EXAFS

The interpretation of the EXAFS data is therefore not unique, and great care should be exerted in the analysis. But on the other hand it provides information that cannot be obtained in any other way. 

The k-space spectrum (as depicted Fig. 4b) represents the interference between outgoing photoelectrons and the backscattered ones. A physical description of the EXAFS - similar to a radial distribution function - can be extracted from the EXAFS by making use of the Fourier Transform  

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  

Because the R term, and the mean-free path of backscattered photoelectrons is small (usually 25 A), typically the total number of shells rarely exceeds 7. The backscattering amplitude, Fj(k), and phase shift, dj(k), for the absorber-neighbor pair may either be extracted from the EXAFS of reference materials or calculated theoretically using widely available codes such as the FEFF developed by John Rehr s group at the University of Washington.  

In electrocatalysis where the user is most interested with extracting N, it is cormnon procedure to analyze only the first coordination shell since the stracture is typically known. Such an analysis is relatively easy to perform and often yields reliable data. Depending on the stmctrrre, first shell fits only require one or two scattering paths, which make the job of fitting much less involved 

The statistical error valnes obtained from a fit do not represent the true accuracies of the parameters and the error a coordination number determination can be on the order of 10 and 30 %. 

For theoretical as well as for practical purposes, a XAS spectrum is normally divided in two regions (1) the X-ray absorption near-edge structure (XANES) region, and (2) the extended X-ray absorption fine structure (EXAFS) region. 

In the absorption coefficient formalism, the EXAFS signal is substantially due to interference of the outgoing photoelectron wave from the absorbing atom with the back-scattered wave from each surrounding atom. Hence EXAFS provides information about the pair distribution function. 

The generally strong scattering power of the atoms of the medium for low kinetic 

The distribution of peaks and the ensuing separation of them in the three region is never straightforward, and in some systems they even overlap to a certain extent. However, if this theoretical description of XANES spectra is adopted (Natoli 1983 Natoli and Benfatto 1986 see Benfatto et al. 2001), then the two alternative theories of single- and multiple-scattering (Sayers et al. 1970 and Lee and Pendry 1975, respectively) can be unified and the treatment of the entire XAS spectrum traced back to a unique, complete, and physically coherent theory. 

The features just above the absorption threshold (called PE features) arise from different mechanisms (1) the quadrupole mechanism (Balzarotti et al. 1980 Drager et al. 1988) (2) the mixture of the transition metal 4/ -states with the Zd ones owing to the non- 

The periodicity of this modulation of the absorption will be dependent upon the inteiatomic distance between the absorbing and back-scat tei i ng atoms, R, and the phase shifts, 5. , encountered when the photoelect i on expeiiences the potentials at these centres. Its intensity will be governed by the number of back-scatterers, Nj and their back-scattering amplitudes, F (k). Finally the amplitude is dampened by disorder (thermal and static), a in the interatomic distance and any inelastic piocesses (related to the mean free path of the election, j)- The recognition of the stiuctural information intrinsic to this phenomenon and the derivation of a tractable formula for the estimation of interatomic distances was the result of the work of Sayers, Lytle and 

V) estimation of coordination numbers (to a maximum precision generally of ca. 10%). In terms of a typical metal catalyst supported on an amorphous oxide surface this is all highly desirable. The surface selectivity required is then derived from the element specificity. 

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EXAFS Extended X-ray absorption fine structure spectroscopy. A spectroscopic technique which can determine interatomic distances very precisely. 

EXAFS Extended x-ray absorption fine structure [177, 178] Variation of x-ray absorption as a function of x-ray energy beyond an absorption edge the probability is affected by backscattering of the emitted electron from adjacent atoms Number and interatomic distance of surface atoms... 

NEXAFS Near-edge EXAFS Variant of EXAFS Variant of EXAFS... 

SEXAFS Surface EXAFS Same as EXAFS Same as EXAFS... 

