Plastic deformation in crystalline materials almost exclusively appears as dislocation along lattice planes. Such deformations are described by the normal vector n of the lattice plane and direction b of the slip. In the case of hexagonal alpha-Titanium with
basal slip is defined by the Burgers vector (or slip direction)
and the slip plane normal
Putting both ingredients together we can define a slip system in MTEX by
The most important slip systems for cubic, hexagonal and trigonal crystal lattices are already implemented into MTEX. Those can be accessed by
Obviously, this is not the only basal slip system in hexagonal lattices. There are also symmetrically equivalent ones, which can be computed by
The length of the burgers vector, i.e., the amount of displacement is
Displacement
In linear theory the displacement of a slip system is described by the strain tensor
This displacement tensor is exactly the same as the so called Schmid tensor
Rotating slip systems
By definition the slip system and accordingly the deformation tensor are with the respect to the crystal coordinate system. In order to transform the quantities into specimen coordinates we have to multiply with some grain orientation