EXAFS as a tool for catalyst characterization: a review of the ... - INT
EXAFS as a tool for catalyst characterization: a review of the ... - INT EXAFS as a tool for catalyst characterization: a review of the ... - INT
from the absorber atom and Σ the summation extends over j coordination shells, the term e -2rj/λ is due to inelastic losses, Aj(κ ) is the backscattering amplitude from each of the N j neighboring atoms and φ j(κ ) is the phase shift between the incident and backscattering wave given by φ (κ ) = φ a(κ ) + φ b(κ ) (7) where φ a(κ ) is the phase shift due to the central atom and φ b(κ ) is the phase of the backscattering amplitude from the neighbor. Multiple scattering effects have been ignored in the derivation of eq. 6. Furthermore, since the intensity of the outgoing wave decreases very fast with increasing R, there is very little contribution to the fine structure of the distant atoms. The raw EXAFS signal obtained with the procedure described above is made of many sinusoidal waves. The Fourier transform is the standard tool used for frequency separation. The Fourier transform of χ(κ ) yields the following radial distribution function (RDF): Since at high κ values, the χ(κ ) is low, function χ(κ ) is multiplied by the factor κ n before the transform is performed in order to obtain more information at those values (Vlaic et al., 1998). Factor κ n is used to weight the data according to the value of κ . Generally, values of n= 1, 2 or 3 are used. The limits of the integral, kmin and kmax, are the experimental minimum and maximum values of κ obtained. Another problem related to FT is that the EXAFS signal has a limited number of points. Therefore, the Fourier integral is truncated. W(κ ) is a window function, where the function is Fourier transformed in a limited range (kmin, kmax). Three types of windows have been used in the literature: HAMMING, HANNING and KAISER (Michalowicz, 1990). HAMMING HANNING KAISER (8) κ min < κ < κ max (9) κ min < κ < κ max (10)
(11) I 0 - modified BESSEL function, degree 0; τ - the shape of the window; κ 1 and κ 2 - window limits. Only the magnitude of the transform is considered (eq.12). It shows a series of peaks, which corresponds to the different coordination shells (Figure 3). Because of the phase shift, φ j (κ ), interatomic distances derived from the peaks of FT(R) have to be properly corrected to coincide with those of X-ray diffraction. (12)
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- Page 3 and 4: Figure 1: Regions of the X-ray abso
- Page 5: The normalized EXAFS spectrum assoc
- Page 9 and 10: Thus, the resulting curves are fitt
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- Page 15 and 16: Bart, J.C.J. and Vlaic, G., Adv.Cat
(11)<br />
I 0 - modified BESSEL function, degree 0;<br />
τ - <strong>the</strong> shape <strong>of</strong> <strong>the</strong> window;<br />
κ 1 and κ 2 - window limits.<br />
Only <strong>the</strong> magnitude <strong>of</strong> <strong>the</strong> trans<strong>for</strong>m is considered (eq.12). It shows<br />
a series <strong>of</strong> peaks, which corresponds to <strong>the</strong> different coordination<br />
shells (Figure 3). Because <strong>of</strong> <strong>the</strong> ph<strong>as</strong>e shift, φ j (κ ), interatomic<br />
distances derived from <strong>the</strong> peaks <strong>of</strong> FT(R) have to be properly<br />
corrected to coincide with those <strong>of</strong> X-ray diffraction.<br />
(12)
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