The generalized Mackenzie distribution: Disorientation angle distributions for arbitrary textures

TitleThe generalized Mackenzie distribution: Disorientation angle distributions for arbitrary textures
Publication TypeJournal Article
Year of Publication2009
AuthorsMason, JK, Schuh, CA
JournalActa Materialia
Volume57
Issue14
Pagination4186 - 4197
Date Published2009/08//
Abstract

A general formulation for the disorientation angle distribution function is derived. The derivation employs the hyperspherical harmonic expansion for orientation distributions, and an explicit solution is presented for materials with cubic crystal symmetry and arbitrary textures. The result provides a significant generalization to the well-known Mackenzie distribution function [Mackenzie JK. Biometrika 1958;45:229] for materials with random crystal orientations. This derivation also demonstrates that the relatively new hyperspherical harmonic expansion provides access to results that have been inaccessible with the more traditional "generalized spherical harmonic" expansion that is in current use throughout the field. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.