Table of Contents
Textures and Microstructures
Volume 6, Issue 3, Pages 167-179
http://dx.doi.org/10.1155/TSM.6.167

Calculation of the Normalization Factor of Incomplete Pole Figures by Cubic Extrapolation

Institut für Metallkunde und Metallphysik der TU Clausthal, Großer Bruch 23, Clausthal-Zellerfeld D-3392, Germany

Received 1 October 1985; Accepted 10 December 1985

Copyright © 1986 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.

Abstract

The calculation of orientation distribution functions from incomplete pole figures can be carried out by a least squares approximation of the texture coefficients Clμν and the normalization factors Nhkl to the available experimental data. This procedure is less susceptable to instabilities due to experimental errors if the normalization factors can be calculated independently of the coefficients Clμν. In the case of cubic materials, the relationship F20 = 0 to be fulfilled by pole figure values provides an independent condition for the calculation of the normalization factor. This condition can still be improved by taking the slopes of the pole density curves at α = αmax and α = 90° into account. An economic way to consider the slope in the pole figures is to use a cubic spline interpolation.