Re: [Ifeffit] Inequivalent sites and multiple shell fits

Paul, may be it will be more clear what you mean by interference of inequivalent sites if you explain it on the example of equivalent sites. In a bulk fcc metal, contributions to EXAFS from neighboring (equivalent) sites do not interfere - and it is why we can use scattering amplitudes and phases extracted from model compounds (or FEFF theory) with one structure to model unknown compound with a (not too) different structure. Had it not been true, the chemical transferability of scattering phase and amplitude wouldn't be working but it does in most cases. So, if it is working for equivalent sites, why should it not for inequivalent sites?

Moreover, this possibility (of interference) is almost always ruled out in FEFF at the state when we assign unique potentials to different atoms, the absorber (0) and its neighbors (1). Sometimes we assign a unique potential 0 to the central atom, and, another unique potential 1 to its first nearest neighbors, to correct for the muffin tin approximation, while the rest of the atoms have the same potential 2 (if there is just one element in the sample). For fcc copper, both models give very similar results for FEFF paths and for the fits. The reason the central atom has different potential than the 1NN is because it is ionized. Had its 1NN been ionized also, its potential would be different too, but we know that we can get away just fine by assigning a neutral atom potential to all the neighbors. Therefore, if FEFF does not worry about interference, how can it be taken into account in principle, and why?

[Anatoly Frenkel] -----Original Message-----
From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit-bounces@millenia.cars.aps.anl.gov]On Behalf Of Scott Calvin
Sent: Friday, January 14, 2005 12:49 PM
To: XAFS Analysis using Ifeffit
Subject: Re: [Ifeffit] Inequivalent sites and multiple shell fits

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 energy!

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.