Title

Tensorial Representation of Two-point Correlation Functions for PolycrystallineMicrostructure by Harmonic Polynomials

Document Type

Article

Journal/Book Title/Conference

Philosophical Magazine A

Volume

72

Issue

1

Publication Date

1995

First Page

199

Last Page

208

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.

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