On the four‐axis hexagonal reciprocal lattice and its use in the indexing of transmission electron diffraction patterns

Abstract A four‐axis hexagonal reference basis can be constructed in the reciprocal space of hexagonal crystals in such a way that the resulting lattice contains as a subset all the points of the conventional reciprocal lattice. All other points not belonging to this subset have no physical significance since they have non‐integral indices and hence cannot represent real crystal planes. Since these points cannot register as spots in an actual diffraction pattern, the four‐axis hexagonal lattice and the conventional reciprocal lattice are physically indistinguishable. _ The interpretation of diffraction patterns of hexagonal crystals is easier when indexing is referred to the four‐axis basis. The necessary crystallographic relationships can be obtained directly in terms of Miller‐Bravais indices using elementary vector analysis and when applied to Kikuchi electron diffraction maps, the problem of determining the foil orientation becomes especially simple.