[Ifeffit] white line intensity v. edge position in determiningoxidation state of Re

[Bruce Ravel]

On Monday 21 May 2007, Sven L.M. Schroeder wrote:
> Edward
>
> Another method to get information on oxidation states from near-edges was
> used relatively commonly in the 1980s and early 1990s, but has gone out of
> fashion since (can someone tell me why? Is the underlying physics flawed?).
>
> You determine the ionisation potential (IP) by fitting the arctan step
> background function simultaneously with Gauss/Lorentz lines for all the
> near-edge resonances. The inflection point of the arctan corresponds to the
> IP. Variations in the IP can be interpreted using the same considerations
> as for binding energy shifts in XPS...
>
> For example, for Au there is an almost perfectly linear relationship
> between IP and oxidation state, from Au(-1) via Au(0) and Au(+1) to Au(+3)
> ! In this case the correlation with oxidation state is a lot stronger than
> for white line intensities and/or the now commonly used 'edge inflection
> points'...
>
> Sven

My understanding of the physics behind the assumption that you can fit
a XANES spectrum by an arctan and some peak-y functions is that you
are assuming that the system is a perturbation from a simple,
Drude-like gas of electrons.  At zero kelvin, the electron density is
a well defined, sharp step function with the step at the Fermi energy.
At finite temperature, that sharp edge step is smeared into a Fermi
function -- essentially an arctan.  As a perturbation, there is some
structure to the electron density that is handled by the peak-y
functions.  To the extent that you can point to the location of the
Fermi energy on a XANES spectrum, the underlying physics of using an
arctan is well-founded.

In the sequence of pure-materials you describe, the arctan method
should work well assuming you are talking about pure phase materials,
even in the case of Au+3 where the "perturbation" (also known as a
rather enormous white line) is not small.

However, I don't think the use of one arctan is well suited to a mixed
phase situation, which is a possibility for what Edward is seeing in
his electrochemistry experiments.  That is, at some intermediate
voltage, a fraction of the sample might be oxidized and a fraction
metallic.  In that case, the XANES spectrum needs two arctans mixed in
some ratio.  Then the fitting of lineshapes has to include a mixing
term to describe the amount of each species.  The line shape fitting
thus inherits some of the systematic uncertainty of the linear
combination approach, along with all the rest of its sources of error.

In the case of mixed species, tracking a feature in the XANES
(inflection, white line position, what have you) can usually be shown
to be as accurate as a linear combination solution assuming the
correct feature can be identified.  And in some systems, fitting a
single arctan might work well also -- but that would not be
generalizable to all systems.

My US$0.02 worth,
B


-- 
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