[IFEFFIT] Polarized FEFF calculation

15 Feb 2024

      Dear XAFS community,

I have a series of Ru K-edge data on a single-crystal RuO2 sample measured
at different incident X-ray angles. Because of the linear polarization of
X-rays, the EXAFS of this single-crystal sample depends on the X-ray angle.
I am trying to fit the four EXAFS spectra simultaneously with one set of
parameters to extract the deltaR and MSRD parameters of this sample.

For oriented samples, N for a certain single scattering path is supposed to
be proportional to 3*cos^2(θ), where θ is the angle btwn the X-ray's
e-vector and the absorber-scatterer vector. Instead of manually calculating
the 3cos^2(θ) for all of the scattering paths in RuO2 (there are 7 single
and 3 multiple scattering paths that need to be included to achieve a good
fit with a reference RuO2 powder sample), I decided to use the polarization
card in my FEFF input. For example, for one of the X-ray angles, the
e-field vector would be (1, 0, 0), so I added the line "POLARIZATION 1 0 0"
in the FEFF input file.

Running this input file gave me a list of paths that had different
importance values for each path compared to the non-polarized (isotropic)
calculation. *Since "importance" is the relative magnitude of each path's
scattering contribution (integration of the chi(k)), I thought that it
would be proportional to 3cos^2(θ).* That is, for path i from a FEFF
calculation for angle a, the "importance" (abbreviated as "Imp") of that
path would be:
Imp(a)_i = C(a) * Imp(iso)_i * 3cos^2(θ_i)
where C(a) is a constant for each angle that accounts for the fact that
importance values are relative (because it is scaled so that the first path
in the list has an importance of 100).

Now, I wanted to check whether the polarized FEFF calculations really
follow this relationship underlined above. So, I tried manually calculating
the values of 3cos^2(θ) for two of the paths from the same polarized FEFF
calculation, then plug them into the above equation to get C(a). But, as
the table below shows, the C(a) values are not the same. FEFF 1 has a
disagreement that is small enough to ignore, but the disgareement of C(a)
values for The disagreement is small enough to ignore for FEFF 1, but for
FEFF 2 and 3 the disagreements are quite large.
[image: image.png]
*FEFF 1, 2, 3 designate individual polarized FEFF calculations. FEFF 1 was
with polarization vector = (1, 0, 0). FEFF 2 and 3 were with polarization
vector = (0.85, 1.13, 0). For this polarization, the two Ru sites gave
different lists of paths.

I do think the qualitative trend of the "importance" values in the
polarized FEFF calculations is correct, and I can get a bad but
not-disastrous fit from simultaneously fitting the data from different
angles. However, the above analysis makes me wonder whether the
"importance" values from polarized FEFF are truly proportional to
3cos^2(θ), and whether my fitting models for different angles, which I
derived from the polarized FEFF calculations, are correct. An alternative
would be to manually calculate 3cos^2(θ) for all the paths, but I'm not
sure how to calculate it for multiple scattering paths.

One note, I am running the FEFF calculation with Larix to get the
importance values (labeled as "amp ratio" in the list.dat file, in the FEFF
output folder). I wonder if the default settings for getting these
amp ratios are not accurate enough for my purposes. It would be nice if I
could just pull out the 3cos^2(θ) terms from the FEFF calculations...

Anyways, thank you very much for reading this rather lengthy question. Hope
it makes sense, and I would appreciate any help regarding this.

Best,
Soyoung

Soyoung Kim

Matthew Newville

Soyoung Kim

Matt Newville

Soyoung Kim

Matthew Newville

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