Thus, the EXAFS contribution from each

Thus, the EXAFS contribution from each backscattering atom j is a damped sine wave in k-space, with an amplitude, and a phase, which are both dependent on k. Additionally, S 0 2 is introduced as an amplitude reduction factor due to shake-up/shake-off processes at the central atom(s). This factor can be set for fits, on the basis of fits to model compounds. Thus, the following EXAFS equation is used to fit the experimental Fourier

isolates using N, R, and σ 2 as variable parameters, $$ \chi (k) = S_0^2 \sum\limits_j \frac f_\textj (\pi ,k) \rightkR_\textaj^2 \,\texte^ – 2\sigma_\textaj^2 k^2 \texte^ – 2R_\textaj /\lambda_j (k)\,\sin (2kR_\textaj + a_\textaj (k)) . $$ (6)From the phase of each sine wave [2kR aj + α aj(k)], the absorber–backscatterer distance R aj can be determined if the phase check details shift α aj(k) is known. The phase shift is obtained

either from theoretical calculations or empirically from compounds characterized Pevonedistat cost by crystallography with the specific absorber–backscatterer pair of atoms. The phase shift α aj (k) depends on both the absorber and the scatterer atoms. As one knows the absorbing atom in an EXAFS experiment, an estimation of the phase shift can be used in identifying the scattering atom. The amplitude function contains the Debye–Waller factor and N j, the number of backscatterers at R aj. These two

parameters are highly correlated, which makes the determination of N j difficult. The backscattering very amplitude function f j(π, k) depends on the atomic number of the scattering atom, and scattering Selleck OSI-906 intensity increases with the electron density (i.e., atomic number) of the scattering atom. In principle, this can be used to identify the scattering atoms. In practice, however, the phase shift and backscattering amplitude function, both of which are dependent on the identity of the backscattering atom, can be used only to identify scattering atoms that are well separated by atomic number (Rehr and Albers 2000). The EXAFS fit-quality is evaluated using two different parameters Φ and ε 2 . $$ \Upphi = \sum\limits_1^N_\textT \left( \frac1s_\texti \right)^2 [\chi^\textexpt (k_\texti ) - \chi^\textcalc (k_\texti )]^2 , $$ (7)where N T is the total number of data points collected, \( \chi^\textexpt (k_\texti ) \) is the experimental EXAFS amplitude at k i, and \( \chi^\textcalc (k_\texti ) \) is the theoretical EXAFS amplitude at k i. The normalization factor s i is given by $$ \frac1s_\texti = \frack_\texti^3 \sum\nolimits_j^N_\textT k_\textj^3 \left .

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