Misorientation
misorientation
allows to determine orientation relationship and misorientation between two crystals
It allows:

Display two crystals at the same time on a stereographic projection which allows the easy determination of orientation relationship

Orient two crystals independently

Determine misorientation between two grains (same crystals)
Misorientation¶
When two crystals are separated by a grain boundary, the neighboring crystals may exhibit a specific orientation relationship that can be defined by an interface and a couple rotation axis, i.e. a common crystal direction, misorientation angle.
Considering the orientation of grains A and B defined by their Euler angles. Their orientation in the reference frame is defined by the orientation matrix O_1 and O_2. The misorientation matrix is given by:
As M is a rotation matrix, one could extract the couple angleaxis, (\theta,\vec{u}) according to:
and
However, because of crystal symmetry, the misorientation between two grains is not unique, i.e. equivalent (\vec{u},\theta) exist. The misorientation axis should then be modified by:
where O_S are the symmetry operations of the crystal. For cubic, it consists of:

Rotations along \langle 100 \rangle of 90°, 180° and 270° (9 rotations)

Rotations along \langle 110 \rangle of 180° (6 rotations)

Rotations along \langle 111 \rangle of 120° and 240° (8 rotations)

Identity operation
Thus 24 symmetry operations can be applied, leading to 24 (\vec{u},\theta) couples.
Equivalent considerations can be made for other crystal systems.
Interface¶
The interface is composed of 3 tabs.

the settings tab is used to enter the 2 crystal inputs, the microscopic settings regarding rotation between tilt axis and image, and the layout. Refer to stereoproj for the details information.

the stereoproj tab is the plotting area

misorientation tab display the misorientation between crystal (if identical crystal are selected)
Procedure¶
Plotting¶

Set the crystal parameter and layout in the setting tab. Refer to stereoproj for the details.

Enter the crystal 1 and 2 orientation in the Euler Angles fields

Plot the stereographic projections using the
Plot
button
Overlay of an aluminium and an zirconium crystal.
 Same additional features as in stereoproj are available: adding poles/directions, planes... and can be performed independently on crystal 1 or 2 by using the Switch button
 Rotations can be performed along x,y,z or along a pole/direction (g) entered in the
Pole/direction
field, either in crystal 1 or 2
Misorientation¶
For 2 crystals of the same structure, the misorientation can be computed after plotting the stereographic projection.
In the misorientation tab:

press the
Find misorientation Plot Angle/Axis
button 
the rotation axes in both crystal are displayed along with the rotation angle

if the
uvw
button is ticked in the setting tab, the axes will be given as directions and not plane normals. 
in the stereographic tab, the axes appear as black dots.

ticking the
show numbers
orshow axes
will display the number corresponding to the angle/axis couples and the axis indices in crystal 1 on the stereographic projection, respectively.