Hi Wojciech,
I have another suggestion.
It is my secret, completely untested belief (which I am now revealing
to everyone on this mailing list!), that some of the cases of
"successful" fits using multiple E0's are masking problems caused by
not considering a third cumulant. For those who may not know the role
of this parameter, it in essence measures asymmetry in the
distribution associated with a path. For example, if a pair of atoms
are more likely to separated by a distance considerably larger than
the mean separation than by a distance considerably smaller than the
mean separation, then the third cumulant is positive. (The
mathematical definition is that the third cumulant is the mean cube
of the difference from the mean, in the same sense that sigma2 is the
mean square of the difference from the mean.)
In most cases, the third cumulant is small. Nevertheless, if it were
0 in all cases, then materials would not show any expansion with
temperature!
Through symmetry arguments, it is pretty clear that the third
cumulant is most likely to be significantly nonzero for
nearest-neighbor paths.
What does this have to do with fitting different E0's? E0 and the
third cumulant both affect the phase of the EXAFS signal, although
they are weighted in different ways by k. Nevertheless, if a nonzero
nearest-neighbor third cumulant is called for, allowing a different
E0 for the nearest-neighbor instead would probably also improve the
fit statistically. In this case, however, while the use of a third
cumulant can be justified on physical grounds relatively easily, the
use of a separate E0 is an arbitrary non-physical attempt to improve
the statistics.
So as far as I am concerned, I am more inclined, if my fit is not
quite working out, to try allowing the third cumulant for paths in
the first coordination shell to vary than I am to introduce multiple
E0's. In fact, I usually do this at some point during the fitting
process even if my fit is behaving fairly well to reassure myself
that the third cumulant is 0 to within the uncertainty of the fit,
and that constraining it to 0 is not distorting the values of the
parameters I am interested it.
Take all of this with a grain of salt; I wrote my dissertation on the
third cumulant, and, to paraphrase Bruce, since I've spent a lot of
time making a nice hammer, everything tends to look like a nail...
--Scott Calvin
Sarah Lawrence College
>
>I would like to address a couple of questions which are partially
>related to my recent struggles in fitting some EXAFS data. I'm
>trying to fit my data using several shells of different neighbors
>including a few single scattering paths and also so multiple
>scattering contributions (mainly collinear multiple scattering
>paths) all calculated with the help of FEFF 8.20. Now, I found once
>in the FEFFIT manual the following suggestion: one might consider
>using several different E0's for different paths in order to improve
>the fit. Ok, the explanation was based on some approximations coming
>from FEFF code which include incomplete core-hole shielding, lack of
>angular variations of the valence charge distribution and charge
>transfer between atoms in polar materials.
>My question is the following: does anyone of you have some
>experience with such procedure? And if yes, shall than distinguish
>between the first shell of nearest neighbors and the rest of the
>atoms in terms of their E0 corrections (using 2 parameters)? Or
>perhaps one can use separate E0's for each path?
