Phi input for PO_Spherical_Harmonics?

mathiasmorch

Hi,

I have some data from a 2D detector binned azimuthally.
The sample is textured, and I would like to refine PO_Spherical_Harmonics with the azimuthal angle as an input (along with alpha which I did get working).

Is it in any way possible to give TOPAS a phi input for the PO_Spherical_Harmonics macro, like it is possible to give an alpha input via sh_alpha?

If not, I was wondering how the sh_Cij_prm are coded for the spherical_harmonics_hkl macro?
It seems to me they are coded internally (I can't find anything in my topas.inc file)
I was hoping that it might be possible to adapt them to include phi, and maybe extend to a higher order in case the texture is too strong.

rowlesmr

Hi Matias

The refinable Cij prms are scaling factors for the Yij equations as outlined in [1].

The simplest way would be to have one dataset per azimuthal angle, and have independent Cij prms. The next layer of complexity would be to write a parametric equation to describe how each Cij changes with azimuth

Matthew

(Question: what is the alpha thing you're talking about?)

[1] Järvinen, M. 1993. "Application of Symmetrized Harmonics Expansion to Correction of the Preferred Orientation Effect." Journal of Applied Crystallography 26 (4): 525-531. https://doi.org/10.1107/S0021889893001219.

mathiasmorch

Hi Matthew,

Thank you for the answer!

The alpha I'm talking about is defined on page 198 in the technical reference.

sh_alpha corresponds to the angle in degrees between the polar axis and the scattering vector; sh_alpha defaults to zero degrees which is required for symmetric reflection as is the case for Bragg-Brentano geometry.

http://topas.dur.ac.uk/topaswiki/doku.php?id=manual_part_2
I have data measured on a pellet in transmission with the pellet in 4 orientations: ω= 0, 15, 30, 45 °, and have used alpha as my input for ω, to refine all 4 datasets, azimuthally summed, with one set of spherical harmonics as in the example posh_for.inp.
From my understanding alpha modifies the θ term in for example 66+: sin⁶(θ) cos(6φ).

But after reading Järvinen[1], Von Dreele[2] and Popa [3] a bit closer, it seems the version of spherical harmonics in Topas (Järvinen), does not take azimuthal variance, I missed that the first time I read it.

Maybe I will give it a go to write something similar to [2]/[3] later, but for now I think I will stick to MAUD for a bit longer, and then revisit it in Topas if the computational time becomes a problem, or I want to consolidate my workflow.

[1] Järvinen, M. "Application of symmetrized harmonics expansion to correction of the preferred orientation effect." Journal of Applied Crystallography 26.4 (1993): 525-531.
[2] Von Dreele, R. B. "Quantitative texture analysis by Rietveld refinement." Journal of Applied Crystallography 30.4 (1997): 517-525.
[3] Popa, Nicolae C. "Microstructural properties: Texture and macrostress effects." Powder Diffraction. RCS Publishing, Cambridge, 2008. 332-375.

rowlesmr

Nice.

I also talk about it a little here [1]. I'll need to read the techref some more.

[1] Rowles, Matthew Ryan, and C. E. Buckley. 2017. "Aberration Corrections for Non-Bragg-Brentano Diffraction Geometries." Journal of Applied Crystallography 50 (1): 240-251. https://doi.org/10.1107/S1600576717000085.