Hi Matt, Thank you very much for your comments. S02 is a variable for me and it gives information about the size of the particles (related to coordination number). For instance, in the case of Pt foil it should be close to 0.85, however it is much smaller (0.20) in the case of platinum nanoparticles (size < 2nm), Anatoly commented that it is normal this low value in the case of nanoparticles. Probably, what you purposed it has more sense than what I did. Then, as I understand, I have to suppose reasonable value of S02, lets say 0.85, or shall I have to use S02 from Pt foil? Secondly, I define the variable amp = S02*N and, shall I write a value of one in the box corresponding to N? I mean, the sight in Artemis shows like this: N:1 X S02:amp. Talking about the Nyquist theorem, a higher number of independent points implies a higher number of variables that can be used and it is especially useful for me when I fit only the first shell (R-range is small) due to the low number of independent points obtained. If I use the formula "+2", I can define more variables. I usually use the crude rule: number of variables < 2/3 Nip. I read this "+2" formula described by D.C. Koningsberger et al (Topics in Catalysis 10 (2000) 143-155) and I though that was ok. What is the origin of this "+2"? I have obtained a value of 0.53 for S02 in the case of Pt foil, it suggests (as people from this e-mailing list said) that a correction of self absorption should be used until reaching a reasonable value for S02 (0.85). After this, I will apply the same correction to the samples because they were measured in fluorescence way too. My samples contain less than 1% of platinum in weight (about 0.80%) and I do not know if there will be self-absorption. Finally, I would like to ask about the detection of low Z scatterers (usually O or C from the support). I read in the aforementioned paper the difference file technique, Artemis includes this possibility? How can low Z scatterers be detected? Thanks a lot Best regards, JA

Hi Anatoly, Sorry very much Anatoly, you are right, I only told you low values for S02 but I did not give any value to you. Which is the minimum reasonable coordiantion number in a fcc structure? Yes, I assumed a fixed value of 12 for N and I left S02 as variable. I realize that my fault was to want to obtain both S02 and N in the same fit, and it seems that I have to do two fits, changing the variable (S02 or N), to obtain both variables. Thank you very much Best regards, JA

Hi Juan, Without getting too much into detail, the trick is to introduce constraints that seem physically reasonable and see what happens. This requires you to use the "a priori" information you have about your system; i.e. the information you have from non-EXAFS theory or experiment. Maybe, for instance, you believe your system to be a mixture of nanoscale fcc Pt and nanoscale Pt3Sn. Further, perhaps you believe the nanoparticles to be roughly round. In that case, only 3 parameters control all of the coordination numbers, no matter how many coordination shells you fit: the average size of the Pt particles, the average size of the Pt3Sn particles, and the fraction of particles which are Pt. From those three variables, all the coordination numbers can be computed. Actually, it's likely you also know the chemical composition; i.e. the ratio of platinum to tin atoms in the sample. If so, then you know the fraction of particles which are Pt, and that cuts down the number of variables to two. Perhaps you have TEM's, and that gives you a hint as to the sizes of the crystallites, so maybe that constrains things further. But of course all this puts you out on a limb. How do you know these assumptions were correct? Well, if you try the fit and it doesn't work very well, then you can be pretty sure the assumptions were not correct, and you can try another set of plausible assumptions. If you try them, and if your fitted variables do work out plausibly and the fit is fairly close to the data, then maybe you're right and maybe you're not. But if you have other reasons for favoring the model you chose in the first place, then the whole thing makes a coherent scientific story, and can be revealed to the world (e.g. published) for others to support or challenge with their own work. I tend to think of EXAFS as a great negative technique: it tells me when I'm wrong, but not when I'm right. But if EXAFS is at least able to say that I might be right, then I might be right, and I can proceed with my claim. And yes, we're talking about pretty sophisticated uses of EXAFS here. I really do suggest you look at articles by any of the "experts" who frequent this list and see what they did in their studies. I think you'll find that in general there are a whole host of constraints used that are not =rigorously= justifiable, but seem reasonable for the system at hand. When I look in detail at one of those papers, I often think "hmmm...I would have done that differently." And yet more times than not, I believe they have properly characterized the substance. It's particularly funny to watch the courses that have been given by Bruce, Shelly, Matt, Anatoly, etc., because one of us is often in the back looking very quizzical while whoever is in front demonstrates how they would attack a particular problem. But we know that the bottom line is being a good scientist, and not whether one particular approach or another is used at any given time... --Scott Calvin Sarah Lawrence College At 04:42 PM 12/21/2006, you wrote:

Hi all,

Thank you very much Scott for your not slow answer and sorry for my very slow one. I think my system is a little bit complicated. I have bimetallic catalysts (PtSn) and I did fits supposing two different structures but I do not know the relative proportion of these two structures. In this sense and as there are paths (from the two structures) with the same Reff I can not calculate coordination numbers for all the paths at the same time, I do not have enough number of independent points. I also tried a mulplied shell fit but the signals in FT decreases considerably in the outer shells (confusing with noise) and it is difficult to perform a good fit.

As an example, the fit of the first shell of a PtSn catalyst with Pt fcc and Pt3Sn structures: I suppose S02 = 0.85, Nip = 6, 3 variables and three different single scattering paths are included in the fit:

Reff = 2.82 Pt-Pt (Pt3Sn) Reff = 2.82 Pt-Sn (Pt3Sn) Reff = 2.77 Pt-Pt (Pt fcc)

I can not assume an average coordination number because each path have a different degeneracy, so I have 3 new variables in the fit and 6 in all. If I will perform a multiplied shell fit the number of varibles (specially coordination numbers) also will increase and there will not be enough number of independen points either. Could I perform a multiplied shell fit considering only CN of the first shell? I mean, a multiplied shell fit to increase the number of independent points and only calculate CN for the first shell.

Sorry for this long e-mail and this crazy questions.

Thank you very much,

Best regards, JA

Scott Calvin ha escrito:

...

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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