Hi all, This got marked spam and rejected when I sent it from home this weekend... :) At 12:48 AM 6/30/2007, you wrote:

Hello,

Thanks Bruce and Matt for the previous comments© I have the following questions and I would appreciate comments about them:

My Questions are: 1- Can we consider sigma^2 of a single scattering path to be a measure of Debey Waller factor?

If you mean the Debye-Waller factor from x-ray diffraction, the answer is no. The EXAFS sigma^2 is the variance in the absorber scatterer distance, the XRD sigma^2 is the variance in the position of an atom relative to its lattice point in the crystal. Thus, IF the motion of the absorber and scatterer were uncorrelated, it would be reasonable to think that the EXAFS sigma^2 would be twice the XRD Debye-Waller factor. For nearest-neighbors, though, this is a terrible assumption, as the atoms will tend to move in a correlated fashion (put another way, acoustic phonons dominate over optical ones). Thus the EXAFS sigma^2 for nearest-neighbors will usually be much less than the XRD Debye-Waller factor. Further confusing matters is terminology. In EXAFS, sigma^2 is sometimes called the Debye-Waller factor...but this Debye-Waller factor is not the same as that from XRD! I've also seen "Debye-Waller factor" used to include all information about the shape of the distribution of the absorber-scatterer distance, so that sigma^2 is "the harmonic part of the Debye-Waller factor," but that seems to be an older usage.

2- Is sigma^2 a measure of ¥or directly proportional to¤ strain in a bond?

Hmm...I'd say no, although I think I know what you're getting at. One major contributor to sigma^2 is thermal vibrations, which of course increase with temperature. I don't think that's generally categorized as "strain" (although I'm wary of the differing definitions that terms such as this can have in different specialties!). Another contributor to sigma^2 is variations in absorber-scatterer distance due to local defects, surface effects, etc., generally lumped together under the term "static disorder." This term itself can be a little misleading, as, e.g., a nanoparticle can have a sigma^2 that varies in a perfectly regular way with distance from the surface--we call that static disorder, even though it is not particularly disorderly. :) At any rate, what material scientists call "strain" can show up as static disorder. But even in that case, note that if all the bonds in a sample were strained, sigma^2 would not reflect it--it's only when some are strained and some are not that it shows up. So yes, I've seen (knowledgeable) people point at a sigma^2 and say "I think that's high because of strain." But that's a kind of short-hand for what's going on.

3- When doing first shell fitting in Artemis, The actual bond length is: r_eff + dr +- delta ¥dr¤© Are the error bars associated with dr values ¥delta¥dr¤ of about 0©001 A¤ realistic? ¥i©e© 0©001 A is too small to detect by XAFS¤©

Your formatting didn't come through very well, but I'll give it a shot. Ifeffit (and thus Artemis) do a pretty good job of putting a lower bound on delta dr, in my opinion. Why a lower bound? Because there are all sorts of systematic errors that could be coming in, e.g. an iffy model--such as a first-shell only fit for a crystalline material, since there's often a bit of spectral leakage from more distant shells. I'd be very surprised if Artemis ever gave a 0.001 A delta dr, though, and absolutely shocked if it did so on a first-shell only model. Are you saying that it did do that for you?

4- What determines the real space resolution in XAFS measurements other than K_max?

k_min, of course. To answer the gist of your question more fully, though, I have to get on my soapbox. :) "Resolution" is often taken to mean something other than it does. Resolution criteria literally mean the point at which you could be expected to distinguish between two peaks. It is NOT the limit to the precision of information that can be retrieved by a clever person. Huh? Let's take an example of, oh, a proposal that there are two slightly different (but consistent) nearest-neighbor distances in some material. If those distances differ by less than the resolution implied by the k-space range, then they will not show up as two peaks in the Fourier transform. Instead, they'll show up as one broad peak; i.e. a peak with an anomalously large sigma^2. If a multiple-shell fit was performed and splitting was known to be a possibility, this anomalously large sigma^2 could be taken as indirect evidence for the splitting. In fact, if there were some way to estimate sigma2's a priori (I'll grant you that's a big if!), then the broad peak could be modeled as two scattering paths, with the splitting as a free parameter. In that case, EXAFS could give information about splitting to a greater precision than the resolution of the measurement. A lot of the lore about the capabilities of EXAFS suffers from a similar lack of subtlety. Joe Woicik recently gave a very interesting talk at the NSLS Users' Meeting. It is generally bandied about that EXAFS cannot distinguish scatterers that differ in atomic number by less than 5. This is kind of true--in a mindless first-shell fit--because in those cases del_r and sigma^2 will usually just slop up the differences in phase and amplitude due to the different atomic number of the scatterer. But if you really really knew del_r and sigma^2 a priori, even a difference of one atomic number stands out like a sore thumb! The upshot is that if you model, say, zinc scatterers as if they were iron, the fit will probably "work," but you'll be introducing substantial systematic errors into your fitted variables. A corollary is that in the case of a highly-constrained fit, you may be able to do considerably better than the usual +/- 5 rule. The bottom line of this little speech is that the oft-quoted limits of EXAFS analysis are usually referring to a fit in which no a priori information is used. If you know (or suspect) anything about the system and incorporate that into your model, greater precision is sometimes possible. Of course, the results are then only as good as the a priori information; the whole thing could be a house of cards ready to collapse. But in favorable cases, multiple lines of evidence can be used to construct a convincing scenario... Hope that helped! --Scott Calvin Sarah Lawrence College