Table of Contents
Textures and Microstructures
Volume 22, Issue 1, Pages 17-27

Approximation of the Pole Figures and the Orientation of Distribution of Grains in Polycrystalline Samples by Means of Canonical Normal Distributions

MIFI (Moscow Engineering Physical Institute), Kashirskoye shosse 31, Moscow 115409, Russia

Received 20 January 1993

Copyright © 1993 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) as determined from experimental pole figures (PF) in a polycrystalline sample by classical spherical harmonics analysis can have ghost effects and regions of negative values. The regions of negative values and the ghosts are a consequence of the loss of information on the “odd” part of ODF.

In the present paper the canonical normal distributions (CND) on the rotation group SO(3) and on the sphere S2 in R3 used in texture analysis are discussed.

The examples of CND on SO(3), S2 and their PF calculated for hexagonal lattice symmetry and for a rolling texture of beryllium are demonstrated.