Coordinate Free Tensorial Representation of the Orientation Distribution Function withHarmonic Polynomials
Document Type
Article
Journal/Book Title/Conference
Textures and Microstructures
Volume
21
Issue
4
Publisher
Hindawi Publishing Corporation
Publication Date
1993
First Page
233
Last Page
250
Abstract
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.
Recommended Citation
"Coordinate Free Tensorial Representation of the Orientation Distribution Function with Harmonic Polynomials", D. D. Sam, E. T. Onat, P. I. Etingof and B. L. Adams, 1993, Textures and Microstructures, 21, 233.
