The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures
Name
Schuh-The generalized Mackenzie distribution.pdf
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516.45 KB
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Author(s)
Mason, J. K.
Schuh, Christopher A.
Date Issued
July 2009
Journal
Acta Materialia
Publisher
Elsevier B.V.
Citation
Mason, J.K., and C.A. Schuh. “The Generalized Mackenzie Distribution: Disorientation Angle Distributions for Arbitrary Textures.” Acta Materialia 57.14 (2009): 4186–4197.
Version
Author's final manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Materials Science and Engineering
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1016/j.actamat.2009.05.016
