Hyperspherical harmonics for the representation of crystallographic texture

The feasibility of representing crystallographic textures as quaternion distributions by a series expansion method is demonstrated using hyperspherical harmonics. This approach is refined by exploiting the sample and crystal symmetries to perform the expansion more efficiently. The properties of the quaternion group space encourage a novel presentation of orientation statistics, simpler to interpret than the usual methods of texture representation. The result is a viable alternative to the Euler angle approach to texture standard in the literature today.