Title

Coordinate Free Tensorial Representation of N-Point Correlation Functions forMicrostructure by Harmonic Polynomials

Document Type

Article

Journal/Book Title/Conference

Materials Science Forum

Publisher

Trans Tech Publications

Publication Date

1994

First Page

287

Last Page

294

Abstract

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.

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