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?