Tables for
Volume A1
Symmetry relations between space groups
Edited by Hans Wondratschek and Ulrich Müller

International Tables for Crystallography (2006). Vol. A1, ch. 3.1, p. 430   | 1 | 2 |

Section 3.1.2. Cell transformations

Ulrich Müllera*

aFachbereich Chemie, Philipps-Universität, D-35032 Marburg, Germany
Correspondence e-mail:

3.1.2. Cell transformations

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When comparing related crystal structures, unit-cell transformations are troublesome. They result in differing sets of atomic coordinates for corresponding atoms; this can make comparisons more complicated and structural relations may be obscured. Frequently, it is more convenient not to interchange axes and to avoid transformations if possible. The use of a nonconventional settingof a space group may be preferable if this reduces cell transformations. For this reason, in the present tables settings of the subgroups were preferentially chosen in such a way that the directions of the basis vectors of a space group and its subgroup deviate as little as possible. If this results in a nonconventional setting of the subgroup, then the way to transform the basis vectors and coordinates to those of the conventional cell is also given.

Subgroups listed in nonconventional settings concern orthorhombic and monoclinic space groups. Their transformations to conventional settings frequently only involve an interchange of axes. In the case of tetragonal subgroups, nonconventional settings with C-centred or F-centred cells are not used; this would have caused nonconventional multiplicities of the Wyckoff positions and would have required listings of all positions in these settings. Equally, face-centred monoclinic cells, B-centred mono­clinic cells for unique axis b, C-centred monoclinic cells for unique axis c and hexagonal H cells are not used.

Monoclinic space groups allow different descriptions, such as unique axis a, b or c, base- or body-centred cells, and glide vectors in different directions. All settings that are listed in Volume A have been considered to be allowed conventional settings. Whenever a cell transformation can be avoided and the subgroup conforms to any of the settings listed in Volume A (b or c as unique axis; cell choices 1, 2 or 3), then this setting has been chosen. Transformations to other settings are not given in these cases.

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