Table of Contents
Textures and Microstructures
Volume 21, Issue 4, Pages 233-250

Coordinate Free Tensorial Representation of the Orientation Distribution Function With Harmonic Polynomials

1Council of Engineering and Applied Science, Yale University, New Haven, Connecticut 06520-2157, USA
2Department of Mathematics, Yale University, New Haven, Connecticut 06520-2155, USA
3Department of Manufacturing Engineering, Brigham Young University, Provo, Utah 84602, USA

Accepted 20 April 1993

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The crystallite orientation distribution function (CODF) is reviewed in terms of classical spherical function representation and more recent coordinate free tensorial representation (CFTR). A CFTR is a Fourier expansion wherein the coefficients are tensors in the three-dimensional space. The equivalence between homogeneous harmonic polynomials of degree k and symmetric and traceless tensors of rank k allows a realization of these tensors by the method of harmonic polynomials. Such a method provides for the rapid assembly of a tensorial representation from microstructural orientation measurement data. The coefficients are determined to twenty-first order and expanded in the form of a crystallite orientation distribution function, and compared with previous calculations.