7 - The determination of space groups

Summary

Tests for the lack of a centre of symmetry

As we have seen in § 1.4 measurements of crystals with an optical goniometer can, in favourable circumstances, reveal the crystal class. Such measurements should be carried out on many crystals for there is a tendency for crystals to exist in a number of slightly different forms in each of which some facets may not be present. By-and-large, when incorrect conclusions are drawn from optical goniometry it is in the direction of assigning too high a symmetry to the crystal. However it is sometimes possible to be reasonably sure by means of such measurements that a crystal structure either has or does not have a centre of symmetry.

There are a number of physical properties of crystals, the measurements of which can be used unequivocally to detect the lack of a centre of symmetry in a crystal structure. We shall briefly consider these, the physical principles involved and the apparatus which may be used for the tests.

Piezoelectric effect

The first physical phenomenon we shall consider is that of piezoelectricity. This is the process whereby when a material is placed in an electric field it undergoes a mechanical strain and, conversely, when the material is mechanically strained it becomes electrically polarized and produces a field in its environment. Let us see what mechanism can produce this effect. In fig. 7.1(a) there is a schematic representation of a pair of atoms with their surrounding electron density. The two atoms are bonded together and the electron density is distorted from the configuration it would have for the superposition of that from two isolated atoms.