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)