[Ifeffit] Questions on Correlated Debye in FEFF6

[Matt Newville]

Hi Doran, Bruce,

Sorry for not responding earlier, and thanks Bruce for giving links.  I'll
make a few comments, which might suggest why I was hesitant to respond
earlier.

On Thu, Jun 11, 2015 at 2:18 PM, Bennett, Doran (D) <dbennett1 at dow.com>
wrote:

>  Hi Everyone,
>
>
>
> I have just recently begun learning about EXAFS and running EXAFS
> simulations using FEFF6. I have a few very basic questions about the
> underlying calculations for the correlated Debye model implemented in FEFF6
> (called by "DEBYE" keyword). For the questions below, I am assuming I input
> a single crystallographic structure and want the correlated Debye model to
> simulate the influence of a thermal distribution on the EXAFS spectrum.  I
> would appreciate any insight you can give me into the questions below. I
> would also welcome any and all references for the original papers where
> that is appropriate.
>
>
>
> 1. Are the Debye-Waller factors calculated for each path individually? (It
> seems like they should be since the paths will have different levels of
> influence from the thermal distribution of atomic positions)
>

Yes, they are.


>
>
> 2. Assuming the DW factors are calculated path-by-path, is the magnitude
> of the DW  factor determined by assuming the total path length R is the
> appropriate length to use for the correlation term in the Debye spectral
> density? It seems like it would not be reasonable to treat all paths of the
> same R as having the same Debye-Waller factor since a single scattering
> path and multiple scattering paths are perturbed by a different set of
> relative atomic motion that are likely to have different correlations. I
> couldn’t locate a clear statement about how this calculations is actually
> done within the code.
>

DW Factors are calculated for each path, R does matter, but so does the
path geometry.  Bruce gave two links to the ifeffit / larch side of the
calculation.  The sigms.f link is the one that really does the meat of the
work.


>
> 3. Is the C1 shift that results from the vibrational motion normal to the
> bond axis along a path incorporated in the calculation? (Presumably using
> \Delta C1 = sigma_perp^2/(2<r>)) And is this formula still appropriate in
> multiple-scattering paths?
>
>

OK, I apologize in advance for ranting here.  The literature is chock full
of this sort of nomenclature and discussions.  In my view, there is much
confusion about this throughout the literature and community.   Yeah, I am
sort of saying "everyone else is wrong".


Single-Scattering XAFS is exactly one-dimensional.  It is sensitive to R.
There is no perpendicular and no parallel.  There is, quite simply, nothing
to be perpendicular to.    Similarly,  sigma is the variance in interatomic
distance.  There is no directionality at all to this quantity.  If you see
sigma_perp or sigma_par in a paper or any discussion of XAFS, you can be
assured that it is wrong.  It would be easy to suggest that this work
should be ignored, but there is so much literature with this in it that it
cannot be ignored.   Many people publishing work understand the subtle
distinctions, but the confusion caused is a problem.


Vibrations give a distribution of interatomic distances, which is all XAFS
is sensitive to.   If you're comparing interatomic distances from XAFS to
the distances between lattice points, then vibrations will indeed cause a
difference in these two distances, with the interatomic distance being
larger than the distance between lattice points.   This difference will
scale as sigma2/r (where sigma is the variance in interatomic distances),
under some assumptions about how the motions of the two atoms around their
respective lattice points are correlated.   This is actually well-described
in the literature.


This difference between interatomic distance and the distance between
lattice points is absolutely NOT accounted for in any part of the XAFS
calculation.  The XAFS calculation is concerned with interatomic distances,
not distance between lattice points.


There is a similar term in the XAFS equation that is a correction to
getting accurate interatomic distances in the presence of vibrations that
also scales as sigma2.   This correction accounts  for the effect of having
a distribution of R in the 1/R^2 term in the XAFS equation.  Again, this is
to get accurate interatomic distances, not distances between lattice points.


To the extent that the formalism applies to multiple scattering, the
angular extent of such vibrations is not directly accounted for, only the
effect on the half path length R.



>  4. Assuming the C1 shift is incorporated, does the correlated Debye
> model assume that the perpendicular and parallel displacements have the
> same spectral density?
>

There is no perpendicular to R.
Sorry for the rant.

--Matt
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