How to choose a crystal reference frame

The crystal reference frame is defined with respect to crystallographic axes. Crystal reference frame can be defined arbitrarily. However, its three axes must be perpendicular to each other. The same crystal reference frame must be used for all the crystallites in the same sample. For cubic system, the crystal reference frame can be chosen simply as that: X axis parallel to [100], Y axis parallel to [010] and Z axis parallel to [001]. For other systems, one may have their own preference of choosing crystal reference frame. In the following, we describe our conventions to choose crystal reference frame.

Examples of choosing crystal reference frame in hexagonal and monoclinic crystal systems are shown in the following figure.

 

For rhombohedral crystal system, crystal reference frame is defined differently in order to make use of the three-fold symmetry along the [111] crystallographic direction. It is selected that X axis is parallel to the [01-1] crystallographic direction, Y axis is parallel to the [2-1-1] crystallographic direction and Z axis is parallel to [111] crystallographic direction as shown in the following figure.