EXAFS oscillation amplitudes

Self-absorption occurs when the path-length is too large [35] and the X-rays emitted have a significant probability of being absorbed by the remainder of the sample before being detected. This has the consequence of reducing the amplitude of the EXAFS oscillations and producing erroneous results. As the sample becomes more dilute this probability decreases. All the atoms in the sample determine the amount of self-absorption hence the need for thin samples. 

The adsorption site, i.e. the chemisorption position of the adatoms on (within, below) the substrate surface, thanks to the polarisation dependence of SEXAFS. Often a unique assignment can be derived from the analysis of both polarisation dependent bond lengths and relative coordination numbers. The relative, polarisation dependent, amplitudes of the EXAFS oscillations indicate without ambiguity the chemisorption position if such position is the same for all adsorbed atoms. More than one chemisorption site could be present at a time (surface defect sites or just several of the ideal surface sites). If the relative population of the chemisorption sites is of the same order of magnitude, then the analysis of the data becomes difficult, or just impossible. 

The quasi-ideality of the (1 x l)Co/Cu(lll) and (1 x l)Co/Cu(110) monolayer interfaces allows a temperature dependent study of the polarisation dependent Debye Waller damping of the EXAFS oscillations i.e the analysis of the amplitude of the mean square relative displacements of the Co atoms parallel to the adsorbate layer, or perpendicular to it. The results are based on the analysis of data collected with the sample temperature T = 77 K and T = 300 K. The S—S and S—B (see above)... 

EXAFS theory was developed in the early 1970s by Sayers et al., providing XAS experimentalists a model in which data could be fit to. In their pioneering work it was observed that the physical phenomenon that gives rise to EXAFS oscillations has two major components, i.e., that of amplitnde and phase as described by the following equations amplitude ... 

The phenomenon of EXAFS has been known for a considerable time (see ref. 126) but it has been applied to obtain structural information within the last decade only. From equation (2) it is seen that neighbour separation depends on the phase of the EXAFS oscillations, while the co-ordination number Nj and thermal correlation factor (Tj depend on the signal amplitude. In 1971 it was shown by Sayers, Stern, and Lytle that an appropriate Fourier analysis of the data gives a radial structure factor (j) R) from which one can locate the positions of the atoms surrounding the atom which absorbs the X-ray photon (for detailed discussion see refs. 123, 128—130). A second method of data analysis, involving curve fitting techniques, has been used also. ... 

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... 

Goulon J, Goulon-Ginet C, Cortes R, Dubois JM (1981) On experimental attenuation factors of the amplitude of the EXAFS oscillations in absorption, reflectivity and luminescence measurements. J Phys 42 539-548... 

When plotted as x( ), EXAFS oscillations have an appearance similar to that shown in Figure 7. The amplitude of the EXAFS oscillations is proportional to the number of scattering atoms, the frequency of the oscillations is inversely proportional to the absorber-scatterer distance, and the shape of the oscillations is determined by the energy dependence of the photoelectron scattering, which depends on the identity of the scattering atom. For quantitative analyses, the EXAFS can be described by an equation such as Equation (3), with the summation taken over all of the scattering atoms near the absorber ... 

The EXAFS amplitude falls off as 1 /R. This reflects the decrease in photoelectron amplitude per unit area as one moves further from the photoelectron source (i.e., from the absorbing atom). The main consequence of this damping is that the EXAFS information is limited to atoms in the near vicinity of the absorber. There are three additional damping terms in Equation (2). The 5 q term is introduced to allow for inelastic loss processes and is typically not refined in EXAFS analyses. The first exponential term is a damping factor that arises from the mean free path of the photoelectron (A(k)). This serves to limit further the distance range that can be sampled by EXAFS. The second exponential term is the so-called Debye-Waller factor. This damping reflects the fact that if there is more than one absorber-scatterer distance, each distance will contribute EXAFS oscillations of a... 

Although Equation (3) provides a complete description of the EXAFS oscillations, it is not a particularly convenient form for visualizing the information content of an EXAFS spectrum. As with NMR spectroscopy, Fourier transformation can be used to decompose a A -space signal into its different constituent frequencies. This is illustrated using the EXAFS data for a THF solution of CuCN 2LiCl. The EXAFS spectrum (Figure 9) clearly contains more than one frequency, based on the complex variation in amplitude. For EXAFS, the canonical variables are k (inA ) and R (in A), and the Fourier transform (FT) of an EXAFS spectrum gives a... 

Figure 6.14 EXAFS and Fourier transform of rhodium metal, showing a) the measured EXAFS spectrum, b) the uncorrected Fourier Transform according to equation (6-10), c) the first Rh-Rh shell contribution being the inverse of the main peak in the Fourier Transform, and d) the phase- and amplitude-corrected Fourier Transform according to (6-11). The Fourier transform is a complex function, and hence the transforms give the magnitude of the transform (the positive and the negative curve are equivalent) as well as the imaginary part, which oscillates between the magnitude curves (from Martens (361).

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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