Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between the Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions
Name
Schuh-Expressing Crystallographic Textures with figures.pdf
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824.49 KB
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6624d3b0a10ca28f1358800ca9321a27
Author(s)
Mason, J. K.
Schuh, Christopher A.
Date Issued
September 2009
Journal
Metallurgical and Materials Transactions A
Publisher
Springer Boston
Citation
Mason, J.K., and C.A. Schuh. “Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions.” Metallurgical and Materials Transactions A 40.11 (2009): 2590-2602.
Version
Author's final manuscript
Abstract
In the analysis of crystallographic texture, the orientation distribution function (ODF) of the
grains is generally expressed as a linear combination of the generalized spherical harmonics.
Recently, an alternative expansion of the ODF, as a linear combination of the hyperspherical
harmonics, has been proposed, with the advantage that this is a function of the angles that
directly describe the axis and angle of each grain rotation, rather than of the Euler angles. This
article provides the formulas required to convert between the generalized spherical harmonics
and the hyperspherical harmonics, and between the coefficients appearing in their respective
expansions of the ODF. A short discussion of the phase conventions surrounding these
expansions is also presented.
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/10.1007/s11661-009-9936-8
