[Ifeffit] my problem

Scott Calvin scalvin at mail.slc.edu
Sat Dec 17 18:48:56 CST 2005

Hi Anatoly,

Yes, Vince's 1996 APL is linear, but check out the paper I 
co-authored with him: APL 81, 3828 (2002). Actually, the better 
reference for this discussion is the longer companion paper, in PRB 
66, 224405 (2002).

I agree with you that the "arbitrary" things I did in that paper (and 
similar ones) do not have airtight justification, and I have no doubt 
whatsoever that the fits I found are not the "true, physical 
minimum." In fact, I say so in my paper. The question is not whether 
such a fit is as true as possible, but whether it is providing useful 
information in which we can have a good degree of confidence. In the 
case of spinels, the effect of A or B sites on the spectrum out at 
the cation-cation distance is HUGE. Sure, I didn't know what is 
the  right way to constrain the sigma2's, and that leads to some 
additional quantitative uncertainty in the site occupancy found. But 
do I believe that I can tell the difference between 30% and 50% 
occupancy by this method? Absolutely. I could (and did) play with 
different constraint schemes, and the results were consistent enough 
to give me confidence.  Of course, having some confirmation from 
probes such as XRD and magnetic measurements helps too.

So I guess I'm saying that such fits must be viewed with caution, but 
they still provide useful information...particularly if we take our 
time and "stress" them a bit to make sure they aren't too sensitive 
to "arbitrary" constraint decisions that we have made.

--Scott Calvin
Sarah Lawrence College

At 07:09 PM 12/17/2005, you wrote:
>Hi Scott,
>Thank you for pointing out at Vince's work on ferrites. It is a nice
>demonstration of the effect of site occupancy by dopants on EXAFS. In
>Vince's APL 68, 2082 (1996), they found the distribution of Zn between A and
>B sites (octahedral and tetrahedral) by including MS, as you described.
>However, he varied only one parameter in the fit to the MS range - site
>occupancy, keeping all other fixed (p. 2083). As such, it is not a
>non-linear least square fit, but a linear least square fit of a (linear)
>combination of fixed functions, and thus the chi-squared of such fit must
>have a single minimum - either within the range of x, or at the boundary
>(x=0 or 1, as they obtained in most cases).
>What Tadej is describing seems more like a general, non-linear least squares
>fit problem, that has N minima in chi squared of which N-1 are false. It is
>counter-intuitive to assume that the contributions of EXAFS from each
>inequivalent Nb can be fixed in the fit except for its fractional occupancy.
>What about sigma2 of different MS paths? They can be equal in certain cases
>of collinear focusing paths, or you can use other constraints, e.g.,
>correlated debye model to calculate them ab initio and constrain in the fit,
>but the former case is very rare for a multi-site system, and the latter
>approach (correlated debye model) is very difficult to test for such a
>complex system before you make sure that you can use these calculations in
>such fits.
>Thus, you obviously reduce the number of variables but you may exclude the
>true, physical, minimum of chi squared from your parameter space.

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