Re: Amplitude and the EXAFS equation
Hi all, I thought I'd add my two cents: I agree with everything Bruce said (!), but I think it is worth emphasizing one aspect of this issue. Basically, unless I'm using a mutiple-element fit with some clever constraints (not yet available in Artemis, but soon, I gather), any determination of coordination number is likely to be pretty uncertain. Not only does N correlate completely with S02 for a single shell fit, it is also likely to correlate strongly with sigma2 (or the Debye or Einstein temperature or whatever I'm using as the free parameter). Multiple-shell fits help when I can use them, but if I don't know the coordination number for the first shell, how likely is it that I know the structure of the material well enough to fit outer shells? Although you may see coordination numbers determined by EXAFS with an "uncertainty" of 1 in publications, this is usually something like the uncertainty reported in IFEFFIT--it probabIy doesn't include systematic errors like the effect of assumptions concerning the Debye-Waller factor or S02. In most cases if I'm looking for a first shell coordination number via EXAFS I'm not counting on better than a factor of two accuracy. That may still be useful in some cases, but doesn't help distinguish between, say, tetrahedral and octahedral coordination. So, if I'm only looking for a factor of 2, and if I'm pretty sure my sample is homogenous and of a consistent and appropriate thickness, I'm happy to just constrain S02 to 0.90 or 0.85 or whatever, knowing that the arbitrary choice of S02 is probably introducing an uncertainty of less than 20% in the coordination number. Since this is still considerably less than I generally believe is introduced by other issues (such as the scheme used for the Debye-Waller factors), it's good enough for me. --Scott Calvin Naval Research Lab --
Scott, Bruce, I agree that getting accurate coordination numbers from EXAFS is difficult, and with Scott's assessment that N is generally no better than 10%. Bruce's explanation of the mechanisms for HOW to untangle So2 from N was right on. Getting N can also be complicated by the concept of 'degeneracy' for a feff path, which generally assumes a sample with high crystallinity and a small number of chemical environments for the absorbing atom. The Atoms/Feff/Ifeffit approach is somewhat biased toward simple crystals. In addition to the analytic issues that Bruce and Scott mentioned in modeling of chi(k), I'd like to add a few other points about EXAFS amplitudes: == Energy resolution and Feff's mean-free-path: The finite energy-resolution of any EXAFS measurement will effect the EXAFS amplitude. This is usually thrown in with the mean-free-path and core-level width terms into a single lambda in the EXAFS equation -- Ifeffit uses an Ei parameter that has units of eV, but it's basically the same thing. While So2 and N are completely correlated, but Ei and So2 are very highly correlated. And, unlike for sigma2, it is not at all easy to independently tweak energy resolution and So2. We usually completely ignore Ei and blame all sins of amplitudes on So2. Feff tries to estimate many of the the physical processes identified as So2. It also estimates lambda, but much more crudely: it interpolates a fit to the *figures* from Rahkonen and Krause (1974). Feff definitely does not include the energy resolution of a Si(111) monochromator at 9keV. Given this, the typical observation that So2 is ~0.8 seems pretty good! I'm not sure anyone can really explain why So2 is "normally 0.8", but I suspect that the energy resolution is as important as any passive electron loss terms that Feff misses. == Measurement and Analytic errors of the edge-step Error in the edge-step are directly correlated with error in N. Determining the edge step better than the 5% level is hard. To do normalization better than this, a constant edge-step may not be good enough. But dividing by the measured mu0(E) is almost always much worse! == Self-absorption effects in fluorescence data Quite a bit of EXAFS data measured in fluorescence has finite self-absorption effects. This also has a direct influence on the coordination number, and making sure these effects are smaller than 5% is not easy. In fact, most experimental errors show up as errors amplitude. == That's all to give more reason to be skeptical of claims of getting N better than 10% from EXAFS. This is a major reason why it's still important to measure and analyze standards. Data measured at the same beamline and under similar conditions will likely have the same energy resolution, so So2 _IS_ likely to be transferable, assuming you make the same systematic choices in finding the edge step for unknowns and standards, and the same systematic choices in doing the Feff calculations. Of course, analyzing standards can also give you confidence that Feff/Ifeffit are working well enough to trust for a real system. --Matt
Hi all, Matt mentioned, but didn't expand upon, yet one more important aspect of the difficult situation of measuring amplitudes in EXAFS. As he pointed out, all of the effects that Matt, Scott, and I discussed are *amplitude* effects. By careful consideration of all these issues, one may obtain coordination numbers to within 10%. In many situations, a sober estimation of uncertainty in coordination may be quite a bit higher that 10%. Note, though, that none of these issues are highly correlated with the phase terms in the EXAFS equation. Specifically, uncertainty (even large uncertainty) in amplitude does not mean that you cannot measure bond lengths precisely. Even if your coordination numbers are highly uncertain, your delta_R numbers may have nice, tight error margins. B -- Bruce Ravel ----------------------------------- ravel@phys.washington.edu Code 6134, Building 3, Room 222 Naval Research Laboratory phone: (1) 202 767 5947 Washington DC 20375, USA fax: (1) 202 767 1697 NRL Synchrotron Radiation Consortium (NRL-SRC) Beamlines X11a, X11b, X23b, X24c, U4b National Synchrotron Light Source Brookhaven National Laboratory, Upton, NY 11973 My homepage: http://feff.phys.washington.edu/~ravel EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/
participants (3)
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Bruce Ravel -
Matt Newville -
Scott Calvin