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

TitleExpressing Crystallographic Textures through the Orientation Distribution Function: Conversion between Generalized Spherical Harmonic and Hyperspherical Harmonic Expansions
Publication TypeJournal Article
Year of Publication2009
AuthorsMason, JK, Schuh, CA
JournalMetallurgical and Materials Transactions a-Physical Metallurgy and Materials Science
Volume40A
Issue11
Pagination2590 - 2602
Date Published2009/11//
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.