Hi Nic,
On Aug 2, 2011, at 6:41 AM, Nicholas.Tse(a)csiro.au wrote:
> Just a sidenote, is the general workflow for fitting XAFS data the
> following:
>
> Fit first shell and get reasonable Enot and Amp and then make set
> them, then incrementally add more of the scatter paths and adjust
> the delR for each path correspondingly. Adjusting degeneracy for
> atom assuming there are slight differences in the atoms spacing.
>
> I know the question is very trivial but I don't seem to be able to
> find a general guideline for knowing when the fitting process is
> over in these type of analysis.
As for your side note, there are several workflows that have success.
The most appropriate one depends both on your level of knowledge about
the material and your personal preference.
I don't particularly favor the one you describe, though, because it's
an attempt to fit a few parameters at a time to avoid wrestling with
correlations. That doesn't end up actually avoiding correlations; it
just locks them in.
For instance, if you first guess amp, find a "best fit" value, set it,
and then run a fit with something else varied (say, a degeneracy),
then you've artificially broken the correlation between amp and
degeneracy. But you've done it in a completely arbitrary way...you
haven't really explored the space of the two varied jointly. (Of
course, if you're only doing a single shell, you can't vary both S02
and N, because they correlate completely. But you certainly can't
pretend you can by first varying S02 with N fixed, and then varying N
with S02 fixed!)
The two most prevalent valid fitting strategies I've seen are:
"Bottom up." (That's my name for it. I've also heard it called "shell
by shell.") In this strategy, you start with a single shell with few
constraints; perhaps you guess N (taking S02 from a standard), E0,
delR, and ss. You try different nearest-neighbors and see what works
best. As you begin to gain knowledge about the system, you add more
distant shells and begin to add reasonable constraints. In a
biological system where you've determined nearest neighbors are
sulfur, for instance, then your knowledge of the particular system may
suggest what ligands are present, which might provide information
about second nearest-neighbors. For instance, the number of second
nearest-neighbor carbons might be equal to the number of near-neighbor
sulfurs, constraining some of the degeneracies.
"Top down." Start with a highly-constrained, multi-shell fit. For
instance, you might include all important paths out to 5 angstroms,
with the only free parameters S02. E0, and a sigma2 parameter or two.
If the fit appears qualitatively close, constraints can then be
relaxed to more realistically model the particular features of the
material (as one example, you can vary degeneracies to allow for
vacancies or nanoscale effects). If the fit does not appear
qualitatively close initially, it is probably the wrong starting
material. (Amplitudes are often far off initially with this approach,
and there may be small phase shifts, but the first few big peaks
should be roughly in the right place. A minor variation on this
approach is to start with a sum of paths rather than fit at all.)
Note that both strategies end up in the same place: a modestly
constrained multi-shell fit. (And no, that's not always possible--
sometimes first shell information is all you can get.)
When do you use each? If your material is a modestly modified version
of a known crystal, top down is a good way to go. For instance, you
might have a doped zinc oxide. You know the structure of zinc oxide;
the question is the effect of the dopant. Why waste effort trying to
fit just a nearest-neighbor first, which can be quite difficult, when
you think you know the rough structure out to several angstroms? On
the other hand, for something like a protein you probably don't
initially know much about the structure at all. Then bottom up works
better. Many problems, such as some environmental problems, fall in
between the two, and either approach might be effective.
A strategy that I've sometimes seen used by beginners in workshops,
which is not a good idea, is to fit one shell, get the results, set
the values of those parameters to the result of the fit, add another
shell, and so on. This is a misunderstanding of the bottom up
approach! Rather than using information from outer shells to achieve
better fits on the inner shells (or vice-versa), you lock in
distortions and make it difficult to evaluate statistically-related
measures such as error bars.
Hopefully that helps!
--Scott Calvin
Sarah Lawrence College
