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

International Tables for Crystallography (2006). Vol. A, ch. 3.1, p. 44

Section 3.1.2. Laue class and cell

A. Looijenga-Vosa and M. J. Buergerb§

aLaboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands, and bDepartment of Earth and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA

3.1.2. Laue class and cell

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Space-group determination starts with the assignment of the Laue class to the weighted reciprocal lattice and the determination of the cell geometry. The conventional cell (except for the case of a primitive rhombohedral cell) is chosen such that the basis vectors coincide as much as possible with directions of highest symmetry (cf. Chapters 2.1[link] and 9.1[link] ).

The axial system should be taken right-handed. For the different crystal systems, the symmetry directions (blickrichtungen) are listed in Table 2.2.4.1[link] . The symmetry directions and the convention that, within the above restrictions, the cell should be taken as small as possible determine the axes and their labels uniquely for crystal systems with symmetry higher than orthorhombic. For orthorhombic crystals, three directions are fixed by symmetry, but any of the three may be called a, b or c. For monoclinic crystals, there is one unique direction. It has to be decided whether this direction is called b, c or a. If there are no special reasons (physical properties, relations with other structures) to decide otherwise, the standard choice b is preferred. For triclinic crystals, usually the reduced cell is taken (cf. Chapter 9.2[link] ), but the labelling of the axes remains a matter of choice, as in the orthorhombic system.

If the lattice type turns out to be centred, which reveals itself by systematic absences in the general reflections hkl (Section 2.2.13[link] ), examination should be made to see whether the smallest cell has been selected, within the conventions appropriate to the crystal system. This is necessary since Table 3.1.4.1[link] for space-group determination is based on such a selection of the cell. Note, however, that for rhombohedral space groups two cells are considered, the triple hexagonal cell and the primitive rhombohedral cell.

The Laue class determines the crystal system. This is listed in Table 3.1.2.1[link]. Note the conditions imposed on the lengths and the directions of the cell axes as well as the fact that there are crystal systems to which two Laue classes belong.

Table 3.1.2.1| top | pdf |
Laue classes and crystal systems

Laue classCrystal systemConditions imposed on cell geometry
[\bar{1}] Triclinic None
[2/m] Monoclinic [\alpha = \gamma = 90^{\circ}] (b unique)
[\alpha = \beta = 90^{\circ}] (c unique)
mmm Orthorhombic [\alpha = \beta = \gamma = 90^{\circ}]
[4/m] Tetragonal [a = b; \alpha = \beta = \gamma = 90^{\circ}]
[4/mmm]
[\bar{3}] Trigonal [a = b; \alpha = \beta = 90^{\circ}; \gamma = 120^{\circ}] (hexagonal axes)
[{\bar 3}m] [a = b = c; \alpha = \beta = \gamma] (rhombohedral axes)
[6/m] Hexagonal [a = b; \alpha = \beta = 90^{\circ}; \gamma = 120^{\circ}]
[6/mmm]
[m\bar{3}] Cubic [a = b = c; \alpha = \beta = \gamma = 90^{\circ}]
[m\bar{3}m]








































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