On Tuesday 04 May 2010 07:09:33 am Enzo Liotti wrote:
> Hello,
> I'm trying to use EXAFS to study the intermetallics present in a complex Al
>  alloy. The three main phases present in the alloy are Al3Ti, Al13Cr2 and
>  Al13Fe4. The first is tetragonal and the other two are monoclinic.
> To create the theoretical model in Artemis I inserted in Atoms the
>  crystallographic informations available in literature and I run it and
>  FEFF. Since in the monoclinic structure the absorbing atom occupies more
>  than one position I created as many FEFF calculations as the number of
>  positions of the Absorbing atom changing every time the core atom in the
>  Atoms page.
> My question now regards the S02 parameter (path amplitude), how do I model
>  it when I've got more than one FEFF calculation for a single compound? and
>  how do I do when I have more than one compound with more than one FEFF
>  calculation each ones (for example if I have a mixture of two similar
>  intermetallics like Al3Ti and Al11Ti5 )?

As a purely practical matter (without any consideration of physics or
of how the theory works), there are two options.  You either make them
all the same or you don't make them all the same.

That's not a very profound answer, I admit, but if you start to
scratch the surface, you'll eventually find a way to think about this
sort of question.

In purely statistical terms, you are asking whether or not to add more
parameters.  In this case, as in every case, that is a simple enough
thing to test.  Try making a fit with all S02 parameters the same,
then try making a fit with two or more being different.  If the fit is
improved in the sense of the reduced chi-square being significantly
smaller, then you may have improved the quality of the fit.  Another
way to state this question is: "Do the data support the evaluation of
more than one such parameter?"  A question of the "do the data support
support" variety is always easy to answer -- you just try it and see.

Of course, these are not arbitrary parameters -- they have specific
meaning.  In the case of S02, this parameter is a measure of the
non-unity overlap of the electronic states of the absorbing atom
before and after the creation of the core-hole.  That is, it is
somehow a measure of the relaxation of the electrons in the presence
of the core hole.  As such, we expect S02 to be a number around, but
smaller than, 1.

However, there are a lot of things that effect the amplitude in an
EXAFS analysis.  Problems with the sample, with the linearity of the
detectors, with the processing of the data, or even with the theory
can all contribute to the evaluation of the EXAFS amplitude.  All
those effects are difficult or impossible to distinguish from the
physical S02 in a statistical sense.  Thus, your measure of S02 in
EXAFS analysis includes the effect of relaxation in the presence of a
core-hole, but it also includes all those others issues that may or
may not exist in your data.

For many years, the concept of "chemical transferability" has been
currency in the EXAFS community.  That is, we presume that for
properly created and measured samples of the same absorber and edge,
the S02 value for one such sample can be used in teh analysis of
another.  Stated another way, S02 is a property of the species of the
absorber.  Some years ago, Frank Bridges and his group published such
a survey.  Recent work from John Rehr's group has elaborated on this,
demonstrating that S02 is, in the strictest sense, neither
transferable nor constant in energy.  However, these effects are small
such that chemical transferability remains a useful and defensible
practice in many EXAFS analyses.

So, back to your question -- how do you deal with S02 in a mixed
compound or in a compound with multiple crystallographic sites?  Or,
more generally, how do you deal with S02 when you have to run Feff
more than once to perform a single fit?

Well ... you either make them all the same or you don't make them all
the same.

Regardless of how you proceed, you need to verify that your choice is
statistically defensible.  More importantly, if you introduce more
than one such parameter, you need to be able justify that decision in
terms of the physics or chemistry.  In the case of a mixed compound,
you need to be able to explain why the amplitudes for the species in
the mixture should be different.  If you have no such physical or
chemical explanation, then you have to ask yourself if the parameter
you added was not just a "fudge factor" that made the fit better
numerically without adding meaning to your results.

Fortunately, Artemis makes it relatively easy to tie parameter values
together and to allow them to float separately.  (Pro tip: Use def

As a general practice, I would start with a single S02 and see how the
fit goes.  If it goes well, I might declare victory and move on.  If
it goes poorly, I might consider introducing other S02 parameters,
taking care that I can defend the choice statistically and physically.



 Bruce Ravel  ------------------------------------ bra...@bnl.gov

 National Institute of Standards and Technology
 Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
 Building 535A
 Upton NY, 11973

 My homepage:    http://xafs.org/BruceRavel
 EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/
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