Hi Juan,
Sorry for the slow response; the end of the term gets busy for me!
I think there are still some loose ends in this
discussion that are worth trying to tie up:
At 03:03 PM 12/11/2006, you wrote:
First of all, I would like to thanks Anatoly for his file and everybody for
useful comments. I have analysed Anatoly's data
and I have obtained a good value
for S02 = 0.85 or 0.82 (depending on the number
of variables used). So, my data
is the problem, and it is not my analysis, but
maybe my measurements need a more
accurate analysis with Athena as Scott suggested.
I was not at synchrotron measuring platinum samples and I only know that are
measured in fluorescent mode. As Bruce said, I have no beamtime now for more
measurements.
I have more questions, related and not related to the last subject, but I am
still thinking about them:
The first one is easy, it is about the Nyquist theorem. I read in a paper that
the formula is 2·deltak·deltaR/pi + 2. The last "+2" is new for me and I am
afraid that Artemis does not consider it. I am sure that it is a silly thing.
For a while, arguing over this +2 (or +1 or +0)
was a popular topic in the EXAFS community.
Eventually it was realized that there isn't
really as much information as implied by the
Nyquist criterion anyway. Crudely, the Nyquist
criterion assumes you have someone trying to
convey as much information as possible in a
signal. Nature isn't so obliging. So it's
becoming more common to leave the +2 off, and
even that is not conservative. If you're running
out of independent points, introducing more
constraints, extending the k-range, or extending
the r-range can be better ways of getting
yourself out of trouble than invoking the +2.
I will try to correct again Ptfoil considering self-absorption in order to
obtain a spectrum similar to Anatoly's or Bruce's one. And then, I will apply
the same correction for supported platinum catalysts, right?
Since your samples have a low concentration of
Pt, the self-absorption correction should not be
necessary for them. You've talked about changing
the variable from S02 to N in subsequent fits to
obtain both variables...if I understand you
correctly, that won't accomplish anything. If it
were that "easy," Ifeffit would include it in its
fitting algorithm! S02 and N for a single-shell
single-sample fit are 100% correlated and values
cannot be obtained for both no matter what you
do. I think the best you can do is fix S02 at
some plausible value (0.85, say, or the result of
a FEFF calculation, or whatever), and then
realize, and explicitly note in publications,
that this assumption introduces an uncertainty of
perhaps 10% in N, in addition to whatever uncertainties are found by Ifeffit.
I also observed that Anatoly's Pt foil shows good signal even for large k (20
A-1). Nevertheless, obviously platinum catalysts spectra possess lower signal
and specially for high values of k where the noise is big. The question is,
despite Pt foil has a good signal until 20 A-1, it is usually used a smaller
k-range (i.e. 3-12 A-1), right? I normally use a k-range of 3-12.
As Matt said, use the data to guide you when
choosing k-range; not some arbitrarily chosen
range. I also find it useful to try varying my
k-range a bit after the fit is done to check that
the results are stable. Of course, if you are
visually comparing Fourier transforms of
different samples, rather than performing fits,
you want to compare over the same k-range.
Finally, at the risk of repeating myself, I'm
going to suggest that your system sounds like it
would benefit from a multiple-shell fit. That's
pretty easy to do for a metallic cluster like
platinum. And it reduces some of your problems.
It's hard, as you've noticed, to determine N for
a single shell, in part because you have to know
S02. But since S02 is the same for all shells,
it's easier to determine the ratio between N for
the first shell and N for the second shell.
That's still a little dicey because sigma2 is
likely to be far different for the first two
shells, and sigma2 correlates to N (but not 100%
correlation; the effect of sigma2 depends on k,
and N does not). If you get to three shells,
though, then the ratios of N3 to N2 to N1 start
to get teased out from the other effects, and you
can start to determine things like crystallite
size, which it sounds like is the thing you're after.
That's the principle that both Anatoly and I have
used in the past to find the size of
nanoparticles or nanocrystals. Our methods differ
in detail--Anatoly's is better for good data and
highly uncertain morphology, because it assumes
less; mine is probably better for iffy data and
roughly known (e.g. "spherical") morphology,
because mine has fewer free parameters. A search
of the literature will reveal several articles by
each of us detailing how to do this kind of
analysis, including the APL I mentioned earlier
on platinum nanoparticles and a JACS article of
Anatoly's on platinum-ruthenium nanoparticles.
--Scott Calvin
Sarah Lawrence College
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