International
Tables for Crystallography Volume A Space-group symmetry Edited by Th. Hahn © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. A, ch. 9.1, p. 742
Section 9.1.2. Lattices^{a}Universität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and ^{b}Institut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany |
A three-dimensional lattice can be visualized best as an infinite periodic array of points, which are the termini of the vectors The parallelepiped determined by the basis vectors a, b, c is called a (primitive) unit cell of the lattice (cf. Section 8.1.4 ), a, b and c are a primitive basis of the lattice. The number of possible lattice bases is infinite.
For the investigation of the properties of lattices, appropriate bases are required. In order to select suitable bases (see below), transformations may be necessary (Section 5.1.3 ). Of the several properties of lattices, only symmetry and some topological aspects are considered in this chapter. Some further properties of lattices are given in Chapter 9.3 .