feff polarization

[Matt Newville <newville@cars.uchicago.edu>]

Hi Bruce,

Polarization dependence in EXAFS is definitely confusing!! Of
course, atoms at crystallographic sites with cubic symmetry
should not show polarization dependence. But neither EXAFS nor
Feff really care whether a system is cubic, so assertions like
"in a cubic crystal, there is NO polarization dependence" miss
the point.  XAFS (and Feff) depend on atomic positions of
clusters, not crystals.  Since crystal surfaces, and systems
with impurities or distortions are never cubic systems, and
since almost all experiments use a polarized source, the
polarization dependence of XAFS needs to be kept in mind most
of the time.

Consider a perfect metal-oxygen octahedron (note that this is
not a crystal but a molecule):
  Metal at   0. 0. 0.
  oxygen  at  -1.8  0  0 , 1.8 0  0,  0 -1.8  0,
               0  1.8  0,  0  0 -1.8,  0  0  1.8

and a x-ray beam polarized along 1 0 0.  Only 2 of the oxygens
actually contribute to the K-edge EXAFS. Of course, the
polarized and unpolarized calculations must give the same
result in this case, and unpolarized should gives a
coordination number of 6 ..... So should the polarized
calculation give degeneracy of 6 or 2?

If you replace the oxygen at (1.8,0,0) with a sulfur, should
Feff report the oxygen coordination is 1, 3, or 5?  It is
definitely confusing.

The outputs from from Feff's pathfinder are confusing because
'degeneracy' ("number of equivalent paths"??)  becomes poorly
defined when a polarization vector is defined. If one could
completely turn degeneracy checking off in the path finder,
forcing any accidental symmetries to be ignored, and have a
single feff.dat file written for every single path, the
situation might be clearer.  That would be a very useful
option, in my opinion.

I'm sure that doesn't help clear up the general confusion on
polarization dependence.  It's just to add my voice to those
who are confused:  Using Feff for polarized XAFS is definitely
harder than it's usually presented to be, and it is too easily
dismissed as trivial.  It is not trivial.

=====

Now, for L-edges, Feff does attempt to include complete
polarization dependence (p->s, p->d, and cross terms), as Alex
says.  I've been trying to understand this for a couple years
now and had some difficulty trying to come up with reasonable
tests of the relative sizes of the different contributions, and
especially what the p->s/p->d ratio is.  I think I now
understand these.  As it turns out, I'm skeptical of the claim
made in the 1997 PRB that FEFF agrees well with the
experimental results of LeFevre et al.

LeFevre et al claim a ratio p->s/p->d ratio of 0.4 for Cd L3
edge, which is pretty different from Heald and Stern, Stohr and
Jaeger, and Citrin and Eisenberger, all of whom found values
around ~0.2 in the late '70s.  When I do Feff calculations for
Cd L3, I get -0.1 (yes, negative), which is very different from
both.  Oddly, Ankudinov and Rehr didn't say what they found the
p->s/p->d ratio to be.  If you're interested, I have an
(incomplete) discussion of this at
  http://cars.uchicago.edu/~newville/FeffPolarization/

I sent this to John and Alex a couple of months ago, asking
them why I get such a different answer from LeFevre while they
got "good agreement" in 1997, and from the often-quoted value
of 0.2, and how to think about what p->s/p->d should be.  I
have not heard a response from Alex or John in months, so I'll
ask here if anyone has any insight on this problem.  If anyone
has access to a beamline that can reach the Cd L3 edges, I'd be
interested in remeasuring this. My sense is the LeFevre work
could be improved, and that no one really understands the L
edge polarizations very well.

For what it's worth, I've tried to use the MULTIPOLE cards in
Feff8 and have never been able to get successful calculations
that I believed.  (I believe I asked about a year ago in this
mailing list).  This is, no doubt, related to my general
inability to use and understand most of the features of Feff8.
If anyone has pointers on how to use the MULTIPOLE card, I'd
love to hear them.

--Matt

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