Tensorial representation of two-point correlation functions for polycrystalline microstructure by harmonic polynomials

Abstract

One important characteristic of polycrystalline microstructures is the set of two-point correlation functions which describe the statistics of spatial correlation of lattice orientations between two points which are separated by a specified vector. Described in this paper is a new mathematical approach to the representation and computation of such functions. The approach allows one to construct coordinate-free tensorial representations of two-point statistics using the theory of harmonic polynomials. The method relies heavily on representation theory of the group of rotations of the three-dimensional space, a brief introduction to which is presented.