[Ifeffit] Contribution of multiple scattering paths - basic question

[Bruce Ravel]

On Thursday 12 May 2005 05:03, Gerrit Schmithals wrote:
> I have learned that it is quite possible that multiple scattering paths
> do not contribute to the spectrum because of their large mean square
> displacement. Is that due to the fact that the mean square displacements
> are large for all atoms and for multiple scattering paths with more
> atoms involved the mean square displacements are multiplied?

Multiplied, eh?  That doesn't sound quite right to me. 

When you measure the sigma^2 you are, as you say, measuring the mean square
displacement about the nominal length of the path.  A three-body path has many
more modes of vibration (or degrees of freedom, if you prefer that language)
than a two-body path.  Each leg of the path has a mean square displacement,
but there are also angular modes of motion.  That is, the atoms are vibrating
along the directions parallel to the line between them, but they are also
vibrating in angle about the scattering angle.  So you can imagine that atoms
are connected by springs and there are springs restoring the angle between
bonds.  Picture something like this (this silly little picture won't make
sense unless you look at it with a monospace font):

     O         O
      \       /
       \-----/
        \   /
         \ /
          X

The springs represented by the slashes might be quite stiff, but the spring
represented by the dashes might be quite floppy.  This situation might result
in a sigma^2 for the three-body path that is quite large compared to the two
body sigma^2s.


> One easy way to obtain a fit that is not too bad was to exclude all multiple
> scattering paths.

That might be ok.  One way to explain that is to say that between the effects
of sigma^2 and the sum of a large number of paths with different phases, the
net effect of all those MS paths is to be reduced to small background signal.  

In general, what you have done so far is a good start to a complicated fitting
problem.  I am a big fan of the strategy whereby you start with the simplest
model, see how it fits the data, then add complexity as the problem warrents.
For a similar approach to the problem of a highly complex system, you might
want to look through Shelly's presentation from last year's NSLS EXAFS school:
  http://cars9.uchicago.edu/xafs/NSLS_2004/Kelly.pdf
The bit around page 25 is particularly relevant to this conversation.

Good luck!
B

-- 
 Bruce Ravel  ----------------------------------- bravel at anl.gov  -or-
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