Optimal bounds on texture coefficients

Let w be the orientation distribution function of a polycrystalline aggregate of crystallites with symmetry G(cr) and with group of texture symmetry G(tex). In this paper we obtain a recipe on how to derive optimal bounds on the texture coefficients W-lmn associated with w. In particular, we find explicit bounds in the case in which G(tex) is a group with orthorhombic symmetry and G(cr) is either a group with cubic symmetry or a group with hexagonal symmetry.