[Ifeffit] Debye-Waller factors for MS paths

[Kelly, Shelly D.]

Hi Peter,

Please see below:
> 
> Dear everyone,
> 
> One of the features of constructing models with Ifeffit is 
> that we are 
> forced to think long and hard about the parameters to use for 
> each path. In 
> particular I have had a great deal of difficulty in deciding how to 
> approach the Debye-Waller factors for with multiple 
> scattering (MS) paths.
> 
> The ideal approach is to define the D-W factors for the MS 
> paths in terms 
> of the factors for the single scattering paths. That way you 
> add no further 
> variables to the model. But if you think about it you will 
> realise that you 
> cannot simply add all the relevant SS factors up to get a sum 
> for your MS 
> path - it all depends on the geometry, the direction of vibration, 
> correlation of vibrations, etc. Its all a bit tricky for those of us 
> dealing with intense MS paths.
> 
> So what I am asking is, does anyone know of a general method 
> or approach to 
> define the Debye-Waller factors for MS paths (in terms of SS paths or 
> otherwise)? How do all you Ifeffiters deal with the problem? 
> I've found a 
> few papers that discuss it (listed below) but they generally 
> assume that 
> all vibrations are uncorrelated, which is seldom a realistic 
> situation in 
> continuous solids.
> 
> Munoz-Paez, A. (2000). Inorganic Chemistry 39(17): 3784-3790. 
> Sakane, H. (1998). Journal of the American Chemical Society 120(40): 
> 10397-10401.
> Haskel, D. (1998). PhD thesis, University of Washington.  (appendix)
>          http://www.aps.anl.gov/xfd/people/haskel/PS/thesis.ps
> 
> Is there anything out there that I've missed? I'd be particularly 
> interested in anything relating to continuous solids or correlated 
> vibrations. Comments/questions/pearls of wisdom very welcome.
> 
> Peter
> 
> 
> Peter Southon
> Research Fellow - School of Chemistry
> University of Sydney, NSW 2006, Australia
> +61 2 9351 4425
> 

There are a couple of ideas that I have found that work pretty well for
determining sigma2 values for a lot of scattering paths. 

Idea 1:  Try to use a correlated debye model or the eins model.  You can
have more than one debye/eins temperature depending on the atom types
and path lengths. 

Idea 2:  Group paths that are similar in distance and atom types and set
their sigma2 values to the same value, including the M.S. paths.
	-use the abs function in defining a value for sigma2 to force it
to be positive.
       sigma2   path1   abs(sig)
       guess   sig   0.010

Idea 3:  Usually, the triangle paths that have a really large degeneracy
end up with their own sigma2 value.  Most models can be close to working
without these paths, and then added them at the end to clean up the fit.


Idea 4:  Linear paths can be quantified in terms of the sigma2 values of
the single scatting paths that contain the end atoms. Another paper that
talks about this is:
 E A Hudson, J J Rehr and J J Bucher. "Multiple-scattering calculations
of the uranium L3-edge X-ray-absorption near-edge structure." Phys. Rev.
B 52(19): pp 13815-3826, 1995.

-For a forward linear path A-B-C,
sigma2(A-B-C-A)=sigma2(A-B-C-B-A)=sigma2(A-C-A)
-For a backward scattering linear path B1-A-B2, and if A is a lot
heavier than B then Sigma2(A-B1-A-B2-A)~sigma2(A-B1-B2-A)~2xsigma2(A-B),
and sigma2(A-B1-A-B1-A)=4xsigma2(A-B) (John Rehr and I had a previous
discussion about this with the subject "relation between DW factors in
uranyls")

Golden Rule:  You have to try A LOT of different models, always try to
start with the simplest model and make it more complex as the data
requires.  For example: Start with a eins model and use only one eins
temp.  See where the model works and were it fails.  In the regions that
it fails add another eins temp...and so on.


Shelly Kelly