[Ifeffit] Inequivalent sites and multiple shell fits

Scott Calvin SCalvin at slc.edu
Fri Jan 14 11:49:17 CST 2005

Hi Paul,

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...

--Scott Calvin
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.
>						Paul
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