[Ifeffit] Fitting mechanism of Artemis

[Matt Newville]

Hi Konstantin,



On Fri, Oct 6, 2023 at 3:11 AM <bikov at phys.uni-sofia.bg> wrote:

> Dear all,
> I have a general question regarding the mechanism employed in the fitting
> procedures implemented in Artemis.
> How exactly is performed a fit?



That is a pretty open-ended question to be able to answer with precision.
Is the question more about how fitting works in general, or about what is
modeled and allowed to change in the mode for EXAFS?

There are plenty of writeups and resources on both topics, including
program documentation.

Do we have a fixed central atom (absorbing/emitting atom) and only the
> distances to the
> neighbors included in the probed pathways are varied, i.e. by varying the
> coordinates of the corresponding neighbor atoms, or during
> the fitting process Artemis can vary the position of the absorption center
> too?



Within the context of the software here, the answer is sort of that the
central atom is fixed.

The way we model EXAFS is effectively (more below,  as some might object to
this) as a 1-dimensional problem.  Single scattering EXAFS depends only on
the scalar distance between the atoms (or path length for the
photo-electron).  Now, some aspects of EXAFS scattering definitely depend
on more than just distance.  The Z of the scattering atom definitely has a
large effect. The angle of the X-ray polarization vector with the
three-dimensional bond direction can also have an effect.   These are
folded into the scattering amplitude and phase shift.   But even the
disorder terms, sigma^2, and so on, are really capturing the disorder in R,
not the 3-D disorder.

For sure, multiple-scattering paths will have 3D information baked into
them. With Feff and the way we use it, this 3D info *is* folded into the
scattering amplitudes and phase shifts calculated for a path and all we
really vary is the distribution of path lengths for those paths.

In 1-D, it does not matter whether the absorber or scatterer moves, the
only thing that matters is the distance.  In fact, to the extent that
neighboring atoms move together in the same direction, there is no effect
on the EXAFS -- an atom in a solution or melt will have EXAFS (it might be
weak, but it does not fall to 0 at a phase transition).  EXAFS is much more
sensitive to "optical phonons" (neighboring atoms moving in opposite
direction) than to "acoustic phonons" (neighboring atoms moving in the same
direction).

Now, one can take a reverse-monte-carlo approach: calculate a lot of
different local structures, sum the EXAFS for each calculation, and see
which is best.   One can also do something sort of in-between:  calculate a
set of "undistorted paths" and one or more sets of "distorted paths" and
then do a linear (or for some multiple-scattering case, quadratic) model to
combine these.


Could the procedure be constrained in such a way that the scattering
> pathways are adjusted by only varying the coordinates of the central atom?
>

Yes. In fact, this has been done several times.  If you imagine a metal ion
(let's say Ti) surrounded by six neighbors (let's say O) in an octahedron,
a common thing to try to model is if that Ti atom moves away from the
center of the octahedron, say in a perovskite-like structure.

For the simplest case (ie, what I would start with ;)), you could calculate
the EXAFS with Ti at the center of a perfect octahedron and get 6
equivalent paths, and add those to give the EXAFS.  If the octahedron is
distorted, you might have 2, 3, 4, or 6 paths.  Let's go all the way to
"general" 6 paths.   Each path would use a different Feff calculation (or a
copy).  You would not be limited to varying the change in each of the six
path lengths (our 'delr' parameter) to have the same delr for all paths.
Instead, you could define 3 new fitting variables, let's say "dx", "dy",
and "dz" for the displacement of the absorbing Ti from the position used in
the Feff calculation (let's just call that "origin").

If you only have "dz", then one path gets shorter by dz, one gets longer by
dz, and the other four get longer by sqrt(reff*2 + dz**2), where "reff" is
the magic "R used for each path Feff calculation.   I'll leave the more
general case for you ;).

Hope that gets you started,

--Matt
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