Table of Contents
Textures and Microstructures
Volume 6, Issue 1, Pages 1-19

The Use of a Quadratic Form for the Determination of Non-negative Texture Functions

Department Metaalkunde, Katholieke Universiteit Leuven, de Croylaan 2, Leuven B–3030, Belgium

Received 11 January 1983

Copyright © 1983 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 classical analysis of measured pole figures of textured polycrystals by the series expansion method does not necessarily produce a non-negative texture function. The main reason for this is, that the method is unable to find the terms of odd rank l of the series expansion.

A new method is proposed, which introduces the non-negativity condition into the series expansion method by the use of quadratic forms. The method is found to be successful when treating sharp textures, which have a considerable zero range in Euler space. The preliminary determination of this zero range by experimental methods is however not necessary.