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

Bruce Ravel bravel at bnl.gov
Mon Mar 16 08:26:13 CDT 2015

```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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