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

Thus, the resulting curves are fitted with the EXAFS formula to
determine R, N and σ . In order to extract information about the local
environment of the absorber, the backscattering amplitude and phase
shift functions must be known. These functions can be obtained
experimentally from EXAFS spectra of model compounds or calculated
theoretically (Teo and Lee, 1979; McKale et al., 1988; Rehr, 1989).
Experimental functions are extracted from reference compounds with
known structures. However, it is not always possible to obtain
experimental functions since the reference compounds do not exist or
it is not possible to extract them (Vlaic et al., 1998). Furthermore,
experimental phase and amplitude functions must be extracted by
using the same integration limits and the same windows to the
unknown sample in order to introduce the same truncation errors.
In general, the accuracy of the analysis is about 0.01-0.02Å for the
interatomic distances, 5 to 15% for the coordination numbers and
20% for σ (Lengeler and Eisenberger, 1980).
The minimization procedure is carried over into the following function
(Michalowicz, 1990):
(14)
where p i are the fitting parameters and W(k) is a weighting function.
A residual factor is also defined by the following expression:
(15)
The number of parameters that can be determined from the EXAFS
signal is related to the number of independent points, N ind , by
N par = N ind – 1 (16)
There is some uncertainty in the literature on how to calculate N ind .
According to Stern (1993), the correct expression is given by
(17)
The fit quality is given by the chi-square function. Particularly in
EXAFS this function is defined as follows:
(18)