General concept of the EDA package is shown on the scheme below, which illustrates main steps of the analysis and indicates the codes involved:
Click on the image to enlarge
One normally starts with the experimental data (I0 and I are intensities from the ionization chambers,
fluorescence detectors, etc), which must be converted into
x-ray absorption coefficient by the EDAFORM code (or any other suitable codes one likes to use).
Thus obtained x-ray absorption coefficient can be used to separate XANES part, located close to the x-ray absorption edge,
by the EDAXANES code
or to extract the total experimental EXAFS signal χ(k) by the EDAEES code.
After total experimental EXAFS signal extraction, one usually performs its Fouier filtering (i.e. direct and
back Fourier transforms (FT) with some suitable "window"-function)
to separate contribution from different structural shells (peaks in FT). This is done by the EDAFT code.
Such approach allows one to "simplify" the analysis, at least, for the first coordination shell of the absorbing atom.
Finally, the EXAFS signal from a single shell can be simulated by different models to obtain structural information.
The EDA package allows one to use three models:
(i) conventional multi-component parametrized model within the Gaussian or cumulant approximation (the EDAFIT code),
(ii) arbitrary radial-distribution fucntion (RDF) model obtained by the regularization-like approach(the EDARDF code),
(iii) the so-called "splice" model (one needs to use the EDAFT and EDAPLOT codes).
To perform simulations, one obviously needs to provide the scattering amplitude and phase shift functions for each scattering path.
These data can be obtained either from experimental EXAFS signal for etalon (reference) compound
or calculated theoretically. In the EDA package, one has possibility to use the theoretical data calculated by the
which can be extracted from the feff****.dat files by the EDAFEFF code.
Different models obtained from the simulations of the EXAFS signal by the EDAFIT code can be further analysed by the FTEST code,
applying the Fisher's F0.95 criterion.
Finally, visualisation, comparison and simple mathematical analysis of all obtained data can be done using the EDAPLOT code.
However, since all data are kept in the simple ASCII format they can be easily transfered to and treated by any other codes.
Basic approach to the EXAFS data analysis using the EDA package and theoretical amplitude and phase shift
functions, calculated by the FEFF code, is shown on the image below:
Click on the image to enlarge
It is crucial to align the experimental data and the theory on the same wavenumber scale (k-scale), since there is strong
correlation between the origin of the photoelectron kinetic energy E0 and the interatomic distances R
(both parameters influence the frequency of the EXAFS signal).
Therefore, one normally starts from the analysis of the EXAFS signal for the reference compound, whose atomic structure
is well known. A good polycrystalline compound with the local structure close to that of the sample under study is a good choice for the reference.
As the first trial, one can set the position of E0 at the maximum of the first derivative of the x-ray absorption
coefficient and extract the EXAFS signal χ(k): this should be done by the EDAEES code.
Besides, one needs to perform calculation
of the theoretical total EXAFS signal χFEFF(k) by the FEFF code.
This requires the construction of the feff.inp file for the reference compound, which can be done
by the ATOMS code.
After executing the FEFF code, the theoretical EXAFS signal should be extracted from
the generated chi.dat file and compared with the experimental one.
If the phases of two EXAFS signals deviate significantly, especially in the low-k range, one needs to adjust the E0 position for the experimental
EXAFS signal. Thus, the whole extraction procedure should be repeated till the two EXAFS signals will be aligned with the accuracy of better than 0.5-1 eV.
When the good position of E0 for the EXAFS spectrum of the reference compound is found, the same E0
value should be used for other EXAFS signals under analysis.
As a result of the FEFF calculation for the reference compound, a set of feff****.dat files is also generated for all scattering paths.
Each feff****.dat file can be used to generate by the EDAFEFF code a pair of files (amp****.dat and pha****.dat)
containing the amplitude and phase shift functions in the format required by the EDAFIT and EDARDF codes.
Here the asterisk symbol should be changed by the required scattering path number, for example, amp0001.dat.
After proper selection of the E0 value, one can continue the analysis of the EXAFS spectrum for the system of interest.
In many cases, due to the presence of the multiple-scattering contributions at large distances, only analysis of the first coordination shell of the absorber
can be rigorously performed, i.e. without further significant approximations.
To do this, one needs first to isolate the contribution of the first shell by performing direct and inverse Fourier transformations (FT) of the experimental EXAFS signal.
This can be done by the EDAFT code. One should take care that exactly the same "windows"-function is used in k-space, and the "window"-function
in R-space selects precisely the range of the first shell. The overlap with the outer shells in R-space, the noise and the presence of the phase shift
must be taken into account to do the isolation procedure properly.
Finally, the isolated first shell EXAFS signal can be best-fitted by the Gaussian or cumulant model using the EDAFIT code, or the first shell RDF function
can be directly reconstructed by the EDARDF code. In both cases, the amplitude (amp****.dat) and phase shift (pha****.dat) functions must be provided.