Table of Contents
Textures and Microstructures
Volume 19, Issue 1-2, Pages 9-27

Approximation of the Orientation Distribution of Grains in Polycrystalline Samples by Means of Gaussians

1MIFI (Moscow Engineering Physical Institute), Kashirskoye shosse 31, Moscow 115409, Russia
2Zentralinstitut fur Kernforschung Rossendorf, PSF 19, Dresden 8051, Germany

Received 19 April 1990; Accepted 30 November 1990

Copyright © 1992 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 orientation distribution function (ODF) obtained by classical spherical harmonics analysis may be falsified by ghost influences as well as series truncation effects. The ghosts are a consequence of the inversion symmetry of experimental pole figures which leads to the loss of information on the “odd” part of ODF.

In the present paper a new method for ODF reproduction is proposed. It is based on the superposition of Gaussian distributions satisfying the central limit theorem in the SO(3)-space as well as the ODF positivity condition. The kind of ODF determination offered here is restricted to the fit of Gaussian parameters and weights with respect to the experimental pole figures. The operating mode of the new method is demonstrated for a rolling texture of copper. The results are compared with the corresponding ones obtained by the series expansion method.