Representation of orientation relationships in Rodrigues–Frank space for any two classes of lattice

The fundamental zones of Rodrigues–Frank (R-F) space applicable to misorientations between crystals of any two Laue groups are constructed by using a unified formulation in terms of quaternion algebra. Some of these regions are fully bounded by planes that are determined solely by the symmetries of the groups, while others have at least one unbounded direction. Each of the bounded fundamental zones falls into one of nine geometrically distinct configurations. The maximum symmetry-reduced angles and the corresponding Rodrigues–Frank vectors for these fundamental zones are evaluated. The use of Rodrigues–Frank space for the representation of orientation relationships between crystals of any two symmetry groups is also addressed. Examples concerning the transition of phases of the same symmetry group,i.e.from face-centered cubic to body-centered cubic, and of different groups,i.e.from body-centered cubic to hexagonal close-packed, are given to illustrate the usefulness of this space for representing orientation relationships during phase transformation or precipitation.