C - Crystallography

Summary

The crystal lattice

An ideal crystal contains atoms arranged in a repetitive three-dimensional pattern. If each repeat unit of this pattern, which may be an atom or group of atoms, is taken as a point then a three-dimensional point lattice is created. A space lattice, such as that shown in figure C.1, is obtained when lines are drawn connecting the points of the point lattice. The space lattice is composed of box-like units, the dimensions of which are fixed by the distances between the points in the three noncoplanar directions x, y and z. These are known as unit cells and the crystal structure has a periodicity (based on the contents of these cells) represented by the translation of the original unit of pattern along the three directions x, y and z. These directions are called the crystallographic axes. Any directions may, in principle, be chosen as the crystallographic axes. However, it is useful to select a set of axes which bears a close resemblance to the symmetry of the crystal. This can result in x, y and z directions that are not at right angles to one another. In figure C.1, the angle between the y and z axes is designated α, between the z and x axes, β, and between the x and y axes, γ.