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

International Tables for Crystallography (2011). Vol. A1, ch. 2.1, pp. 80-81   | 1 | 2 |

## Section 2.1.4.3.1. Enlarged unit cell, index 2

Hans Wondratscheka* and Mois I. Aroyob

aInstitut für Kristallographie, Universität, D-76128 Karlsruhe, Germany, and bDepartamento de Física de la Materia Condensada, Facultad de Ciencias, Universidad del País Vasco, Apartado 644, E-48080 Bilbao, Spain
Correspondence e-mail:  wondra@physik.uni-karlsruhe.de

#### 2.1.4.3.1. Enlarged unit cell, index 2

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For sublattices with twice the volume of the unit cell, the sequence of the different cell enlargements is as follows:

• (1) Triclinic space groups:

 (i) , (ii) , (iii) , (iv) A-centring, (v) B-centring, (vi) C-centring, (vii) F-centring.

• (2) Monoclinic space groups:

• (a) with P lattice, unique axis b:

 (i) , (ii) , (iii) , (iv) B-centring, (v) C-centring, (vi) A-centring, (vii) F-centring.

• (b) with P lattice, unique axis c:

 (i) , (ii) , (iii) , (iv) C-centring, (v) A-centring, (vi) B-centring, (vii) F-centring.

• (c) with C lattice, unique axis b: There are three sublattices of index 2 of a monoclinic C lattice. One has lost its centrings such that a P lattice with the same unit cell remains. The subgroups with this sublattice are listed under Loss of centring translations'. The block with the other two sublattices consists of , C-centring and I-centring. The sequence of the subgroups in this block is determined by the space-group number of the subgroup.

• (d) with A lattice, unique axis c: There are three sublattices of index 2 of a monoclinic A lattice. One has lost its centrings such that a P lattice with the same unit cell remains. The subgroups with this sublattice are listed under Loss of centring translations'. The block with the other two sublattices consists of , A-centring and I-centring. The sequence of the subgroups in this block is determined by the No. of the subgroup.

• (3) Orthorhombic space groups:

 (a) Orthorhombic space groups with P lattice: Same seq­uence as for triclinic space groups. (b) Orthorhombic space groups with C (or A) lattice: Same sequence as for monoclinic space groups with C (or A) lattice. (c) Orthorhombic space groups with I and F lattice: There are no subgroups of index 2 with enlarged unit cell.

• (4) Tetragonal space groups:

• (a) Tetragonal space groups with P lattice:

 (i) . (ii) C-centring. The conventional set­ting results in a P lattice. (iii) F-centring. The conventional setting results in an I lattice.

• (b) Tetragonal space groups with I lattice: There are no subgroups of index 2 with enlarged unit cell.

• (5) For trigonal and hexagonal space groups, holds.

For rhombohedral space groups referred to hexagonal axes, , , or , , holds.

For rhombohedral space groups referred to rhombohedral axes, , , or , , , F-centring holds.

• (6) Only cubic space groups with a P lattice have subgroups of index 2 with enlarged unit cell. For their lattices the following always holds: , , , F-centring.