text: The effect of crystal symmetry on misorientations is to reduce the fraction of the full orientation space necessary to uniquely represent all possible misorientation relationships.  For example, cubic crystals (i.e. FCC) have 24 symmetrically related orientations.  Each of these orientations is physically indistinguishable, though mathematically distinct.  Therefore, the size of orientation space is reduced by a factor of 24.  This defines the fundamental zone (FZ) for cubic symmetries.  For the misorientation between two cubic crystallites, each possesses its 24 inherent symmetries.  In addition, there exists a switching symmetry, defined by:
  which recognizes the invariance of misorientation to direction; A→B or B→A.  The fraction of the total orientation space in the cubic-cubic fundamental zone for misorientation is then given by:<br />
  or 1/48 the volume of the cubic fundamental zone.  This also has the effect of limiting the maximum unique misorientation angle to 62.8°<br />
  <br />
  Disorientation describes the misorientation with the smallest possible rotation angle out of all symmetrically equivalent misorientations that fall within the FZ (usually specified as having an axis in the standard stereographic triangle for cubics).  Calculation of these variants involves application of crystal symmetry operators to each of the orientations during the calculation of misorientation.<br />
  <br />
  where O denotes one of the symmetry operators for the material.