International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 9.1, p. 742

Section 9.1.2. Lattices

H. Burzlaffa and H. Zimmermannb*

aUniversität Erlangen–Nürnberg, Robert-Koch-Strasse 4a, D-91080 Uttenreuth, Germany, and bInstitut für Angewandte Physik, Lehrstuhl für Kristallographie und Strukturphysik, Universität Erlangen–Nürnberg, Bismarckstrasse 10, D-91054 Erlangen, Germany
Correspondence e-mail:  helmuth.zimmermann@knot.uni-erlangen.de

9.1.2. Lattices

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A three-dimensional lattice can be visualized best as an infinite periodic array of points, which are the termini of the vectors [{\bf l}_{uvw} = u{\bf a} + v{\bf b} + w{\bf c},\quad u, v, w \hbox{ all integers}.] The parallelepiped determined by the basis vectors a, b, c is called a (primitive) unit cell of the lattice (cf. Section 8.1.4[link] ), 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[link] ). 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[link] .








































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