EXAFS as a tool for catalyst characterization: a review of the ... - INT

and EXAFS stem from the same phenomenon. The difference between
them is due to the kinetic energy of the photoelectron in each case.
At a low energy, the mean free path is high, which induces an
important multiple scattering effect. On the other hand, at the EXAFS
region, the mean free path of the photoelectrons is limited.
Therefore, single scattering is the major process.
The fine structure χ(E) associated to a particular absorption edge is
thus:
where µ(E) is the measured absorption coefficient, µ 1 (E) is the
absorption coefficient of the isolated atom and µ 0 (E) is the smooth
background absorption before the edge. µ 0 (E) andµ 1 (E) can not be
obtained directly and must be estimated.
The advantage of this procedure is based on the fact that µ 0 (E) is
determined directly from the pre-edge region before the calculations
for the EXAFS region. However, the µ 0 (E) extrapolation can produce
anomalous behavior for µ 1 (E) - µ 0 (E), since it is highly sensitive to the
energy range of the pre-edge chosen. Therefore, generally, the
Lengeler-Eisenberger method is used to calculate µ 0 (E) (Lengeler and
Eisenberger, 1980). This method is based on the following formula:
(2)
First µ 1 (E) is calculated after the edge by a polynomial of degree n (n
= 4, 5 or 6) or cubic splines. Then µ 0 (E) is determined from equation
(3).
In order to relate χ (E) to structural parameters, it is convenient to
perform a transformation to χ (κ) in the photoelectron
wavevector κ space, where
(3)
(4)
After conversion of energy to the k scale using eq. (4), the
normalized EXAFS function χ (κ ) is obtained as follows:
(5)