Open AccessDiscussion of the representation of intercrystalline misorientation in cubic materials
Author(s) -
Adams B. L.,
Zhao J.,
Grimmer H.
Publication year - 1990
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
eISSN - 1600-5724
pISSN - 0108-7673
DOI - 10.1107/s0108767390000435
Subject(s) - quaternion , mathematics , euler angles , cubic form , invariant (physics) , euler's formula , pure mathematics , geometry , lattice (music) , misorientation , mathematical analysis , crystallography , physics , microstructure , chemistry , acoustics , grain boundary , mathematical physics
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 (Σ ≤ 49), Euler angles and axis-angle parameters is given.