Geometric representation of polycrystalline material texture by axis-angle parametrization

Abstract

Texture is the preferential orientation of crystallographic axes in polycrystal. For its mathematical modeling, the orientation distribution function of the crystallographic axes is used. Traditionally, the orientation distribution function is written with the help of directional cosine matrices, Miller indices or Euler-Krylov angles. Recently, texture has increasingly often been described using quaternions, Rodrigues parameters and the vector space of axis-angle parameters. Axis-angle parameters allow us to describe all possible rotations of the SO(3) group, which corresponds to all possible orientations of crystallographic axes in polycrystalline materials. The SO(3) group is a set of rotations to all possible angles around all possible axes given by all vectors of the unit sphere. The set of such rotations corresponds to points set on a ball of radius π in three-dimensional Euclidean space. The description of the crystallographic texture using axis-angle parameters made it possible to visualize the distribution of crystallographic axes and obtain a new geometric representation of the texture. © 2018 Author(s).