On 03/15/2015 09:50 AM, Samy OuldChikh wrote:
- Distances : 1) a spherical expansion term was used to describe distance variation in [hkl] direction (reff*alpha1) with l considered as "large" when compared to h,k (reff*alpha1)
2) another spherical expansion term was used to describe distance variation in pure [hk0] direction (reff*alpha2)
3) a rough average of two previous expansion terms for [hkl] direction when h,k are comparable to l (reff*(alpha2+alpha1)/2).
- For modeling disorder, the correlated Debye model was used with 3 parameters dt, dt2, dt3 (t =293K): 1) [hkl] direction with l considered as "large" : debye(t,dt) 2) pure [hk0] direction: debye(t,dt2) 3) for [hkl] direction with h,k comparable to l : debye(t,(dt+dt2)/2)
But does this choice of parametrization is really reasonable? It seems very rough to me but when I look at the fit results it looks ok.
It's not unreasonable to treat different directions with different parameters in this manner. One of the nice things about doing EXAFS analysis is that you get to try any model you can cook up and test it against the data. You even get to try crazy ideas just to see if they can give any insight into your problem. Of course, once you settle upon a model, you need to be honest about uncertainty and honest about understanding the physical meaning of the fitted parameters. If a model is defensible, it is likely publishable. In a hexagonal material, there is a physical difference in different directions. So your concept might be reasonable. The sorts of questions you need to ask yourself are things like: (1) do the values you get in the different directions makes sense in the context of other things you know about the system? (2) are the values in the different directions different from one another outside their uncertainties? and so on.
- Uncertainty on : 1) Distances : is it simply delta(r) = reff*delta(alpha) ?
You are correct in thinking that uncertainties are intended to be propagated in the manner that one computes standard deviation of dependent variables. If you do not have a favorite book on error analysis, I'd suggest "Data Reduction and Error Analysis for the Physical Sciences" by Bevington and Robinson. It's a beautifully written little book.
2) Debye-Waller : I can't figure out how to relate the uncertainty computed for the Debye temperatures (dt, dt2) to the uncertainties of the debye-waller terms for each scattering paths. Although I spent some times trying to understand this paper,http://journals.aps.org/prb/pdf/10.1103/PhysRevB.20.4908, I can't write a simple relation at the end.
The correlated Debye model does not have a simple expression that makes it easy to do error propagation on the back of an envelope. Here is what Larch uses, which was taken directly from Feff6: https://github.com/xraypy/xraylarch/blob/master/dylibs/FeffLib/sigms.f Rather than trying to do error propagation analytically, I would think it would be easier to do so numerically. I believe that's what Larch does. Ifeffit never did that, so Artemis (when using Ifeffit) does not report uncertainties porpagated to the paths. You have to do it yourself. :( B -- Bruce Ravel ------------------------------------ bravel@bnl.gov National Institute of Standards and Technology Synchrotron Science Group at NSLS-II Building 535A Upton NY, 11973 Homepage: http://bruceravel.github.io/home/ Software: https://github.com/bruceravel Demeter: http://bruceravel.github.io/demeter/