Table of Contents
Textures and Microstructures
Volume 26 (1996)–27

The Smoothing of the Orientation Distribution Density Introduced by Calculation Methods

Polish Academy of Sciences, Aleksander Krupkowski Institute of Metallurgy and Materials Science, 30-059 Krakow, ul. Reymonta 25, Poland

Received 10 December 1995

Copyright © 1996 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 values of the orientation density distribution function (ODF) depend as a rule on the applied calculation method. In the series expansion method the calculation result is influenced by truncation of the series. With decreasing of the expansion order lmax the width of smoothing around the ODF maximum increases and its height decreases.

It is shown that the smoothing of the orientation density caused by series truncation can be described analytically by a Gaussian type function. Disturbing undulations of negative and positive values around ODF maxima characteristic for harmonic expansion can be suppressed by using additional smoothing functions.