TENSORIAL REPRESENTATION OF 2-POINT CORRELATION-FUNCTIONS FOR POLYCRYSTALLINE MICROSTRUCTURE BY HARMONIC POLYNOMIALS

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 whic h are separated by a specified vector. Described in this paper is a ne w mathematical approach to the representation and computation of such functions. The approach allows one to construct coordinate-free tensor ial representations of two-point statistics using the theory of harmon ic polynomials. The method relies heavily on representation theory of the group of rotations of the three-dimensional space, a brief introdu ction to which is presented.