I have obtained some data after EBSD analysis of the copper specimen. The example of information I`ve got is in 'Example.png'. As I know, crystal orientation can be described with use of three Euler angles (φ1, Φ, φ2). In the table I have attached there are parameters "Mean orient. E1 [°]", "Mean orient. E2 [°]", "Mean orient. E3 [°]" – Euler angles. The first parameter (E1) takes a value greater than 90°, but considering cubic symmetry of copper this angle should be limited by 90°.
Since only the last two Euler angles are related to the cubic symmetry. The first always runs between 0 and 360° in order to align the c axis for an optimized following rotation, see e.g.
Article Euler angles and crystal symmetry
Evgeny,
the Euler angles help to describe the rotation of not only cubic lattice but a body of any shape in space and not the body symmetry. You can rotate your cubic cell around the first and third Euler axis up to 360°, second angle up to 180°.
But in case of symmetry you can dicide whether you will take the range from -180° to 0° and 0° to 180° as euquivalent and use only 0 to 180° in your study. Same is for second angle it can be equivalent for -90° to 0° and 0° to 90°. So you can reduce the description only to 0 to 90°. But this is a special case.
all the best,
Anton
Anton Pshenichnikov :
You are in principle right, but you should not mix "everything".
1. He is especially talking about crystals and not rigid body rotation (which is definitely similar but not relly comparable because of inherent symmetry of the object which enables "reductions" not allowed for rigid body rotations).
2. He is not talking about the second angle. (Maybe you are also not talking about the second but the third?)
There are still other inconsistencies considering active or passive rotations and positive and negative rotations. I did not want to mention this since it mainly confuses everybody. Moreover, the rotations around different axis or using a different sequence also change the Euler angles. I am shure that you know this but I think. if you start to confuse people then do it right :-).
Summarizing, I still think that the first answer is the sufficient on the question of Evgeny.
It is up to Evgeny to decide which explanaition helped him to understand the nature of these angles.
Additionally, there are tutorials in application to EBSD, please search "Euler EBSD". Or another general tutorial for positioning in 3D space https://www.mecademic.com/resources/Euler-angles/Euler-angles
Evgeny, you will understand it much better than after my confusing explanation).
Regards,
Anton
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