Shaofeng Wang asked this question on the mailing list that some may not have seen because it got marked as spam somewhere along the line. Kinda weird. Not quite sure why that happened....
I have a question about sigma square. Must this parameter be in the range of 0.003-0.02? I obtained some of it in the range of 0.0001-0.002. Is this reasonable? Could please provide some reference?
There are no hard rules for anything. That sigma^2 is 0.00something is a good guideline and often the case, but not an actual rule. The problem with a sigma^2 in the range of 0.0something is that it tends to attenuate the path so much that it doesn't really have an impact on the quality of the fit. In that case the uncertainty is often very large precisely because the path no longer contributes significant spectral weight to the fit. A sigma^2 in the range of 0.000something means that the bond is very stiff. In some situations, that would be correct. As an example, consider the sort of negative thermal expansion material that is a network of metal-ligand octahedra. The NTE effect happens in that case because, as the material heats, up the octahedra tilt within the network, pulling the network inwards. This happens because the metalligand (usually metal-oxygen) bond is very strong -- much stronger than the forces connecting the octahedra. In an EXAFS measurement of an NTE material, you will likely find a very small sigma^2 for the first shell. (And a very large one for the second shell.) Regardless of the size of sigma^2, the bottom line is that the value is defensible. This means that you can understand and explain why sigma^2 is the size that it is. It also means that the uncertainty is such that you can support your conclusion. While the red line might overplot the blue with sigma^2=0.0003+0.001, that may be a troubling result because sigma^2 is not positive definite! Executive summary: a reasonable value is a defensible value. If you are willing to explain a result to your thesis committee or let one of us review it in a manuscript, then the result is probably reasonable. HTH, B -- Bruce Ravel ------------------------------------ bravel@bnl.gov National Institute of Standards and Technology Synchrotron Science Group at NSLS-II Building 743, Room 114 Upton NY, 11973 Homepage: http://bruceravel.github.io/home/ Software: https://github.com/bruceravel Demeter: http://bruceravel.github.io/demeter/
Hi Bruce,
A side comment on a topic you’ve raised before. You said to Shaofeng that:
On Jul 26, 2016, at 8:39 AM, Bruce Ravel
Thanks, Scott. When I started writing that email, it was my intention to discuss correlations between sigma^2 and other parameters. By the time I got to the end of the email, I had forgotten all about it. You closing comment about how a weird, indefensible value for sigma^2 (or any parameter) is a hint that something is flawed in the model is another very important point. So, Shaofeng, please consider what Scott has to say. B On 07/26/2016 09:39 AM, Scott Calvin wrote:
Hi Bruce,
A side comment on a topic you’ve raised before. You said to Shaofeng that:
On Jul 26, 2016, at 8:39 AM, Bruce Ravel
mailto:bravel@bnl.gov> wrote: It also means that the uncertainty is such that you can support your conclusion. While the red line might overplot the blue with sigma^2=0.0003+0.001, that may be a troubling result because sigma^2 is not positive definite!
I’m not convinced that it should be disturbing at all if a fit for sigma2 yields a result that is not positive /definite/.
Suppose, for a moment, that the true sigma2 for a scattering path is 0.0003 Å^2 , and that data is being analyzed up to /k/ = 9 Å^-1 . The EXAFS equation tells us that the effect of sigma2 on chi(k) is quite modest in that case, and is also relatively insensitive to the precise value of sigma2. According to the EXAFS equation, at the top of the data range, where it’s effect is greatest, the sigma2 factor, e^(-2k^2 sigma2), is multiplying the amplitude by 0.95. Suppose further that the uncertainty was +/- 0.0005 Å^2 . That would imply the sigma2 factor was at the top of the range was as small as 0.88 or as large as 1.03. It doesn’t seem terribly different to me than a fit which yields an S02 of 0.95 +/- 0.08. Or, in a case where coordination number is expected to be either 4, 6, or a mixture of the two, N = 5.7 +/- 0.5. The latter result is not generally considered troubling, even though the range implied by the uncertainty overlaps with values (N > 6) that might be considered wildly implausible for the system being studied.
The comparison to coordination number or S02 is not perfect, because sigma2 is sensitive to the difference between the amplitude of chi(k) at low k and at high k, whereas S02 or N correspond to a uniform suppression. Still, in a case when the true value of sigma2 was 0.0003 Å^2 , the difference between the chi(k) amplitude at the bottom of the /k/-range and the top is quite modest, and might reasonably be statistically indistinguishable from no difference at all, particularly if it is for one path in a multi-path fit, if the data is somewhat noisy, or if the /k/-range is small.
To borrow a similar example from another specialty in physics, for quite some time, measurements of the square of the electron neutrino mass often yielded results that were not positive definite. This was taken neither as evidence that the neutrino mass was imaginary, nor that the data was bad.
I worry that sending the message that it is troubling to get a result for sigma2 that is not positive definite can lead to beginners rejecting such fits, thus introducing a bias toward larger values of sigma2. Such a user might prefer a model that generates sigma2 = 0.0020 Å^2 +/- 0.0018 to one that gave 0.0003 Å^2 +/- 0.0005, for example. To me, all else being equal, the second result is better, because it is more precise.
Of course, a result that was negative definite, such as sigma2 = -0.0009 Å^2 +/- 0.0004, would indeed be troubling, and good evidence that something about the model or the data was problematic.
—Scott Calvin Sarah Lawrence College
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-- Bruce Ravel ------------------------------------ bravel@bnl.gov National Institute of Standards and Technology Synchrotron Science Group at NSLS-II Building 743, Room 114 Upton NY, 11973 Homepage: http://bruceravel.github.io/home/ Software: https://github.com/bruceravel Demeter: http://bruceravel.github.io/demeter/
Dear Scott and Bruce,
Thanks a lot for your detail explaination.
Shaofeng
--------------------------------------
Shaofeng Wang, Ph.D of Geochemistry
Environmental Molecular Science Group
Institute of Applied Ecology, Chinese Academy of Sciences
Shenyang, 110016, China
wangshaofeng@iae.ac.cn
www.iae.cas.cn
From: Scott Calvin
Sent: Tuesday, July 26, 2016 9:39 PM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] about sigma square
Hi Bruce,
A side comment on a topic you’ve raised before. You said to Shaofeng that:
On Jul 26, 2016, at 8:39 AM, Bruce Ravel
participants (3)
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Bruce Ravel
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Scott Calvin
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Shaofeng Wang