Application of the Rodrigues vector to tilt and twist components of a grain boundary

Abstract

The Rodrigues method, formulated first as a geometrical construction and later in vector notation, provides a simple and direct means of visualizing and calculating the total rotation resulting from two sequential rotations. In this paper the case of the five degrees of freedom for a grain boundary are considered. The Rodrigues method is applicable since the total misorientation is a tilt followed by a twist rotation, and calculations are much simplified since vectors rather than matrices are involved.