The composition and chemical state of the surface atoms or molecules are very important, especially in the field of heterogeneous catalysis, where mixed-surface compositions are common. This aspect is discussed in more detail in Chapter XVIII (but again see Refs. 55, 56). Since transition metals are widely used in catalysis, the determination of the valence state of surface atoms is important, such as by ESCA, EXAFS, or XPS (see Chapter VIII and note Refs. 59, 60). 

As we have seen, the electron is the easiest probe to make surface sensitive. For that reason, a number of hybrid teclmiques have been designed that combine the virtues of electrons and of other probes. In particular, electrons and photons (x-rays) have been used together in teclmiques like PD [10] and SEXAFS (or EXAFS, which is the high-energy limit of XAES) [2, Hj. Both of these rely on diffraction by electrons, which have been excited by photons. In the case of PD, the electrons themselves are detected after emission out of the surface, limiting the depth of sampling to that given by the electron mean free path. 

Rehr J J 1995 Multiple-scattering approach to surface EXAFS—theory versus experiment Surf. Rev. Lett 2 63-9... 

Kongingsberger D C and Prins R (ed) 988 X-Ray Absorption Principies, Appiications, Techniques of EXAFS, SEXAFS and XANES (New York Wiley)... 

Blum L, Abruna FI D, White J, Gordon J G, Borges G L, Samant M G and Melroy 1986 Study of underpotentially deposited copper on gold by fluorescence detected surface EXAFS J. Chem. Phys. 85 6732-8... 

Marcus M A ef a/1991 Structure of capped CdSe clusters by EXAFS J. Phys. Chem. 95 1572... 

Very recently the first x-ray study (EXAFS) has been performed on hydrophobic hydration. ... 

Acronyms abound in phofoelecfron and relafed specfroscopies buf we shall use only XPS, UPS and, in Sections 8.2 and 8.3, AES (Auger elecfron specfroscopy), XRF (X-ray fluorescence) and EXAFS (exfended X-ray absorption fine sfmcfure). In addition, ESCA is worth mentioning, briefly. If sfands for elecfron specfroscopy for chemical analysis in which elecfron specfroscopy refers fo fhe various branches of specfroscopy which involve fhe ejection of an elecfron from an atom or molecule. Flowever, because ESCA was an acronym infroduced by workers in fhe field of XPS if is mosf often used to refer to XPS rather than to electron spectroscopy in general. 

Figure 8.34 Experimental method for extended X-ray absorption fine structure (EXAFS)...

Work on EXAFS then progressed very little until the advent of the synchrotron radiation source (storage ring), described in Section 8.1.1.1. This type of source produces X-ray radiation of the order of 10 to 10 times as intense as that of a conventional source and is continuously tunable. These properties led to the establishment of EXAFS as an important structural tool for solid materials. 

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... 

In an EXAFS experiment the measurable quantity is the absorption coefficient a of Equation (8.16). If Qq is the absorption coefficient in the absence of EXAFS, deduced from the steeply falling background shown in Figure 8.32, then x k), the fractional change of a due to EXAFS, is given 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... 

Figure 8.38 Curve fitting of Mo extended X-ray absorption fine structure (EXAFS) for Mo(SC6H4NH)3, taking into account (a) sulphur and (b) sulphur and nitrogen atoms as near neighbours. (Reproduced, with permission, trom Winnick, H. and Doniach, S. (Eds), Synchrotron Radiation Research, p. 436, Plenum, New York, 1980)...

The EXAFS method can be used for different elements in the same material or for different absorption edges, such as lx, 2s or 2p, in the same element. 

EXAFS spectra of platinum metal, having a face-centred cubic crystal stmcture, have been obtained at 300 K and 673 K. Explain what qualitative differences you might expect. How many nearest-neighbour atoms are there in this stmcture Illustrate your answer with a diagram. 

Teo, B. (1986) EXAFS Basic Principles and Data Analysis, Springer, Berlin. 

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