Table of Contents
Textures and Microstructures
Volume 8 –9

ODF Calculation by Series Expansion From Incompletely Measured Pole Figures Using the Positivity Condition: Part II—All Crystal Symmetries

1Institut für Metallkunde und Metallphysik der TU Clausthal, Großer Bruch 23, Clausthal-Zellerfeld D-3392, Germany
2GKSS-Forschungszentrum, Max-Planck-Straße, Geesthacht D-2054, Germany

Received 3 September 1987

Copyright © 1988 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 calculation of orientation distribution functions (ODF) from incomplete pole figures of any crystal symmetry can be carried out by an iterative procedure taking into account the positivity condition for all pole figures. During the iterative procedure the pole figures are normalized and the pole figure inversion leads to stable results, i.e. the coefficients for higher degrees of series expansion keep small.