The generalized Mackenzie distribution: Disorientation angle distributions for arbitrary textures

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...

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Veröffentlicht in:	Acta materialia 2009-08, Vol.57 (14), p.4186-4197
Hauptverfasser:	Mason, J.K., Schuh, C.A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Analytical methods Applied sciences Exact sciences and technology Grain boundaries Metals. Metallurgy Texture
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container_title	Acta materialia
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creator	Mason, J.K. Schuh, C.A.
description	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.
doi_str_mv	10.1016/j.actamat.2009.05.016
format	Article
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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.</description><identifier>ISSN: 1359-6454</identifier><identifier>EISSN: 1873-2453</identifier><identifier>DOI: 10.1016/j.actamat.2009.05.016</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Analytical methods ; Applied sciences ; Exact sciences and technology ; Grain boundaries ; Metals. 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title	The generalized Mackenzie distribution: Disorientation angle distributions for arbitrary textures
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