Reflection conditions

Conditions de réflexion (Fr).

Definition

The reflection conditions describe the conditions of occurence of a reflection (structure factor not systematically zero). There are two types of systematic reflection conditions for diffraction of crystals by radiation:

(1) General conditions. They apply to all Wyckoff positions of a space group, i.e. they are always obeyed, irrespective of which Wyckoff positions are occupied by atoms in a particular crystal structure. They are due to one of three effects:

(i) Centred cells. 

The resulting conditions apply to the whole three-dimensional set of reflections hkl. Accordingly, they are called integral reflection conditions. They are given in Table 1.

(ii)Glide planes.

The resulting conditions apply only to twodimensional sets of reflections, i.e. to reciprocal-lattice nets containing the origin (such as hk0, h0l, 0kl, hhl). For this reason, they are called zonal reflection conditions. They are listed in Table 2.

(iii) Screw axes. 

The resulting conditions apply only to onedimensional sets of reflections, i.e. reciprocal-lattice rows containing the origin (such as h00, 0k0, 00l). They are called serial reflection conditions. They are listed in Table 2.

(2) Special conditions (‘extra’ conditions). They apply only to special Wyckoff positions and occur always in addition to the general conditions of the space group.

See also

Section 2.2.13 of International tables of Crystallography, Volume A

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Integral reflection conditions for centred lattices.

Reflection condition	Centring type of cell	Centring symbol
None	Primitive	P R* (rhombohedral axes)