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Hi Soyoung, 

On Tue, Feb 27, 2024 at 6:50 PM Soyoung Kim <soykim@lbl.gov> wrote:

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Dear Matthew,

Thank you so much for your input. I followed your advice, and indeed the ratios of integrated chi(k) values between the polarized and isotropic cases matched reasonably well with the 3*cos^2(θ) values I calculated. To be exact, I integrated the scattering amplitude f(k) (i.e., the mag[feff] column in the path file) and took their ratios.

That seems reasonable to me.

In the process, I noticed that the f(k) is slightly different for the same kind of paths. For example, there are two Ru-Ru single scattering paths at 3.10 and 3.54 angstroms, and below is the f(k) of the two paths (from a non-polarized FEFF calculation):

Is this discrepancy just an artifact of the FEFF calculation?

I think that is pretty close, but I don't know for sure what the differences there are.  I guess those are not from the same Feff run, so there might be some subtle differences in potentials or path details.  Posting more details of what you did (inputs, feffNNNN.dat files) would probably clarify that....

While I'm not worried about such a small discrepancy for my project, this makes me wonder how exactly the FEFF calculates the effective scattering amplitudes and phases. While I will try to digest the FEFF user guide more, if you have any quick words of advice, I would appreciate it.

Well, Feff is calculating the intensity of the scattering by the near-neighbor atoms by the photo-electron originating from the Ru absorber.  Electron-electron scattering is "a little complicated"  ;).  There are a few good books and a few good review articles on this.  The tutorial information at

https://xafs.xrayabsorption.org/tutorials.html might be a good starting point.

--Matt

Thank you very much,

Soyoung

On Mon, Feb 19, 2024 at 12:28 PM Matthew Newville <newville@cars.uchicago.edu> wrote:

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Hi Soyoung, 

I would not place too much importance to the value of the "Importance" factor ;)    That is, it is a quick estimate of the importance of a Path so that it might be filtered out.    As you'll notice, the first path always has an Importance factor of 100, making comparisons between calculations difficult. 

If you want to check how the scattering amplitude varies with angle, say to check how close it is to cosine-squared, I recommend reading in the Path files and integrating the magnitude of chi(k).

---

From: Ifeffit <ifeffit-bounces@millenia.cars.aps.anl.gov> on behalf of Soyoung Kim <soykim@lbl.gov>
Sent: Thursday, February 15, 2024 3:01 PM
To: XAFS Analysis using Ifeffit <Ifeffit@millenia.cars.aps.anl.gov>
Subject: [Ifeffit] [IFEFFIT] Polarized FEFF calculation

 

This Message Is From an External Sender

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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.

*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

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--Matt Newville <newville at cars.uchicago.edu> 630-327-7411

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