Debye factor and S02 correlation
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?
Hi Paul,
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.
Yes, this trick of 'multiple k-weights' is so useful that the feffit() command should probably have as an easy-to-use option for this, say by supplying a list of kweights: path(1, feff=feff0001.dat, s02=my_amp, sigma2=my_ss2) feffit(data=my_data.chi, 1, ..., kweight='1,2,3') ^^^^^^^^^^^^^^^ That would probably be much easier on the user than using the multiple data set mechanism. This does not currently exist, but it would not be too difficult to implement. How to manage the automatically generated array outputs is not obvious. I'd probably have the array outputs use only the first k-weight in the list (which wouldn't need to be the lowest k-weight). Of course, other outputs can be made with ff2chi() and fftf() after the fit. I don't currently know how the use of restraints would impact a fit with multiple k-weights. This should go in the core so that a 'multiple k-weight' fit counts as only one data set in a multiple-data-set fit (and so that I can use it from the command line!). Bruce and I are almost ready to release 1.0075, so this may have to wait a few weeks. Are there any preferences on how this should work? Any requests for similar things?
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?)
John may have a different view on this, but 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.
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?
So2 _is_ calculated (if crudely in Feff6 and 7 -- I don't know if 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 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). --Matt
Hi folks: My US$0.02 on the topic of multiple k-weight fits: There is actually value to both of the k-weighting tricks mentioned by Paul and Matt. While I agree 100% that Ifeffit and/or Artemis should include some slight of hand to manage corefinement of two or more k-weights of the same data, it is not obvious to me that a multi-k-weight co-refinement will necesarily yield the same result as the constrained parameter space mapping that Paul described. For many situations I suspect that they will, but it is easy to imagine a chi-square manifold that has many false minima deep enough to trap even a multi-k-weight co-refinement. So I think that there is still value to the procedure that Paul decribed, even in the presence of technological advancements by Matt. Indeed, I think that parameter mapping is so important that something like the procedure described in Biochemistry 35 (1996) pp. 9014-9023 (and in other articles by that crowd) is on my list of things to do in Artemis, albeit down on the list after some other stuff and not likely to appear in the next few months. ;-( As for the mechanism of how the multi-k-weight thing should be implemented -- well, I am not sold one way or the other on whether it should be a native part of the ifeffit() command or whether it should be something that Artemis in her madness should deal with. On one hand it would probably be easier for me to have Artemis generate text to do multi-k-weight as a multiple data set fit that it would be for Matt to modify the core. On the other hand, doing a multi-k-weight fit **DOES NOT** increase th amount of infomration available for the fit. Having it be a part of the ifeffit() command would guarantee that a silly user would not convince himself that the information was doubled simply by doing a k1/k3 fit. That is probably an important enough point that it suggests that ifeffit() is a better place for it. As Matt said, keep your eyes open for a new release of ifeffit and of my codes later this week. There have been some huge improvements in Artemis in the last two weeks. The next release will be a big step forward in functionality and stability. Yay! 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 -
Dr. Paul Fons -
Matt Newville