Remarks on Texture Coefficients of Polycrystals with Improper Crystallite Symmetry

The orientation distribution function (ODF) in classical texture analysis is defined on the rotation group SO(3). For polycrystalline aggregates with crystallite symmetry defined by a crystallographic point group Gcr which is not a subgroup of SO(3), the improper group Gcris routinely replaced by its proper peer (i.e., a subgroup of SO(3)) in the same Laue class. In this note we examine how the texture coefficients obtained from such a practice are related to their counterparts that pertain to the corresponding ODF defined on the orthogonal group O(3) as it should.