Table of Contents
Textures and Microstructures
Volume 19, Issue 3, Pages 147-167

Tensorial Representation of the Orientation Distribution Function in Cubic Polycrystals

Department of Mechanical Engineering, Yale University, New Haven, CT 06520, USA

Accepted 22 July 1991

Copyright © 1992 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.


A precise definition for the crystallite orientation distribution function (codf) of cubic polycrystals is given in terms of the set of distinct orientations of a cube. Elements of the classical Fourier representation of the codf, in terms of (symmetrized) generalized spherical harmonics, are reviewed. An alternative Fourier representation is defined in which the coefficients of the series expansion are irreducible tensors. Since tensors can be defined without the benefit of a coordinate frame, the tensorial representation is coordinate free. A geometrical association between irreducible tensors and a bouquet of lines passing through a common origin is discussed. Algorithms are given for computing the irreducible tensors and basis functions for cubic polycrystals.