November 2002 - Ifeffit - millenia.cars.aps.anl.gov

rebinning data
by Carlo U. Segre 05 Nov '02

05 Nov '02

hello All: This is to bring back up a subject that was discussed a few months ago on the list. We have been diligently working on a python algorithm for rebinning XAFS data from high point density slew scans. I have been testing it and I hope that there will be a complete version available shortly. It is in the form of a unix filter which takes a few parameters (edge energy, energy above the edge where rebinning is to begin, step size in k for rebinning) and spits out a modified file for each input file. There are just a couple of small glitches in how it handles data points with the same energy (this causes athena to pop up an annoying dialog) but that should be solved this week. I am more than happy to send it to anyone who would like it. Matt, I remember that you had suggested that we send code. Carlo -- Carlo U. Segre -- Professor of Physics Associate Dean for Research, Armour College Illinois Institute of Technology Voice: 312.567.3498 Fax: 312.567.3494 Carlo.Segre(a)iit.edu http://www.iit.edu/~segre

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Re: [Ifeffit] Debye factor and S02 correlation
by John J. Rehr 05 Nov '02

05 Nov '02

Matt's test of fitting the inelastic losses using So2 and an effective mean free path (via a constant imaginary shift Ei in the net lifetime width in FEFFIT) is quite interesting. In particular the results are consistent with our current understanding of the physics, namely that the inelastic losses are generally overestimated by the plasmon-pole self energy. Thus one expects Ei to be negative to compensate for errors in this self-energy model. Also it's particularly encouraging that one can fit *both Ei and So2*. I'm not too worried by the evident correlation between these parameters since they both smoothly affect the overall amplitude; what matters is the value of Ei when So2 is about 0.9. Matt wrote: >This seems like a fine approach to me, and it could be automated, >at least somewhat. Feffit/Ifeffit have Ei as a path parameter, >so setting So2 to 0.9 and floating Ei is possible right now. >Using Ei instead of So2 has a couple possible benefits: > 1. Not completed correlated with N (though see below!) > 2. Can accomodate measurement resolution issues. > 3. Might be a little easier conceptually on the new people. > >For one variation on the canonical 'Cu 10K first shell fit', >with sigma2 varying as well, I get these values: > So2 Ei chi_square r-factor > 0.93(0.03) 0.00(fix) 119. 0.0017 > 1.00(fix) 0.55(0.25) 128. 0.0018 > 0.95(fix) 0.14(0.24) 120. 0.0017 > 0.90(fix) -.29(0.23) 116. 0.0016 > 0.85(fix) -.75(0.23) 116. 0.0016 > > 0.87(0.14) -.58(1.27) 116. 0.0016 > >The last one had both So2 and ei (and sigma2!!) floating. The >correlation between them was 0.98, higher than that between So2 >and sigma2, which was a mere(!) 0.94. So it looks like, for this >data, So2 really does want to be ~0.90 +/ 0.05, and Ei wants to >be 0.00 +/- 0.25. As I read the numbers for the minimum chi_square, I would say that the results suggest Ei = -.52 +/- .3 I don't believe the error bar on So2 of +/- .14. Probably +/- .05 is more like it, so the error bar on Ei will be much smaller than 1.27. Also, I think if you look at plots of the fits, they look better with a slightly negative Ei. We would very much like to see more evidence for the inadequacy of the plasmon pole self energy. Thus I would encourage more fits to include E_i as a fitting parameter, with So2 kept under control (e.g. fixed or floating in a range 0.9 +/- .05, assuming edje jump is well defined). J. Rehr

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Re: [Ifeffit] Debye factor and S02 correlation
by John J. Rehr 04 Nov '02

04 Nov '02

Hi Everyone, I agree with Matt's assessment: > ... my view is that the >errors in the calculated mean-free path may have a much stronger >energy dependence than the errors in the calculated So2. From >the analysis point-of-view, I prefer to think of So2 as >k-independent, and put all k-dependent pieces go into lambda(k) >or F(k). Feff tries to include all loss terms as well as it can. There are two ingredients in the mean free path lambda(k) lambda_k approx k/[Im Sigma(E) + Gamma] 1) The core hole lifetime Gamma - FEFF estimates this by interpolating from tabulated values. This rough estimate should not lead to serious errors, in my view, since a 10% error in the lifetime translates to only few percent error at worst in the loss factor exp(-2 lambda R). 2) The self energy Sigma - FEFF uses an electron gas plasmon pole approximation. which can easily be off by 1-2 eV. This is the most serious error and leads to large energy dependent errors in lambda_k. >So2 _is_ calculated (if crudely in Feff6 and 7 -- I don't know if FEFF6-8 will make an atomic value of So2 if one sets S02 = 0 in the HOLE card. This approximation is unsatisfactory since it can't account well for the valence electron contributions or interference effects which dominate So2. I don't think it can be trusted - at least to better than 10%. >Luke Campbell's work on improved So2 is included in Feff8 yet). >So one might even expect that So2 should be 1, and even find it a Luke Campbell's routines are not in FEFF8 yet as they are not yet fully automated or ready to be integrated. This will us take some months. Moreover, Luke still uses a plasmon-pole self energy, which we want to improve. >little strange that it's usually around 0.9. Clearly, there are >loss terms that are not taken into account well enough in Feff. >My view is that it's not well known whether this is dominated by >an k-dependent term (ie, should be put into F or lambda) or a >k-independent term (So2). The remarkable bit of physics here is that interference terms between extrinsic and intrinsic losses and hence tend to suppress shake-up/shake-off effects. In any case, my suggestion in fits would be to treat the loss terms using a constant and an effective mean free path: a) set So2 = constant approx 0.9 b) fit the mean free path, e.g., by fitting the core-hole effective lifetime. I'd be interested in feedback on this suggestion. Can it be automated within FEFFIT? Cheers, John Rehr

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Debye factor and S02 correlation
by Dr. Paul Fons 04 Nov '02

04 Nov '02

I meant to send this off to the list (instead I sent it to Scott Calvin only). Ahh the wonders of email. I thought I would parrot back something I read in one of Bruce's tutorials (that seemed to work well for me), namely that the Debye factor, sigma has a k dependence while S02 does not. This means that if you can Fourier isolate the first shell (and you can assume a coordination number), you can determine a value for S02 by a fit using different k weights. You simply fit sigma for various fixed values of S02 (e.g. 0.6 - 1.0) and repeat the process for different k weights (e.g. k, k^2, k^3). The resulting plot of sigma vs. S02 will result in a straight line for a given k weighting. The three different k weights will intersect at a single point (or almost so) and the value of S02 at this point will be the value of S02 for the sample. While we are discussing S02, I thought I would ask a little more about it myself. 1. S02, the passive electron reduction factor is a term that encompasses many body effects, in particular the effect of the core hole. It is also as such said to have a "weak energy and path dependence" [J.J. Rehr and R.C. Albers in Reviews of Modern Physics, v. 72, no. 3 (2000)]. The question is how fair is it to assume that S02 is a constant independent of shell, or in other words should S02 be allowed to vary with shell (e.g. with significant multiple scattering contributions?) 2. I don't remember the paper offhand, but as I recall, in a paper by Bruce, the value of S02 was ascribed a value greater than unity. I didn't grok the explanation at the time, and was wondering if Bruce (or anyone else) in his ever-expanding knowledge of exafs has an explanation for when/if S02 can be greater than unity. Certainly if you consider Rehr's definition of the overlap integral of the N-1 electron wavefunction with and without a core hole, the value of S02 cannot be greater than unity[same reference, p. 636]. Any comments?

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