[Ifeffit] Inequivalent sites and multiple shell fits

Anatoly Frenkel frenkel at bnl.gov
Fri Jan 14 12:55:54 CST 2005


Re: [Ifeffit] Inequivalent sites and multiple shell fitsPaul, 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?

Regards,

Anatoly

Anatoly Frenkel
Yeshiva University






[Anatoly Frenkel]  -----Original Message-----
From: ifeffit-bounces at millenia.cars.aps.anl.gov
[mailto:ifeffit-bounces at 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


  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 energy!


  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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