Transformations for monoclinic crystal symmetry in texture analysis

Monoclinic crystals can be described in two settings: in the first setting the C₂ rotation axis is parallel to the z axis and in the second setting it is parallel to the y axis. Transformations of lattice parameters, Miller and zone indices, and atomic coordinates is straightforward; the situation is far more complex for texture analysis with orientation distributions and corresponding representations. This article gives explicit transformations that need to be applied, not only for texture analysis but also for calculations of physical properties of materials with preferred orientation. In texture research the relationship between the Cartesian crystal coordinate system and the unit cell must be unambiguously defined and a uniform convention is desirable.