Emeritus Professor Mike Glazer

Abstract:

The notion of periodicity in crystals is examined and how this can be varied in practice. In particular, the article discusses first of all the concept of superstructures, in which some sort of alternating motif occurs thus changing the repeat distance in a lattice. Crystals of this type are often incorrectly called in the literature superlattices: first of all they cannot be called lattices at all as they consist of atoms (a lattice must only consist of points). In any case such a superstructure is formed from a sublattice rather than a superlattice. In addition, some crystals do not have normal periodicity within a three-dimensional space, and are known as aperiodic crystals. Despite being aperiodic, they are still ordered. In mathematical terms they can by described with respect to a higher-dimension space and then projected back onto three dimensions. This generalizes our notion of what is meant by a crystal.