EXAFS theory

4 EXAFS Theory. - The observed EXAFS, (k), is defined empirically as  

The most commonly adopted formalism for calculating (k) from structural parameters has been according to a s ngle-scattering 

In addition to the terms defined above, there is an amplitude reduction factor which allows for the multi-electron processes at the central atom such as shake up and shake off. Difficulties arise from the estimation of the back-scattering factors and phase shifts. These are sometimes considered to be empirical parameters 

Alternatively, theoretical values can be used, either per se or as a basis for empirical adjustment. There has been speculation 

A second approximation was the consideration of single-scattering events only. In many cases, especially when there are linear arrays of atoms, multiple scattering can be not 

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

Fig. 13. Pictorial view of the final-state radial wave functions relevant for core transitions in a molecule. The core transitions take place in an effective molecular potential seen by the excited photoelectron. The final states in the continuum XANES region are quasi-bound multiplescattering resonances (MSR), also called shape resonances. Below the continuum threshold E0 transitions to unoccupied valence states appear. 0 is the energy of the core ionization potential (from ESCA). Ec is the energy where the wavelength of initially excited photoelectrons conforms to the interatomic distance. For E < E0, discrete transitions to unoccupied valence states. E0 < E < Ec, continuum XANES. For < Ec, the EXAFS theory breaks down. The dotted curves show the wave functions of the initially excited photoelectron. From Bianconi (30).

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 ... 

Details of EXAFS theory and analysis are given in numerous reviews and books The main features only will be recalled in this paper. 

Belli M, Scafati A, Bianconi A, Mobilio S, Palladino L, Reale A, Burattini E (1980) X-ray absorption nearedge stractures (XANES) in simple and complex Mn compounds. Solid State Commun 35 355-361 Benfatto M, Congiu Castellano A, Daniele A, Della Longa S (2001) MXAN A new software procedure to perform geometrical fitting of experimental XANES spectra. J Synchrotron Rad 8 267-269 Benfatto M, Natoli CR, Brouder C, Pettifer RF, Ruiz Lopez MF (1989) Polarized curved wave EXAFS Theory and apphcation. Phys Rev B39 1936-1939... 

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