Coordinate Free Tensorial Representation of N-Point Correlation Functions forMicrostructure by Harmonic Polynomials
Materials Science Forum
Trans Tech Publications
Perhaps the most important characteristic of a microstructure is its N-point correlation function which describes the statistics of the distribution of crystal lattice orientations in its grains. Described in this paper is a new mathematical approach to representation and computation of such functions. This approach allows one to construct so called coordinate free tensorial representations of N-point statistics for a given microstructure using the theory of harmonic polynomials. It will be shown how to compute 1-point and 2-point using this method. The method relies heavily on representation theory of the group of rotations of the 3-dimensional space, a brief introduction to which is presented.
"Coordinate Free Tensorial Representation of N-Point Correlation Functions for Microstructure by Harmonic Polynomials”, B. L. Adams, P. I. Etingof and D. D. Sam, 1994, Material Science Forum, 157-162, 287.