International Tables for Crystallography

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Transformations of the coordinate system (unit-cell transformations)
H. Arnold. International Tables for Crystallography (2006). Vol. A, ch. 5.1, pp. 78-85  [ doi:10.1107/97809553602060000510 ]

Abstract

Transformations of the coordinate system are useful when nonconventional descriptions of a crystal structure are considered, for instance in the study of relations between different structures, of phase transitions and of group–subgroup relations. Unit-cell transformations occur particularly frequently when different settings or cell choices of monoclinic, orthorhombic or rhombohedral space groups are to be compared or when `reduced cells' are derived. In this chapter, matrix notation is used to describe a general transformation. Selected frequently occurring transformation matrices are tabulated and illustrated by diagrams.


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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.