Keywords

axis-angle parameters, coincidence site lattice, cubic-cubic misorientation, Euler angles, quaternion representation, rectilinearity

Abstract

BLA and JZ acknowledge the support of the Office of Basic Energy Science of the US Department of Energy under grant No. DE-FG02-88ER45355. Help from Stuart Wright with the figures is gratefully acknowledged. Salient features of various parameterizations of cubic-cubic misorientation are discussed. It is proposed that the quaternion representation of rotations, as a pair of antipodal points on the surface of a four-dimensional sphere, encompasses the most desirable properties of other proposed representations, viz rectilinearity, a closed form for the composition of successive rotations, and an equivalence between the Euclidean measure on its parameter space and the invariant measure in the space of rotations. The classification of cubic-cubic misorientations according to group multiplicity is described in Euler angle and quaternion representations. A correspondence between coincidence site lattice (CSL) boundaries (E <= 49), Euler angles and axis-angle parameters is given.

Original Publication Citation

Acta Cryst. (199). A46, 62-622