[Ifeffit] Inequivalent sites and multiple shell fits
SCalvin at slc.edu
Fri Jan 14 11:49:17 CST 2005
I think we're getting confused over what we each mean by "interfere."
Whether sites are equivalent or inequivalent, neighboring or far
apart, the wave functions do not interfere at all, in part because
the odds of two x-ray photons being absorbed by sites close to each
other at nearly the same time is very very small--if it wasn't, your
material would disintegrate in an instant!
The idea behind the path expansion used in EXAFS analysis by ifeffit,
however, is that the chi(k) for each possible scattering event by a
single electron can be computed separately, and then the results
added (I'll defer to John or Matt or whoever for a clear explanation
of why this is justified). In other words, the EXAFS spectra can be
thought of as if there were a contribution from an electron
scattering off a near-neighbor, another scattering off a
2nd-nearest-neighbor, another doing a multiple-scattering thing, etc.
(all weighted, of course, by the relative contributions of these
scattering events). These are literally just added. Given that
system, if there really are multiple sites that are each having their
own scattering events, then it is perfectly appropriate to treat them
in exactly the same way--just add. So, depending on your terminology,
either we are combining all scattering paths coherently or we are
adding none of them coherently, regardless of whether they correspond
to the same absorbing site or not. It would not be correct to add,
say, the magnitudes of the FT's for the separate contributions...the
phase of the FT indicates where the peaks and troughs are in k-space
(and thus energy-space), and it certainly matters whether a given
scattering path has enhanced or suppressed absorption at a given
Hope that helps...
Sarah Lawrence College
P.S. I've published several analyses of systems with inequivalent
sites. If you'd like a pdf of one of those papers, let me know.
>Thanks for the message. I guess what I wanted to say was that from
>what I understand due to lifetime effects the "effective" radius
>about the absorbing site for which the outgoing scattered wave
>"exists" is on the order of 2 nn (I have big lattice constant
>material). It would seem to me then that the inequivalent sites
>being physically separated by more than this distance (we are
>talking about crude approximations here) would not interfere. In
>reality, with bond lengths on the order of 3 Angstroms and 2nn along
>the lines of 4.5 Angstroms, my case is somewhere in between the
>coherent interaction and the dilute dopant -- e.g. every site is by
>itself -- extreme. Certainly, in the latter case it would be wrong
>to add the signals together coherently! What is the consensus for
>this sort of thing? The different E0's is a good point too.
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