# [Ifeffit] sigma^2 values for multiple scattering paths

Bruce Ravel bravel at bnl.gov
Wed Oct 6 09:02:24 CDT 2010

```On Wednesday 06 October 2010 01:26:55 am Han Sen Soo wrote:
> Hello,
> I briefly read through the FAQ about this but I'm not sure if it answers my
>  question. Are there situations where the sigma^2 for a multiple scattering
>  path can be smaller than the direct paths? So small that they're on the
>  order of 0.001-0.003 for a degeneracy of 12 such paths? I'm working on a
>  fitting model that does not work well with additional shells but it looks
>  almost perfect with a multiple scattering path included. I'm skeptical
>  however, because of the small sigma^2 values. I am also not discounting
>  the fact that the data quality may be poor. But I would appreciate any
>  physical reasons for small sigma^2 values. Thanks! han sen

Han Sen,

It is always useful to remember the physical meanings of the
parameters use in the EXAFS equation.  sigma^2 is a mean square
variation in the distance between the absorber and a scatterer.

Suppose we have this configuration:

X------O------Y

that is, absorber X, scatterer Y and a colinear O atom in between.

The path length for the path X-Y-X is the same as for X-O-Y-X and for
X-O-Y-O-X.  If we just consider thermal motion of the atoms along that
axis, then the mean square variation in paths lengths for those three
paths must also me the same.  That's neither deep nor complicated --
its just geometry.

The argument in the last paragraph neglected the prospect of the O
atom experiencing thermal motion perpendicular to that axis.  That
effect means that

sigma^2(X-O-Y-O-X) > sigma^2(X-O-Y-X) > sigma^2(X-Y-X)

A common approximation made in data analysis is that this perpendiular
effect is small compared to the uncertainties in sigma^2 and so those
three sigma^2 values are constrained to be the same.

In no case can I understand a physical explanation for the the MS
sigma^2 being smaller than for the SS.

That said, you have a fit and a result.  When you float the MS sigma^2
it comes out smaller.  I would suggest that is telling you something
about the fitting problem rather than something about the physics of
the atomic configuration.

A smaller sigma^2 means that the contribution from those paths is
being enhanced.  That might be due to a correlation with an amplitude
parameter.  It might be due to a data quality problem.  It might be
due to a mistake in the implementation of your fitting model.

This sort of thing happens all the time.  I frequently analyze data
and come up with a curious, unphysical result like this.  It hasn't
yet meant that I have discovered some wonderous new physics.  Very
occassionally, it means that I have uncovered a shortcoming in Feff,
but that is exceedingly rare.  Usually it means that I have a problem
with my data or I have made a mistake filling in all the boxes in
Artemis.

B

--

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

National Institute of Standards and Technology
Synchrotron Methods Group at NSLS --- Beamlines U7A, X24A, X23A2
Building 535A
Upton NY, 11973

My homepage:    http://xafs.org/BruceRavel
EXAFS software: http://cars9.uchicago.edu/~ravel/software/exafs/

```