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Re: feff polarization
Hi FEFF users,
Below I am addressing Matt Newville's questions about polarization.
I agree with Matt that it is not straightforward to analyze
polarization dependent data (EXAFS or XANES). It will be interesting
to make a general protocol for analyzing EXAFS data. In that case
it will be probably more clear, which additional FEFF output might be
helpful for the users.
On Thu, 25 Apr 2002, Matt Newville wrote:
> 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?
Good point. It will be even more confusing if you analyze L3
edge. There planar 4 oxygens contribution will contibute about
1/2 of 2 axial contributions (1+3cos^2 \theta term dominates).
So should one report 6, 3 or 2? So analyzing one polarization
is not useful to get coordination numbers.
I think that number of nearest neighbors should be obtained from
polarization
average data. Polarization dependent data should help to
construct appropriate model: e.g. orientation of molecule
on a surface.
>
> 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.
Analyzing polarization average data again will remove confusion.
Polarization dependent data will help to analyze orientation of
MeSO_5 molecule on a surface.
>
> 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
I have to disagree. E.g. for linear polarization along
arbitrary axis FEFF uses the following symmetry operations
in the pathfinder: all rotations about the polarization vector
and reflection in plane perpendicular to that axis. If one path
can be transformed into another using these operations they are
considered to be equivalent. However, if one changes orientation
or polarization with respect to crystal axes, the degeneracy
will depend on polarization vector.
> 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.
It is easy to turn off the degenracy checker inside the code.
In subroutine mpprmp one should use icase=7. (comments lines
are at the top of that subroutine). Simply comment out lines
after statement icase = 7 in that routine as follows:
icase = 7
c if (ipol.eq.0) then
c icase = 1
c elseif (ispin.eq.0) then
c if (ipol.eq.1 .and. (.not.lkvec)) icase = 2
c if (ipol.eq.1 .and. lkvec) icase = 3
c if (ipol.eq.2) icase=4
c else
c if (ipol.eq.2 .and. lkz) icase = 5
c if (ipol.eq.1 .and. .not.lkvec .and. lez) icase = 5
c if (ipol.eq.1 .and. lkz .and. evec(3)**2.lt.eps4) icase = 6
c endif
There still might be degeneracy 2 due to path reversal operation
for 3 and more legged paths.
If many other people besides Matt are interested in turning off
the degeneracy checker, I can add new card to feff.inp.
>
> 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.
I agree with Matt that even EXAFS analysis of polarization dependent
data is not trivial. The usage of FEFF may need clarification too.
>
> =====
>
> 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 looked at Matt's analysis and must to disagree with it.
As in Heald and Stern he assumes the same phase shifts for
l=0 and l=2. This was critisized by Stohr and Jaeger, who showed
that the difference in phase shifts has strong energy dependence.
For Cd I performed calculation with MULTIPOLE 0 1 (l-->l+1)
and MULTIPOLE 0 -1 (l-->l-1), and by taking ratio of mu_0
(column 5 in xmu.dat M_21^2 and 0.5 M_01^2) in Angstrom^2,
I obtained |c| = 0.24 and is mostly energy independent.
To see difference in phase shift I used PRINT 0 2 0 0 0 0
to obtaine phmin00.dat file which has phase shifts
for l=0,1,2 (feff8.2 has a bug, so I actually used feff8.1 here).
The difference looks similar to Teo,Lee curve presented in
LeFevre et al paper.
>From the angular dependence analysis of polarization dependent
data it is easy to single out term proportional to (1-3cos^2 \theta).
i.e. \chi_2 term in LeFevre et al.. Since this is reliable
determination, that is why in our paper we compare calculated
\chi_2 term vs. experiment. Actually one can see that calculated
\chi_2 is about 1.5 times smaller in amplitude, which suggest
that experimental c_exp= 1.5 *c_feff = 0.36, which is in agreement
with 0.4 obtained by LeFevre et al.
The extracted phase shifts difference \delta (LeFevre,Fig.9) from \chi_2
has a very bad agreement with Teo.Lee result. The FEFF calculation
are close Teo,Lee, and not to LeFevre experimental \delta.
I think this part of their analysis is really questionable.
probably due to presence of 2 close shells of Cd atoms splitted
by 0.3 A. Ideally one wants to make EXAFS FT and then FT back the
region of the nearest shell for \chi_1 and \chi_2. But it is probably
impossible to separate two shells. Typically there is a fast pi change
in phase once one goes through the "beat" i.e. the point where
two signal nearly cancel each other.
> 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
Sorry for the late response, but I spent 2 days to prepare
this answer, and it is hard to find time. In fact, I even rederived
Heald/Stern results, but I got different sign for the cross term.
So their c might have a sign problem, unless I made sign mistake.
> 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.
In general I like the LeFevre et al. work. The exraction of \chi_2
seems to be reliable. (unlike the phase shift difference.)
As I said by comparing with FEFF calculations C_exp=0.36,
which is close to 0.4 cited in their paper.
LeFevre work can be improved by extending the energy range
(their data goes only to k=7, what is C at k=20?).
The procedure to extract C and \delta from \chi_2 and \chi_1 probably can
be improved. A factor 1.5-2 discreapancy between calculated and
experimental value of C or amplitude of \chi_2 needs explanation.
(Can it be TDLDA effect for the final s-state?)
>
> 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
I had no problems with MULTIPOLE card in feff8.2 for Cd. Give
me a call or send e-mail to clarify the problem.
Best wishes
Alex Ankudinov