Crystal Geometry

Introduces key concepts about the MTEX representation of specimen directions, crystal directions, crystal symmetries, rotations and orientations.

Specimen DirectionsHow to represent directions with respect to the sample or specimen reference system.
RotationsRotations are the basic concept to understand crystal orientations and crystal symmetries.
Crystal SymmetriesThis section covers the unit cell of a crystal, its space, point and Laue groups as well as alignments of the crystal coordinate system.
Crystal DirectionsCrystal directions are directions relative to a crystal reference frame and are usually defined in terms of Miller indices. This sections explains how to calculate with crystal directions in MTEX.
Crystal OrientationsExplains how to define crystal orientations, how to switch between different convention and how to compute crystallographic equivalent orientations.
MisorientationsMisorientation describes the relative orientation of two grains with respect to each other. Important concepts are twinnings and CSL (coincidence site lattice),
FibresThis sections describes the class <fibre_index.html fibre> and gives an overview how to work with fibres in MTEX.
Antipodal SymmetryMTEX allows to identify antipodal directions to model axes and to identify misorientations with opposite rotational angle. The later is required when working with misorientations between grains of the same phase and the order of the grains is arbitrary.
Fundamental Regions Thanks to crystal symmetry the orientation space can be reduced to the so called fundamental or asymmetric region. Those regions play an important role for the computation of axis and angle distributions of misorientations.