This sections covers the definition of orientations as MTEX variables. The theoretical definition can be found in the section Theory and MTEX vs Bunge Convention.
Technically, a variable of type orientation
is nothing else then a rotation
that is accompanied by a crystal symmetry. Hence, all methods for defining rotations (as explained here) are also applicable for orientations with the only difference that the crystal symmetry has to be specified in form of a variable of type crystalSymmetry
.
% load copper cif file
cs = crystalSymmetry.load('Cu-Copper.cif')
cs = crystalSymmetry
mineral : Copper
symmetry: m-3m
elements: 48
a, b, c : 3.6, 3.6, 3.6
Most importantly we may use Euler angles to define orientations
ori = orientation.byEuler(30*degree,50*degree,10*degree,cs)
ori = orientation (Copper → xyz)
Bunge Euler angles in degree
phi1 Phi phi2
30 50 10
or a 3x3 rotation matrix
M = eye(3)
ori = orientation.byMatrix(M,cs)
M =
1 0 0
0 1 0
0 0 1
ori = orientation (Copper → xyz)
Bunge Euler angles in degree
phi1 Phi phi2
0 0 0
Miller indices
Another common way to specify an orientation is by the crystal directions point towards the specimen directions Z and X. This can be done by the command orientation.byMiller
. E.g. in order to define the GOSS orientation (011)[100] we can write
orientation.byMiller([0 1 1],[1 0 0],cs)
ans = orientation (Copper → xyz)
Bunge Euler angles in degree
phi1 Phi phi2
0 45 0
Note that MTEX comes already with a long list of predefined orientations.
Random Orientations
To simulate random orientations we may apply the same syntax as for rotations and write
ori = orientation.rand(100,cs)
ori = orientation (Copper → xyz)
size: 100 x 1
Specimen Symmetry
If one needs to consider also specimen symmetry this can be defined as a variable of type specimenSymmetry
and passed as an additional argument to all commands discussed above, e.g.,
% define orthotropic specimen symmetry
ss = specimenSymmetry('orthorhombic')
% define a corresponding orientation
ori = orientation.byEuler(30*degree,50*degree,10*degree,cs,ss)
ss = orthorhombic specimenSymmetry
ori = orientation (Copper → xyz (mmm))
Bunge Euler angles in degree
phi1 Phi phi2
30 50 10
Symmetrisation will now result in a very long list of symmetrically equivalent orientations
ori.symmetrise
ans = orientation (Copper → xyz (mmm))
size: 384 x 1