Using a misorientation vector in specimen reference frame

[angus0997]

Hi Everyone,

I would like to define a misorientation vector, as used in this paper: https://doi.org/10.1107/S1600576719004035.
The misorientation vector should link two orientations in the specimen reference frame, and be used to convert the one orientation into the other. The norm of this vector should be the misorientation angle, and the direction of this vector should be the misorientation axis, in specimen coordinates.

Working in the crystal reference frame, we can do the following:
ori1=ebsd(1).orientations;
ori2=ebsd(2).orientations;
mori=inv(ori1)*ori2;
And now mori defines the misorientation in the crystal reference frame, and can be used to convert ori1 to ori 2: ori1*mori = ori2;.

Working in the specimen reference frame, we can do the following:
mori_axis = axis(ori1,ori2) % Misorientation axis in Specimen frame
mori_angle = angle(ori1,ori2)/degree % Corresponding misorientation angle
Now a misorientation vector can be defined:
mori_vec = mori_angle * mori_(axis)

My question is: How can this misorientation vector be used to convert ori1 to ori2?

Best,
Angus

[kilir]

Hi,
one way would be the following:

rot = rotation.byAxisAngle(-mori_vec,norm(mori_vec));
o2new = rot * ori1
angle(ori2,o2new)/degree

Cheers,

Rüdiger

[angus0997]

Hi Rüdiger, thank you for your reply.
I had tried using rotation.byAxizAngle this way, but it seems not to work. I do not know why.
For example, picking the following two arbitrary orientations I get a 25.8° angle between ori2 and o2new:

ori1 = orientation.byEuler(30*degree,50*degree,10*degree,cs);
ori2 = orientation.byEuler(100*degree,50*degree,60*degree,cs);
mori_axis = axis(ori1,ori2); % Misorientation axis in Specimen frame
mori_angle = angle(ori1,ori2)/degree; % Corresponding misorientation angle
mori_vec = mori_angle * mori_axis;
rot = rotation.byAxisAngle(-mori_vec,norm(mori_vec));
o2new = rot * ori1;
angle(ori2,o2new)/degree
Warning: The rotation angle appears to be quite large. Maybe you forgot '* degree' to switch from degree to radians. 
> In axis2quat (line 36)
In rotation.byAxisAngle (line 17) 

ans =

  25.7880

Best,
Angus

[kilir]

Hi,
yes, for mori_angle you should skip the degree and stay in radians or convert back to radians when using the norm.
Cheers,
Rüdiger

[angus0997]

Thank you, this works:

ori1 = orientation.byEuler(30*degree,50*degree,10*degree,cs);
ori2 = orientation.byEuler(100*degree,50*degree,60*degree,cs);
mori_axis = axis(ori1,ori2); % Misorientation axis in Specimen frame
mori_angle = angle(ori1,ori2); % Corresponding misorientation angle
mori_vec = mori_angle * mori_axis;
rot = rotation.byAxisAngle(-mori_vec,norm(mori_vec));
o2new = rot * ori1;
angle(ori2,o2new)/degree

ans =

     0