The Bravais polar lattice as a didactic tool for diffraction beginners

When undergraduate students discover crystallography for the first time, they are usually already familiar with the phenomenon of diffraction as the `bending' of waves around small obstacles. The special (periodic) nature of crystals acting as `diffraction gratings' that produce interference of diffracted waves is typically rationalized in terms of the reciprocal lattice of the crystal. The concept of the reciprocal lattice, however, remains somewhat abstract for beginners, until they perform a diffraction experiment. It can be made more easily understandable through an intermediate step, namely its ancestor, the Bravais polar lattice. By means of a short historical trip through pre-X-ray crystallography, a generalized introduction to the notion of the dual lattice is given, of which the reciprocal lattice is the most common but by no means the only example, and it is shown how the use of the Bravais polar lattice can ease the introduction of the reciprocal lattice.