International
Tables for Crystallography Volume A Spacegroup symmetry Edited by Th. Hahn © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. A, ch. 2.2, pp. 2932
Section 2.2.13. Reflection conditions^{a}Institut für Kristallographie, RheinischWestfälische Technische Hochschule, Aachen, Germany, and ^{b}Laboratorium voor Chemische Fysica, Rijksuniversiteit Groningen, The Netherlands 
The Reflection conditions^{5} are listed in the righthand column of each Wyckoff position.
These conditions are formulated here, in accordance with general practice, as `conditions of occurrence' (structure factor not systematically zero) and not as `extinctions' or `systematic absences' (structure factor zero). Reflection conditions are listed for all those three, two and onedimensional sets of reflections for which extinctions exist; hence, for those nets or rows that are not listed, no reflection conditions apply.
There are two types of systematic reflection conditions for diffraction of crystals by radiation:
These are due to one of three effects:

Reflection conditions of types (ii) and (iii) are listed in Table 2.2.13.2. They can be understood as follows: Zonal and serial reflections form two or onedimensional sections through the origin of reciprocal space. In direct space, they correspond to projections of a crystal structure onto a plane or onto a line. Glide planes or screw axes may reduce the translation periods in these projections (cf. Section 2.2.14) and thus decrease the size of the projected cell. As a consequence, the cells in the corresponding reciprocallattice sections are increased, which means that systematic absences of reflections occur.
^{†}Glide planes d with orientations (100), (010) and (001) occur only in orthorhombic and cubic F space groups. Combination of the integral reflection condition (hkl: all odd or all even) with the zonal conditions for the d glide planes leads to the further conditions given between parentheses.
^{‡}For rhombohedral space groups described with `rhombohedral axes' the three reflection conditions imply interleaving of c and n glides, a and n glides, b and n glides, respectively. In the Hermann–Mauguin spacegroup symbols, c is always used, as in R3c (161) and , because c glides occur also in the hexagonal description of these space groups. ^{§}For tetragonal P space groups, the two reflection conditions (hhl and with ) imply interleaving of c and n glides. In the Hermann–Mauguin spacegroup symbols, c is always used, irrespective of which glide planes contain the origin: cf. P4cc (103), and . ^{¶}For cubic space groups, the three reflection conditions imply interleaving of c and n glides, a and n glides, and b and n glides, respectively. In the Hermann–Mauguin spacegroup symbols, either c or n is used, depending upon which glide plane contains the origin, cf. , , vs , , . 
For the twodimensional groups, the reasoning is analogous. The reflection conditions for the plane groups are assembled in Table 2.2.13.3.

For the interpretation of observed reflections, the general reflection conditions must be studied in the order (i) to (iii), as conditions of type (ii) may be included in those of type (i), while conditions of type (iii) may be included in those of types (i) or (ii). This is shown in the example below.
In the spacegroup tables, the reflection conditions are given according to the following rules:
Note that the integral reflection conditions for a rhombohedral lattice, described with `hexagonal axes', permit the presence of only one member of the pair hkil and for (cf. Table 2.2.13.1). This applies also to the zonal reflections and , which for the rhombohedral space groups must be considered separately.
Example
For a monoclinic crystal (b unique), the following reflection conditions have been observed:
Line (1) states that the cell used for the description of the space group is C centred. In line (2), the conditions 0kl with , h0l with and hk0 with are a consequence of the integral condition (1), leaving only h0l with as a new condition. This indicates a glide plane c. Line (3) presents no new condition, since h00 with and 0k0 with follow from the integral condition (1), whereas 00l with is a consequence of a zonal condition (2). Accordingly, there need not be a twofold screw axis along [010]. Space groups obeying the conditions are Cc (9, b unique, cell choice 1) and (15, b unique, cell choice 1). On the basis of diffraction symmetry and reflection conditions, no choice between the two space groups can be made (cf. Part 3 ).
For a different choice of the basis vectors, the reflection conditions would appear in a different form owing to the transformation of the reflection indices (cf. cell choices 2 and 3 for space groups Cc and in Part 7 ).
These apply either to the integral reflections hkl or to particular sets of zonal or serial reflections. In the spacegroup tables, the minimal special conditions are listed that, on combination with the general conditions, are sufficient to generate the complete set of conditions. This will be apparent from the examples below.
Examples

For the cases where the special reflection conditions are described by means of combinations of `OR' and `AND' instructions, the `AND' condition always has to be evaluated with priority, as shown by the following example.
Example: (218)
Special position or , and .
This expression contains the following two conditions:
(a) ;
(b) and and .
A reflection is `present' (occurring) if either condition (a) is satisfied or if a permutation of the three conditions in (b) are simultaneously fulfilled.
Note that in addition nonspacegroup absences may occur that are not due to the symmetry of the space group (i.e. centred cells, glide planes or screw axes). Atoms in general or special positions may cause additional systematic absences if their coordinates assume special values [e.g. `noncharacteristic orbits' (Engel et al., 1984)]. Nonspacegroup absences may also occur for special arrangements of atoms (`false symmetry') in a crystal structure (cf. Templeton, 1956; Sadanaga et al., 1978). Nonspacegroup absences may occur also for polytypic structures; this is briefly discussed by Durovič in Section 9.2.2.2.5 of International Tables for Crystallography (2004), Vol. C. Even though all these `structural absences' are fortuitous and due to the special arrangements of atoms in a particular crystal structure, they have the appearance of spacegroup absences. Occurrence of structural absences thus may lead to an incorrect assignment of the space group. Accordingly, the reflection conditions in the spacegroup tables must be considered as a minimal set of conditions.
The use of reflection conditions and of the symmetry of reflection intensities for spacegroup determination is described in Part 3 .
References
International Tables for Crystallography (2004). Vol. C, 3rd ed., edited by E. Prince. Dordrecht: Kluwer Academic Publishers.International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Revised editions: 1965, 1969 and 1977. Abbreviated as IT (1952).]
Engel, P., Matsumoto, T., Steinmann, G. & Wondratschek, H. (1984). The noncharacteristic orbits of the space groups. Z. Kristallogr., Supplement Issue No. 1.
Sadanaga, R., Takeuchi, Y. & Morimoto, N. (1978). Complex structures of minerals. Recent Prog. Nat. Sci. Jpn, 3, 141–206, esp. pp. 149–151.
Templeton, D. H. (1956). Systematic absences corresponding to false symmetry. Acta Cryst. 9, 199–200.