EXAFS waves

The overall EXAFS of a system can be broken down to the individual wave properties of each resolvable absorber-scatterer (as) interaction. The frequency of each EXAFS wave depends on the distance between the absorber and scatterer. During the forward and backscattering process. 

Fig. 14. Fourier transform of the k k) spectrum shown in Fig. 12. The Fourier transform is resolved into three peaks. The dashed lines indicate the window used to generate the Fourier-filtered second peak, whose inverse Fourier transform is shown in Fig. 15. The apparent distance is shorter than the actual distance to a given neighboring atom because of the contribution of the phase shift to the frequency of the EXAFS wave, as explained in the text.

The EXAFS technique is used primarily for investigations of disordered materials and amorphous solids. Figure 8.35(b) shows how interference occurs between the wave associated with a photoelectron generated on atom A and the waves scattered by nearest-neighbour atoms B in a crystalline material. 

In the theory of EXAFS it is usual to consider the wave vector k of the wave associated with the photoelectron rather than the wavelength X. They are related by... 

Figure 8.39 shows some results of EXAFS following absorption by iron atoms in proteins with three prototype iron-sulphur active sites. In the example in Figure 8.39(a) application of a 0.9-3.5 A filter window before Fourier retransformation shows a single wave resulting... 

EXAFS is observed as a modulating change in the absorption coefficient caused by the ejected electron wave back-scattering from the surrounding atoms, resulting in interference between ejected and back-scattered waves. It is defined as ... 

Extended X-ray absorption fine structure (EXAFS) measurements based on the photoeffect caused by collision of an inner shell electron with an X-ray photon of sufficient energy may also be used. The spectrum, starting from the absorption edge, exhibits a sinusoidal fine structure caused by interferences between the outgoing and the backscattered waves of the photoelectron which is the product of the collision. Since the intensity of the backscattering decreases rapidly over the distances to the next neighbor atoms, information about the chemical surroundings of the excited atom can be deduced. 

The Mo K-edge EXAFS spectra for the catalysts and reference compounds (MoSj and NajMoOJ were measured on the BL-lOB instruments of the Photon Factory at the National Laboratory for High Energy Physics by using a synchrotron radiation. The EXAFS spectra were obtained at room temperature without exposing the sample to air by using an in situ EXAFS cell with Kapton windows [12]. Data analysis was earned out assuming a plane wave approximation. 

In this chapter, I will try to present an introduction to these various techniques with emphasis on EXAFS and X-ray standing waves and their application to the study of electrochemical interfaces. Each technique will be treated from theoretical and experimental points of view, and selected examples from the literature will be employed to illustrate their application to the study of electrochemical interfaces. 

Figure 7. Depiction of origin of EXAFS. An X-ray photon is absorbed by A, resulting in the photoionization of a core-level electron represented as an outgoing ( + ) photoelectron wave which is backscattered (<- ) by a near neighbor, B.

Here p E) is the total absorption coefficient at energy E and /jl0 is the smooth atomlike absorption coefficient. In order to be able to extract structural information from the EXAFS, we need to go from the energy to the wave vector form using the formulation ... 

In order to extract structural information, we need to convert the EXAFS expressed in terms of energy to wave vector form. To... 

Examination of the EXAFS formulation in wave vector form reveals that it consists of a sum of sinusoids with phase and amplitude. Sayers et al32 were the first to recognize the fact that a Fourier transform of the EXAFS from wave vector space (k or direct space) to frequency space (r) yields a function that is qualitatively similar to a radial distribution function and is given by ... 

In addition to surface EXAFS and X-ray standing waves, X-ray diffraction can be employed in the study of electrochemical interfaces. Although an extensive treatment of X-ray diffraction techniques is beyond the scope of this chapter, some brief statements are appropriate. 

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