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

International Tables for Crystallography (2006). Vol. A, ch. 5.1, p. 78

Section 5.1.1. Introduction

H. Arnolda

aInstitut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany

5.1.1. Introduction

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There are two main uses of transformations in crystallography.

  • (i) Transformation of the coordinate system and the unit cell while keeping the crystal at rest. This aspect forms the main topic of the present part. Transformations of coordinate systems 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.

  • (ii) Description of the symmetry operations (motions) of an object (crystal structure). This involves the transformation of the coordinates of a point or the components of a position vector while keeping the coordinate system unchanged. Symmetry operations are treated in Chapter 8.1[link] and Part 11[link] . They are briefly reviewed in Chapter 5.2[link] .

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