absorber. Thus, one needs to consider the effects of thermal vibration and static disorder, both of which will have the effect of reducing the EXAFS amplitude. These effects are considered in the so-called Debye-Waller factor which represents the mean-square relative displacement along the absorber-backscatterer direction and is given by... 

After a successful conversion ol the raw data in the final y(k) function, the last step of data analysis consists of the determination of the structural parameters rj, Nj and oj. To do this, one tries by variation of these parameters according to equation (10.4), to describe the experimental, V(4) function optimally wilh a minimal basis sol. i.e. preferably few backscatterers. Frequently, the experimental EXAFS function is, however, first dismantled by means of the Fourier filtering... 

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... 

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