A fibre in orientation space is essentially a line connecting two orientations and can be represented in MTEX by a single variable of type fibre. To illustrate the definition of a fibre we first define cube and goss orientation
and then the fibre connecting both orientations
Finally we plot everything into the Euler space
Alternatively, we may visualize the fibre also in axis angle space
Obviously, f is not a full fibre. Since, the orientation space has no boundary a full fibre is best thought of as a circle that passes trough two fixed orientations. In order to define the full fibre us the option 'full'
An important difference to orientation plots is that fibres are not automatically symmetrised when plotted. To achieve this use the command symmetrise.
Inverse pole figures are by default restricted to the fundamental sector. You may use the option 'complete' to plot the entire sphere.
Defining a fibre by directions
Alternatively, a fibre can also be defined by a pair of a crystal and a specimen direction. In this case it consists of all orientations that alignes the crystal direction parallel to the specimen direction. As an example we define the fibre of all orientations such that the c-axis (001) is parallel to the z-axis by
If both directions of type Miller the fibre corresponds to all misorientations which have these two direcetion parallel.
Finally, a fibre can be defined by an initial orientation ori1 and a direction h, i.e., all orientations ori of this fibre satisfy
The following code defines a fibre that passes through the cube orientation and rotates about the (111) axis.
MTEX includes also a list of predefined fibres, e.g., alpha, beta, gamma, epsilon, eta, tau and theta fibres. Those can be defined by
Lets plot an overview of all predefined fibres with respect to orthorhombic specimen symmetry
Note, that it is straight forward to define a corresponding fibre ODF by the command fibreODF
Visualize an ODF along a fibre
We may also visualize an ODF along a fibre
Compute volume of fibre portions
or compute the volume of an ODF in a tube around a fibre using the command volume