Wrong misorientation angle when an orientation is outside the Fundamental Region

[DorianDepriester]

What do you want to do?
Compute the misorientation angle between two orientations, with one lying in the FR, whereas the other one is outside.

What data do you have?
When an orientation is outside the FR, it seems that its misorientation w.r.t its projection in the FR is not always zero, depending on the way the misorientation is computed.

What code do you use?

CS=crystalSymmetry('-42m');
o=orientation.byEuler(2.234919482291208,1.537250516696899,3.380850749436786,CS);
op=o.project2FundamentalRegion;

%% Double check that o and op are aligned
figure
millers={Miller(1,0,0,CS),Miller(1,1,0,CS),Miller(0,0,1,CS)};
plotPDF(o, millers)
hold all
plotPDF(op, millers, 'Marker', 'x')

%% Compute misorientation angle
angle(o,op)        % Bad
angle(inv(o)*op)   % Good
angle(inv(op)*o)   % Good

What result do you get

ans =   1.570796326794896

ans =     0

ans =     0

What result do you expect
0 in any case

What MTEX version do you use?
5.8.0

[ralfHielscher]

Hi Dorian,

the problem is a bit complicated. The main issue is that "-42m" is neither a purely rotational group nor a Laue group. This means there are symmetry elements that involve changing sign but do not have a rotational counterpart. Now the question is how to deal with such symmetry elements.

It appears that MTEX switches for some operations to the Laue group, but not for all. This switch to the Laue group appears in op=o.project2FundamentalRegion, angle(inv(o)*op) and angle(inv(op)*o)

The switch to the Laue group does not happen in angle(o,op) . That's why the contradictory results.

I'm a bit unsure, what is the best way to deal with it. Most likely, we should be strict in any function. Hopefully this would not confuse those who expect Laue results.

Is there a particular reason, why you are considering this specific symmetry?

Ralf.

[DorianDepriester]

Hi Ralf!
Thank you for your clear response, I (almost) understand now 😉

I am working with Copper indium gallium diselenide (CIGS), and have used -42m according to the materials project. Which symmetry do you suggest instead?

[DorianDepriester]

I have switched to 4/mmm and it indeed works way better!