International Tables for Crystallography

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Reduced bases
P. M. de Wolff. International Tables for Crystallography (2006). Vol. A, ch. 9.2, pp. 750-755  [ doi:10.1107/97809553602060000518 ]

Abstract

In this chapter, reduced bases (reduced cells) are described. The treatment starts with the definition of the reduced basis and the reduced form in terms of the metric tensor and lists the conditions (both main and special) for reduced bases of type-I cells and type-II cells. This is followed by a detailed and systematic geometric explanation of these conditions. The resulting 44 lattice characters are defined and tabulated, and the relations between the lattice characters and the conventional cell parameters of the 14 Bravais lattices are listed and discussed.


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About International Tables for Crystallography

International Tables for Crystallography is the definitive resource and reference work for crystallography. The multi-volume series comprises articles and tables of data relevant to crystallographic research and to applications of crystallographic methods in all sciences concerned with the structure and properties of materials.