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

International Tables for Crystallography (2006). Vol. A, ch. 9.1, p. 745

Table 9.1.7.1 

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

Table 9.1.7.1| top | pdf |
Two-dimensional Bravais lattices

Bravais latticeLattice parametersMetric tensorProjections
ConventionalPrimitive/transformation to primitive cellConventionalPrimitiveRelations of the components
mp [\matrix{a, b\hfill\cr \gamma\hfill\cr}] [\matrix{a, b\hfill\cr \gamma\hfill\cr}] [\matrix{g_{11} &g_{12}\hfill\cr &g_{22}\hfill\cr}] [\matrix{g_{11} &g_{12}\hfill\cr &g_{22}\hfill\cr}]   [Scheme scheme15]
op [\matrix{a, b\hfill\cr \gamma = 90^{\circ}\hfill\cr}] [\matrix{a, b\hfill\cr \gamma = 90^{\circ}\hfill\cr}] [\matrix{g_{11} &0\hfill\cr &g_{22}\hfill\cr}] [\matrix{g_{11} &0\hfill\cr &g_{22}\hfill\cr}]   [Scheme scheme16]
oc [\matrix{a_{1} = a_{2}\hfill, \gamma\hfill\cr {\bi P}(c)\hfill}] [\matrix{g'_{11} &g'_{12}\hfill\cr &g'_{22}\hfill\cr}] [\matrix{g'_{11} = {\textstyle{1 \over 4}}(g_{11} + g_{22})\hfill\cr g'_{12} = {\textstyle{1 \over 4}}(g_{11} - g_{22})\hfill\cr g_{11} = 2(g'_{11} + g'_{12})\hfill\cr g_{12} = 2(g'_{11} - g'_{12})\hfill\cr}] [Scheme scheme17]
tp [\matrix{a_{1} = a_{2}\hfill\cr \gamma = 90^{\circ}\hfill\cr}] [\matrix{a_{1} = a_{2}\hfill\cr \gamma = 90^{\circ}\hfill\cr}] [\matrix{g_{11} &0\hfill\cr &g_{11}\hfill\cr}] [\matrix{g_{11} &0\hfill\cr &g_{11}\hfill\cr}]   [Scheme scheme18]
hp [\matrix{a_{1} = a_{2}\hfill\cr \gamma = 120^{\circ}\hfill\cr}] [\matrix{a_{1} = a_{2}\hfill\cr \gamma = 120^{\circ}\hfill\cr}] [\matrix{g_{11} &-{\textstyle{1 \over 2}}\;g_{11}\hfill\cr &g_{11}\hfill\cr}] [\matrix{g_{11} &-{\textstyle{1 \over 2}}\;g_{11}\hfill\cr &g_{11}\hfill\cr}]   [Scheme scheme19]
The symbols for Bravais lattices were adopted by the International Union of Crystallography in 1985; cf. de Wolff et al. (1985)[link].
[{\bi P}(c) =\textstyle{1 \over 2}(11/\bar{1}1).]