Crystallographic Formulae for Hexagonal Lattices

For structures with hexagonal symmetry, three different axial systems (rhombohedral, orthorhombic, and hexagonal) are in general use to define the indices of directions and planes. The hexagonal axial system is the one in which confusion is most likely to occur if the axes and the notation are not clearly defined since, for this one crystal system, three distinct sets of crystallographic formulae arise. The difference between these formulae is demonstrated. The advantages of using the ortho‐hexagonal variant of the orthorhombic system are indicated. The relevant direct and reciprocal lattice bases are defined and the required crystallographic formulae given using both vector and tensor notations. Recommendations are made on nomenclature and notation.