Re: [Ifeffit] Debye factor and S02 correlation
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
A few comments on this S02 and Ei thing: 1. I am not particularly encouraged by the fact that Matt was just barely able to co-refine S02 and Ei in a copper foil. In many ways a copper foil is a very contrived exafs problem. I would like to see a careful study by someone who understands the statistics well on a wide variety of well-ordered and disordered materials before I would suggest to anyone that they consider reporting both S02 and Ei in the literature. I am sure that S02 and Ei will always be highly correlated and I doubt that, for most problems, they will have reasonable best-fit values despite their large correlations. Of course, I would be pleased to be proven wrong. 2. I don't quite agree with John's assessment of the error bars. The two parameters are almost completely correlated. I don't think it is reasonable to say that two parameters which are that highly correlated and which have values of the same order of magnitude should have error bars of different orders of magnitude. I understand that we have other reasons to know what an appropriate value for S02 should be and so I understand why John wants to state the S02 can be 0.9+/-0.05, but from the vantage point of interpreting the statistics of the fit, you are NOT at liberty to assert an error bar. This is particularly true for a real research problem with difficult sample prep or detector issues. The amplitude really may be something like 0.75 after the fit accommodates such systematic uncertainties. What's more, correlations with the various sigma^2 parameters used in a fit to a disordered material may drive up the error bar on S02 to something like 0.1 or 0.2 or higher. In short, I have to caution everyone reading this list about the dangers of drawing conclusions about hard analysis problems from the results of an easy one like a copper foil. 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 (2)
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Bruce Ravel -
John J. Rehr