Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between the Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions
Author(s)
Mason, J. K.; Schuh, Christopher A.
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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.
Date issued
2009-09Department
Massachusetts Institute of Technology. Department of Materials Science and EngineeringJournal
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
ISSN
1073-5623
1543-1940