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