[Ifeffit] Fitting using Experimental standard

[Bruce Ravel]

On Monday 04 January 2010 10:16:15 pm you wrote:
> Dear all,
> Can somebody please explain to me what is theoretical standard and what is
> experimental standard. My understanding of theoretical standard is the
> crystallographic data. However, it is first time I heard experimental
> standard.
> Thanks
>

While certainly not wrong, I don't think any of the answers given last
night answered Fiona's question as I would have liked.

The paradigm for interpreting EXAFS data offered by a real-space
multiple scattering program like Feff relies upon the so-called path
expansion.  This means that the EXAFS from a given configuration of
atoms can be expressed as the sum of the contributions from each
scattering path.  That is

  chi_total(k) = sum_over_all_paths [ chi_path(k) ]

In this language, a "scattering path" is some closed loop wherein the
photoelectron ejected from the atom by the incident photon scatters
from one or more atoms in the cluster before closing the loop back at
the absorbing atom.

For each such path, chi(k) is evaluated like so:

            N S_0^2 F(k)
  chi(k) = ------------- sin( 2kR + phi(k) ) exp( -2k^2sigma^2 )
              2kR^2

There is also an exponetial term considering the photoelectron
mean-free-path that I am neglecting in this discussion.  There might
also, in some approaches, be additional disorder terms expressed as
cumulants, adding an additional term to the sine and an additional
exponential term. 

In a fitting program like Artemis, the parameters of this equation
come in two flavors.  

One flavor includes the terms 2R (the length of the path), sigma^2
(the mean square disorder about that path length), N (the number of
such paths), S_0^2 (the amplitude reduction factor that has to do with
the details of the behavior of the other electrons in the system), and
a handful of others.  The parameters of this type are the things that
may be parameterized in Artemis to yield answers to questions such as
"What is the coordination number of the absorber?" and "How far is the
absorber from the atoms in the second coordination shell?"

The other flavor of parameters includes the terms F(k) and phi(k).
These are the scattering amplitude and phase shift.  These are
k-dependent functions that have to do with the details of the atomic
species of the absorber and scatterer(s), the number of legs that the
scattering path has, and the angles through which the photoelectron
scatters as it traverses the path.  In Artemis, parameters of this
type are computed by Feff and typically not altered during the
course of the fit.  That is, Artemis takes the Feff calculations of
the various F(k) and phi(k) functions as gospel and uses them as the
basis for determining the values of the first flavor of parameters.

Abhijeet's original question was whether Artemis is only able to
determine the F(k) and phi(k) functions using a Feff calculation or if
it is able to somehow extract approximations of F(k) and phi(k) from
another set of experimental data using a technique like those
discussed by Matthew and Anatoly.

The short answer is "no, Artemis cannot use experimentally extracted
F(k) and phi(k) functions -- it does require the use of Feff."

The longer answer is that Matthew's request from his last email of the
night -- that someone code up a way to automate the extraction the
F(k) and phi(k) from experimental data and save it in a form that
Artemis or some other Feff-using program could use -- has long been on
my list of potential things to do with my software and may actually
happen one of these days.

The very valid question whenever the topic of empirical standards
comes up is "Why do you think you need it?"  I am unconvinced that
empirical standards are ever needed.  Of course, I am also unconvinced
that I am right in saying that!  So who knows...?  There is some
evidence that empirical standards might be preferable in certain
specific cases, such as the case in which a hydrogen atom is collinear
or nearly collinear with an absorber and scatterer.

From a the persepective of "guy who writes programs" I suppose the
fact that there is interest in having the capability of using
empirical standards is itself good enough reason to include it.

HTH,
B

PS: Please note that, strictly speaking, I was describing Feff,
Ifeffit, and Artemis.  Other real-space multiple scattering programs
and other fitting programms using Feff incorporate important
differences from what I explained above.  But the bottom line
distinction between theoretical and empirical standards is about the
same in all cases.



> Fiona R. Kizewski
> Ph.D. Candidate
> Department of Chemistry
> North Carolina State University
> Raleigh North Carolina 27695
> 
> > On Monday 04 January 2010, 09:15:37 am, abhijeet gaur wrote:
> >> Generally the fitting is done using theoretical standards. For that in
> >> Artemis, we give input as crystallographic data. But If we want to use
> >> an
> >> experimental standard instead of
> >> theoretical standard, how that can be done. Is it possible to use
> >> experimental standard in Artemis? or we have to use some other method.
> >
> > Artemis does not do fitting with experimental standards, although Athena
> > does
> > have a dialog for doing log-ratio/phase-difference analysis.
> >
> > B
> > _______________________________________________
> > Ifeffit mailing list
> > Ifeffit at millenia.cars.aps.anl.gov
> > http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit
> 

-- 

 Bruce Ravel  ------------------------------------ bravel at 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/