[Ifeffit] Re: Amplitude and the EXAFS equation

[Matt Newville]

Scott, Bruce,

I agree that getting accurate coordination numbers from EXAFS is
difficult, and with Scott's assessment that N is generally no
better than 10%.

Bruce's explanation of the mechanisms for HOW to untangle So2
from N was right on.  Getting N can also be complicated by the
concept of 'degeneracy' for a feff path, which generally assumes
a sample with high crystallinity and a small number of chemical
environments for the absorbing atom.  The Atoms/Feff/Ifeffit
approach is somewhat biased toward simple crystals.

In addition to the analytic issues that Bruce and Scott mentioned
in modeling of chi(k), I'd like to add a few other points about
EXAFS amplitudes:

== Energy resolution and Feff's mean-free-path:

The finite energy-resolution of any EXAFS measurement will effect
the EXAFS amplitude.  This is usually thrown in with the
mean-free-path and core-level width terms into a single lambda in
the EXAFS equation -- Ifeffit uses an Ei parameter that has units
of eV, but it's basically the same thing.  While So2 and N are
completely correlated, but Ei and So2 are very highly correlated.
And, unlike for sigma2, it is not at all easy to independently
tweak energy resolution and So2.  We usually completely ignore Ei
and blame all sins of amplitudes on So2.

Feff tries to estimate many of the the physical processes
identified as So2.  It also estimates lambda, but much more
crudely: it interpolates a fit to the *figures* from Rahkonen and
Krause (1974).  Feff definitely does not include the energy
resolution of a Si(111) monochromator at 9keV.

Given this, the typical observation that So2 is ~0.8 seems pretty
good!  I'm not sure anyone can really explain why So2 is
"normally 0.8", but I suspect that the energy resolution is as
important as any passive electron loss terms that Feff misses.

== Measurement and Analytic errors of the edge-step

Error in the edge-step are directly correlated with error in N.
Determining the edge step better than the 5% level is hard.  To
do normalization better than this, a constant edge-step may not
be good enough.  But dividing by the measured mu0(E) is almost
always much worse!

== Self-absorption effects in fluorescence data

Quite a bit of EXAFS data measured in fluorescence has finite
self-absorption effects.  This also has a direct influence on the
coordination number, and making sure these effects are smaller
than 5% is not easy.  In fact, most experimental errors show up
as errors amplitude.

==

That's all to give more reason to be skeptical of claims of
getting N better than 10% from EXAFS.

This is a major reason why it's still important to measure and
analyze standards.  Data measured at the same beamline and under
similar conditions will likely have the same energy resolution,
so So2 _IS_ likely to be transferable, assuming you make the same
systematic choices in finding the edge step for unknowns and
standards, and the same systematic choices in doing the Feff
calculations.  Of course, analyzing standards can also give you
confidence that Feff/Ifeffit are working well enough to trust for
a real system.

--Matt