Emeritus Professor Mike Glazer

Abstract:

Natural optical activity (NOA), the ability of a material to rotate the plane of polarized light, has traditionally been associated with structural chirality. However, this relationship has often been oversimplified, leading to conceptual misunderstandings, particularly when attempts are made to correlate structural handedness directly with optical rotatory power. In reality, the relationship between chirality and NOA is more nuanced: optical activity can arise in both chiral and achiral crystal structures, and the sign of the rotation cannot necessarily be inferred from the handedness of the space group. In this work, we conduct a first-principles investigation of NOA in SiO2 and AlPO4 crystals, focusing on their enantiomorphic structural phase transition from high-symmetry hexagonal (P6422 or P6222) to low-symmetry trigonal (P3121 or P3221) space groups. This transition, driven by the condensation of a zone-centre Γ3 phonon mode, reverses the screw-axis type given by the space-group symbol while leaving the sign of the optical activity unchanged. By following the evolution of the structure and the optical response along the transition pathway, we clarify the microscopic origin of this behaviour. We demonstrate that the sense of optical rotation is determined not by the nominal handedness of the screw axis given in the space-group symbol but by the atomic-scale handedness of the most polarizable atoms of the structure.

Abstract:

It is pointed out that many authors are unaware that the particular choice of unit‐cell origin determines the irreducible representations to which octahedral tilts in perovskites belong. Furthermore, a recommendation is made that the preferred option is with the origin at the B‐cation site rather than that of the A site.

Abstract:

The description of crystal structures is given starting with some fundamental notions of crystal symmetry. The topics of lattices and space groups are briefly introduced and how these can be used with unit cell contents to describe the crystal structure. This leads to crystallographic databases where information on crystal structures is stored and can be searched. A brief discussion on refinement of diffraction information is given, together with the resulting geometric parameters.

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.