Misorientation in mtex

[trudator]

Hi everyone,

Let say I have 2 crystals with orientation in Bunge convention as below. How to calculate a misorientation (by Euler) about a certain axis (for example, <001>)?

  Bunge Euler angles in degree
  phi1     Phi    phi2    Inv.
   360 20      30       0
   270 45      10       0

[ralfHielscher]

Can you explain what you mean by misorientation about a certain axis?

[trudator]

My question may be misunderstood. I have adjusted to a proper one. Let say that I have 2 orientations listed below. The misorientation basically just a phi_1 deviation of +/- 90 degree rotation about ND. However, the misorientation returns with an unexpected result.

ori_1 = orientation.byEuler(180*degree,35*degree,45*degree,cs);
ori_2 = orientation.byEuler(90*degree,35*degree,45*degree,cs);
misorientation= inv(ori_2) * ori_1

Misorientation result:

  Bunge Euler angles in degree
     phi1     Phi    phi2    Inv.
  84.3227 47.8549 354.323       0

[ralfHielscher]

There are several aspects to consider:

1. inv(ori_2) * ori_1 computes the misorientation in crystal coordinates, i.e., from one crystal reference of crystal A into crystal reference frame from crystal B. There is no ND in these reference systems
2. ori_1 * inv(ori_2) would compute the misorientation in specimen coordinates - however ignoring crystal symmetry. I'm not sure whether this is what you want to have.
3. axis(ori_1,ori_2) gives the rotational axis in specimen, taking crystal symmetry into account. angle(ori_1,ori_2)/degree is the corresponding angle

Ralf.

[trudator]

The second bullet is exactly what I wanted. Thanks Ralf so much!

Just a quick follow-up question. Is there any difference between:

ori_1= orientation.byMiller([1 1 2],[1 1 0],cs)
ori_2 = orientation.byMiller([1 1 2],[1 1 1],cs)
axis(ori_1,ori_2)

and

ori_1= orientation.byMiller([1 1 2],[1 1 0],cs)
ori_2 = orientation.byMiller([1 1 2],[1 1 1],cs)
misorientation =  inv(ori_1) * ori_2
misorientation.axis

It generated two different results.

[ralfHielscher]

The first one is the misorientation axis in specimen symmetry, while the second one is the misorientation axis in crystal coordinates.
Have a look at https://mtex-toolbox.github.io/orientation.axis.html

Ralf

[trudator]

Thanks Ralf!