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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier B.V.
2012
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| Online Access: | http://hdl.handle.net/1721.1/69552 https://orcid.org/0000-0001-9856-2682 |
| _version_ | 1826206575416573952 |
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| author | Mason, J. K. Schuh, Christopher A. |
| author2 | Massachusetts Institute of Technology. Department of Materials Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Materials Science and Engineering Mason, J. K. Schuh, Christopher A. |
| author_sort | Mason, J. K. |
| collection | MIT |
| 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. |
| first_indexed | 2024-09-23T13:34:48Z |
| format | Article |
| id | mit-1721.1/69552 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:34:48Z |
| publishDate | 2012 |
| publisher | Elsevier B.V. |
| record_format | dspace |
| spelling | mit-1721.1/695522022-10-01T15:49:16Z The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures Mason, J. K. Schuh, Christopher A. Massachusetts Institute of Technology. Department of Materials Science and Engineering Schuh, Christopher A. Schuh, Christopher A. Mason, J. K. 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. National Science Foundation (U.S.) (Contract #DMR-0346848) 2012-03-01T19:13:34Z 2012-03-01T19:13:34Z 2009-07 2009-04 Article http://purl.org/eprint/type/JournalArticle 1359-6454 1873-2453 http://hdl.handle.net/1721.1/69552 Mason, J.K., and C.A. Schuh. “The Generalized Mackenzie Distribution: Disorientation Angle Distributions for Arbitrary Textures.” Acta Materialia 57.14 (2009): 4186–4197. https://orcid.org/0000-0001-9856-2682 en_US http://dx.doi.org/10.1016/j.actamat.2009.05.016 Acta Materialia Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Elsevier B.V. Prof. Schuh via Angie Locknar |
| spellingShingle | Mason, J. K. Schuh, Christopher A. The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures |
| title | The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures |
| title_full | The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures |
| title_fullStr | The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures |
| title_full_unstemmed | The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures |
| title_short | The generalized Mackenzie distribution: disorientation angle distributions for arbitrary textures |
| title_sort | generalized mackenzie distribution disorientation angle distributions for arbitrary textures |
| url | http://hdl.handle.net/1721.1/69552 https://orcid.org/0000-0001-9856-2682 |
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