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

In the analysis of crystallographic texture, the orientation distribution function of the grains is generally expressed as a linear combination of the generalized spherical harmonics. Recently, an alternative expansion of the orientation distribution function—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 paper 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 orientation distribution function. A short discussion of the phase conventions surrounding these expansions is also presented. † corresponding author: [email protected]