[Ifeffit] Evaluation of uncertainty using correlated Debye model + advices for the fitting of an hexagonal Co-foil

[Samy OuldChikh]

Many thanks Bruce for your previous answer.

I continue to work on the fitting of the Co metallic foil with an hexagonal structure.
I have "cooked" a new model which involve the variation of cell parameters of the hexagonal lattice (new fit attached).
This allow to express analytically all the distances for single and multiple scatterings paths with only two parameters and get rid of the spherical expansion terms.
For Debye-Waller factors, I had to keep the previous idea (modeling anisotropy with 3 Debye temperatures).

And surprise ! : the new model give worse results in term of R-factor and reduced chi(square) whereas I was expecting a better or at least a similar agreement.
Some attempts to fit Debye-waller factors independently, lead me to think that the Debye-Waller factors are under evaluated especially for multiple scattering paths.

I try to find some reference which could mention this issue. I found from "Theoretical X-Ray Absorption Debye-Waller Factors, Fernando D. Vila, J. J. Rehr, H. H. Rossner, H. J. Krappe, Phys. Rev. B 76, 014301 (2007)" :

"However, these approaches are unsatisfactory for several reasons. First, there are typically many more independent DW factors in the XAFS MS path expansion than can be fit reliably to the available data. Second, the semiempirical models require separate fits to appropriate Debye or Einstein temperatures for each multiple-scattering path. And third, these models typically ignore anisotropic contributions, and hence do not capture the detailed structure of the phonon spectra and associated DW factors."

I do not understand why for the case of multiple-scattering paths, separate fits of Debye Temperature are needed ?
If each multiple scattering paths requires a different Debye temperature, I don't see the point to use the correlated Debye model.
Or maybe it is still valid to group some multiple scattering paths like I did with one Debye temperature ?

 Thanks for the help.


Best Regards,
Samy Ould-Chikh

KAUST Catalysis Center
Bldg.3,Level 4, #4231
4700 King Abdullah University of Science & Technology
Thuwal 23955-6900
Kingdom of Saudi Arabia

Tel: +966 12 8084486
E-mail: samy.ouldchikh at kaust.edu.sa
Website:  http://kcc.kaust.edu.sa/Pages/Home.aspx






-----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov [mailto:ifeffit-bounces at millenia.cars.aps.anl.gov] On Behalf Of Bruce Ravel
Sent: Monday, March 16, 2015 4:26 PM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] Evaluation of uncertainty using correlated Debye model + advices for the fitting of an hexagonal Co-foil

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 at 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/
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