Table of Contents
Textures and Microstructures
Volume 23, Issue 2, Pages 115-129

Examination of the Iterative Series-Expansion Method for Quantitative Texture Analysis

lnstiut für Metallkunde und Metallphysik, RWTH Aachen, Kopernikusstr Str 14, Aachen 52056, Germany

Received 1 November 1994

Copyright © 1995 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.


Three-dimensional orientation distributions of grains in polycrystalline aggregates are referred to as crystallographic textures. Commonly, they are computed from two-dimensional centro-symmetric pole figures by employment of series expansion techniques or so called direct inversion methods. Both approaches lead to inaccuracies which are due to the absence of the odd coefficients and by truncation errors in the first case and to the under-determination of the set of linear equations combining cells in the pole figures and in the three-dimensional orientation space in the second case. For both types of calculation methods various correction procedures were suggested. In case of the series expansion methods the introduction of the non-negativity condition was reported to considerably improve the obtained solution. However, before large series of experimental data can be processed by such a method, its reliability has to be checked by use of analytical tools. Hence, in the present study a recently introduced iterative series-expansion method which accounts for the non-negativity condition is examined by use of standard functions.