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