EXAFS multiple scattering

Di Cicco, A., and Minicucci, M., Solid and liquid short-range structure determined by EXAFS multiple-scattering data analysis, /. Synchrotron Rad., 6, 255-257,1999. 

Filipponi A, Di Cicco A (2000) GNXAS a software package for advanced EXAFS multiple-scattering calculations and data-analysis. Task Quarterly 4 575-669 Filipponi A, Di Cicco A, Benfatto M, Natoli CR (1990) The three-body correlation function in amorphous silicon probed by X-ray absorption spectroscopy. Europhys Lett 13 319-325 Filipponi A, Di Cicco A, Tyson TA, Natoli CR (1991) Ab initio modeling of X-ray absorption spectra. Solid State Commun 78 265-275... 

EXAFS multiple scattering occurs when the photoelectron is scattered by... 

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

Surface atomic structure. The integrated intensity of several diffracted beams is measured as a fimction of electron beam energy for different angles of incidence. The measurements are fitted with a model calculation that includes multiple scattering. The atomic coordinates of the surfiice atoms are extracted. (See also the article on EXAFS.)... 

The quantification of the extra-framework titanium species in titanium silicalites of MFI structure, TS-1, was performed using either XANES at the Ti K-edge or XPS Ti (2p) photolines. In addition, two different framework sites, [Ti(OH)(OSi)3] and [Ti(OSi)4], were characterized in dehydrated samples using Diffuse Reflectance UV-visible, multiple scattering analysis of EXAFS, H and Si NMR spectroscopies. 

Fig. 22. Best fit between experimental results and computed EXAFS employing the full multiple scattering method. The model is depicted in the bottom right figure [Reprinted from Thomas and Sankar (104) with permission. Copyright (2001) American Chemical Society].

Briefly, XANES is associated with the excitation process of a core electron to bound and quasibound states, where the bound states interacting with the continuum are located below the ionization threshold (vacuum level) and the quasibound states interacting with the continuum are located above or near the threshold. Thus, XANES contains information about the electronic state of the x-ray absorbing atom and the local surrounding structure. However, as stated above, unhke EXAES, since the excitation process essentially involves multielectron and multiple scattering interactions, interpretation of XANES data is substantially more complicated than that of EXAFS data. 

Multiple scattering, where the photoelectron wave samples severd scatteiers before returning to the absorbCT, is only important in KAFS for cases where two scatterers and the absc rber are nearly coUinear. In such cases, the EXAFS amplitude of the outer scatterer will be significantly enhanced. See Teo, B.K., /. Am. Chem. Soc., 1981,103,3990-4001. 

Fig. 1. X-ray absorption spectrum (XAS) of Cu—Zn metallothionein at the Cu and Zn K-edges. The structure near the edge, referred to as XANES is dominated by multiple scattering events while the extended structure, referred to as EXAFS, at photoelectron energies greater than 30-50 eV is primarily due to single scattering events...

Fig. 5. Single and multiple scattering pathways which make a significant contribution to the EXAFS data of an imidazole-containing compound...

Data analysis procedures have developed substantially over the last few years. In particular, use of least square refinement methods have been developed. Recent progress with theoretical development for the treatment of multiple scattering has resulted in Ugand group refinement such as an imidazole. We can expect further development in this area which ought to lead us to restrained least square refinement procedures for EXAFS data analysis. This type of restrained refinement is commonly used for macromolecular crystallographic structure determination where a similar problem of imderdeterminancy exists... 

It is at once obvious that Fourier transformation of equation (2.2) should yield information about all the j shells in direct space that contribute to the EXAFS. The Rjs so obtained are, however, shortened by the k-dependent part of /k). Since the intensity of the outgoing spherical wave decreases very rapidly with increasing R, distant atoms contribute very little to the fine structure. Multiple scattering effects are also relatively unimportant and these have indeed been ignored in the derivation of equation (2.2). EXAFS should contain no information about shadowed or eclipsed atoms, but there are exceptions to this. Other theoretical approaches also use similar effects to explain the EXAFS. 

The spectral features of XANES have been interpreted as the result of multiple-scattering resonances of the low kinetic energy photoelectrons. Examples of the strong and sharp XANES peaks above the continuum threshold and below the beginning of the weak EXAFS oscillations in the absorption spectra of condensed molecular complexes, are shown in Fig. 4.6. 

N,Sq is a term that modifies the amplitude of the EXAFS signal. The subscript i denotes that this value can be different for each path of the photoelectron. For a single scattering path, N, represents the number of coordinating atoms within a particular shell (at the same radial distance from the absorber). For multiple scattering, N, represents the number of identical paths. The passive electron reduction factor, Sg, usually has a value between 0.7 and 1.0. It accounts for the slight relaxation of the remaining electrons in the presence of the core hole vacated by the photoelectron. 

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