[Ifeffit] delR and sigma2 models for multiple Scattering Paths

Bruce Ravel bravel at bnl.gov
Wed Jan 18 12:47:19 CST 2017

On 01/18/2017 01:27 PM, Mikhail Solovyev wrote:
> I'm currently trying to Artemis fit a molecule that is highly symmetric
> with multiple scattering paths playing a large role.
> delR and sigma2 have been handled rather well for all of the single paths.
> I am, however, confused as to how to handle it for multiple scattering
> paths.
> Reff for them seems to be close to the value of the furthest atom, but
> is always ~5-10% off. (which would be my second question, how is Reff
> determined for multiple scattering paths)
> I've looked at the presentation and examples, such as FeS2.
> I am trying to incorporate all of the same variables used in single
> scattering paths for multiple scattering paths the best i can.


The definition of Reff is /always/ "half-path-length".

For a single scattering path, this is trivial.  It's simply the 
inter-atomic distance.

For a multiple scattering path, you add up the length of each leg, then 
divide by 2.  For the case of strictly collinear multiple scattering 
path, Reff is the distance between the two atoms farthest apart. 
However, if there are scattering angle that are something other than 0 
or 180 degrees, Reff will be related to interatomic distances via some 
kind of trigonometric relationship that has to do with scattering angles.

You are wise to try to build constraints between SS and MS paths in your 
fit.  For DeltaR parameters, trigonometry helps, but may only be an 
approximation.  Possibly a good approximation, but an approximation 

Scott discusses how to parameterize sigma^2 in his book:


There are some situations (see https://doi.org/10.1103/PhysRevB.54.156) 
where MS sigma^2 can be related exactly to SS.  In general, though, MS 
sigma^2s usually can only be approximated by constraint with the SS 



  Bruce Ravel  ------------------------------------ bravel at bnl.gov

  National Institute of Standards and Technology
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