Another reason, from my point of view, is
that FEFF wasn't accurate enough to use on its own without references.
Also, it still can be argued that
the process of data reduction and
filtering produces distortions which aren't captured by using FEFF
alone. Further, if one is comparing
very similar systems, e.g. bulk and nano of
the same stuff, then with the exception of multiple scattering, the one system
should be an ideal
reference for the other.
A trick I used to do: Suppose, for
instance, that I wanted to fit a shell of Zn surrounded by Si (not an actual
case). There's no Si-rich
zinc silicide to use as a reference, but
it's not too hard to make theta-CuAl2, a compound in which all Cu atoms are
surrounded by Al in the
first shell (this was done). From
this, amp and phase functions could be extracted which refer to Cu looking at Al
(Cu->Al). Next, to transform this into
the desired Zn->Si, I would do FEFF
calculations on identical structures with the atoms changed around and
take:
A(Zn->Si, semi-empirical) = A(Cu->Al,
expt)*[A(Zn->Si, FEFF)/A(Cu->Al, FEFF)]
phi(Zn->Si, semi-empirical) =
phi(Cu->Al, expt)+[Phi(Zn->Si, FEFF)-phi(Cu->Al, FEFF)]
with A, phi being amplitude and phase for a
given shell, and appropriate account being taken of the distance differences
involved.
This makes sense if you consider A~ =
A*exp(i*phi) to be one of the factors in a complex chi~ such that chi =
Im(chi~), and you're
essentially making a correction to
ln(A~). Yes, this was low-rent and subject to errors, but it seemed to
make sense provided
one didn't try to take it too far, for
instance trying to change Al for Au or an oxide for a metal.
Brings back memories, not all of them fond
:-)
mam
----- Original Message -----
Sent: Friday, October 22, 2010 2:38
PM
Subject: Re: [Ifeffit] Asymmetric error
bars in IFeffit
On a related subject, now I understand
why we use the concept of chemical transferability of amplitudes and phases by
recycling the same FEFF path for different systems. The true reason is
historic: back then it took one hour for one FEFF
calculation....
Anatoly
Hi all,
I'm puzzling over an issue with my latest analysis, and it seemed like
the sort of thing where this mailing list might have some good ideas.
First, a little background on the analysis. It is a simultaneous fit to
four samples, made of various combinations of three phases. Mossbauer has
established which samples include which phases. One of the phases itself has
two crystallographically inequivalent absorbing sites. The result is
that the fit includes 12 Feff calculations, four data sets, and 1000 paths.
Remarkably, everything works quite well, yielding a satisfying and informative
fit. Depending on the details, the fit takes about 90 minutes to run. Kudos to
Ifeffit and Horae for making such a thing possible!
Several of the parameters that the fit finds are "characteristic
crystallite radii" for the individual phases. In my published fits, I often
include a factor that accounts for the fact that a phase is nanoscale in a
crude way: it assumes the phase is present as spheres of uniform radius and
applies a suppression factor to the coordination numbers of the paths as a
function of that radius and of the absorber-scatterer distance. Even though
this model is rarely strictly correct in terms of morphology and size
dispersion, it gives a first-order approximation to the effect of the reduced
coordination numbers found in nanoscale materials. Some people, notably
Anatoly Frenkel, have published models which deal with this effect much more
realistically. But those techniques also require more fitted variables and
work best with fairly well-behaved samples. I tend to work with "messy"
chemical samples of free nanoparticles where the assumption of sphericity
isn't terrible, and the size dispersion is difficult to model
accurately.
At any rate, the project I'm currently working on includes a fitted
characteristic radius of the type I've described for each of the phases in
each of the samples. And again, it seems to work pretty well, yielding values
that are plausible and largely stable.
That's the background information. Now for my question:
The effect of the characteristic radius on the spectrum is a strongly
nonlinear function of that radius. For example, the difference between the
EXAFS spectra of 100 nm and 1000 nm single crystals due to the coordination
number effect is completely negligible. The difference between 1 nm and 10 nm
crystals, however, is huge.
So for very small crystallites, IFeffit reports perfectly reasonable
error bars: the radius is 0.7 +/- 0.3 nm, for instance. For somewhat larger
crystallites, however, it tends to report values like 10 +/- 500 nm. I
understand why it does that: it's evaluating how much the parameter would have
to change by to have a given impact on the chi square of the fit. And it turns
out that once you get to about 10 nm, the size could go arbitrarily higher
than that and not change the spectrum much at all. But it couldn't go that
much lower without affecting the spectrum. So what IFeffit means
is something like "the best fit value is 10 nm, and it is probable that the
value is at least 4 nm." But it's operating under the assumption that the
dependence of chi-square on the parameter is parabolic, so it comes up with a
compromise between a 6 nm error bar on the low side and an infinitely large
error bar on the high side. Compromising with infinity, however, rarely yields
sensible results.
Thus my question is if anyone can think of a way to extract some sense of
these asymmetric error bars from IFeffit. Here are possibilities I've
considered:
--Fit something like the log of the characteristic radius, rather than
the radius itself. That creates an asymmetric error bar for the radius, but
the asymmetry the new error bar possesses has no relationship to the
uncertainty it "should" possess. This seems to me like it's just a way of
sweeping the problem under the rug and is potentially misleading.
--Rerun the fits setting the variable in question to different values to
probe how far up or down it can go and have the same effect on the fit. But
since I've got nine of these factors, and each fit takes more than an hour,
the computer time required seems prohibitive!
--Somehow parameterize the guessed variable so that it
does tend to have symmetric error bars, and then calculate the
characteristic radius and its error bars from that. But it's not at all clear
what that parameterization would be.
--Ask the IFeffit mailing list for ideas!
Thanks!
--Scott Calvin
Sarah Lawrence College
_______________________________________________
Ifeffit mailing
list
Ifeffit@millenia.cars.aps.anl.gov
http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit