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.
Article
Coordinate Free Tensorial Representation of the Orientation Distribution Function withHarmonic Polynomials
Textures and Microstructures
Document Type
Article
Publisher
Hindawi Publishing Corporation
Publication Date
1-1-1993
Disciplines
Abstract
Citation Information
"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.