[Ifeffit] my problem
Anatoly Frenkel
frenkel at bnl.gov
Sat Dec 17 18:09:07 CST 2005
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.
Anatoly
-----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces at millenia.cars.aps.anl.gov]On Behalf Of Scott
Calvin
Sent: Saturday, December 17, 2005 5:29 PM
To: XAFS Analysis using Ifeffit
Subject: RE: [Ifeffit] my problem
Hi Tadej,
I agree with the general drift of Anatoly's comment--this is what
Shelly meant by saying it sounds like a tough problem! But I think it
came off sounding a little more harsh than I suspect Anatoly meant it
to be, particularly considering some of the systems he himself has
examined! Anatoly's description is fair IF only a nearest-neighbor
fit is performed. But it's possible that inequivalent sites have very
different environments at greater Reff, particularly since niobium is
so much heavier than oxygen! For example, there's been a lot of work
done that shows that there is a screamingly large difference in the
EXAFS spectra of A and B sites in the spinel structure (Vince Harris
did a lot of this, for example). In such a case, Artemis is able to
find the site occupancy without too much trouble, using a strategy
such as Shelly explained.
Of course, =seven= freely-floating sites sounds likely to yield
nonsense fits. It would help if you could use some physical intuition
to try to simplify the problem, at least at first. Consider also
using the "restraint" feature in Artemis/Ifeffit liberally in your
early fits to keep the fit from wandering off into nonsensical territory.
--Scott Calvin
Sarah Lawrence College
At 12:14 PM 12/15/2005, Anatoly wrote:
>boundary="----_=_NextPart_001_01C6019A.F6711239"
>
>You cannot resolve these sites from EXAFS analysis. Even if you had
>only 2 inequivalent sites of the same central atom with occupancies
>N1 and N2, you would not be able to resolve N1 and N2 in the fit
>because different Nb atoms would have similar environments (e.g., 4
>and 6 oxygens), and they will have similar Nb-O distances around
>each site. The best you can do is to try to fit the first nearest
>neighbor peak as an average Nb-O contribution (if it is a well
>isolated peak) and try to make use of sigma2 that may turn out to be
>larger than in some well known Nb oxide reference that you should
>analyze first.
>
>Anatoly
>
>Dear collegues,
>
>my name is Tadej Rojac and I'm writing from the Institute Jozef
>Stefan in Ljubljana, Slovenia. I work in the Department of
>electronic ceramics. Actually, I'm working on a EXAFS spectra with
>Artemis. What I am trying to do is mainly to describe an EXAFS
>spectrum with a model concerning the structure of Nb2O5. I'm working
>togheter with prof. Iztok Arcon, who is a specialist in the field.
>My main problem is that I have to do some suppositions. In fact
>Nb2O5 structure is quite complicated. It is composed of seven
>different Nb positions which I took into account using 7 feffs in
>Artemis. I don't know the exact occupancies of the seven positions.
>In order to make the search easier I did at first a supposition
>that all the occupancies must be positive, which is realistic. I set
>this with the command "abs" in each feff file. Secondly, I need to
>supose that the sum of all occupancies is 1. In that way the search
>for the result is much easier, otherwise I get the sum greater than
>one, which, for sure, is not the case. My question is how can I do
>that? For example, if the occupancies are O1, O2, O3, O4, O5, O6 and
>O7 and I define them with a starting value (let use say the same, so
>1/7) than I can do O = O1+O2+O3+O4+O5+O6+O7. Finally I need to do O
>=1, but here Artemis doesn't want to define the same parameter (O in
>this case) twice. So, how can I insert the conditions, that the sum
>of all the occupancies is 1, into Artemis? I hope you can help me.
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