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)
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.
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?