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In the analysis of crystallographic texture, the orientation distribution function (ODF) of thegrains 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 hypersphericalharmonics, has been proposed, with the advantage that this is a function of the angles thatdirectly describe the axis and angle of each grain rotation, rather than of the Euler angles. Thisarticle provides the formulas required to convert between the generalized spherical harmonicsand the hyperspherical harmonics, and between the coefficients appearing in their respectiveexpansions of the ODF. A short discussion of the phase conventions surrounding theseexpansions is also presented.National Science Foundation (U.S.) (contract DMR- 0346848)National Science Foundation (U.S.) (contract DMR-0855402

metallurgical and materials transactions. a, physical metallurgy and materials science

Expressing Crystallographic Textures through the Orientation Distribution Function: Conversion between Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions