Difference between revisions of "Reflection conditions"
From Online Dictionary of Crystallography
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==See also ==
==See also ==
Section ..of ''International Tables of Crystallography, Volume A''
Revision as of 16:35, 10 April 2017
Conditions de réflexion (Fr). Condizioni di diffrazione (It). 消滅則 (Ja).
The reflection conditions describe the conditions of occurrence 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:
- Centred cells.
- Glide planes.
The resulting conditions apply only to two-dimensional 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. For instance, for a glide plane parallel to (001):
|type of reflection||reflection condition||glide vector||glide plane|
|0kl||k = 2 n||b/2||b|
|l = 2 n||c/2||c|
|k + l = 2 n||b/2 + c/2||n|
|k + l = 4 n|
k, l = 2n
|b/4 ± c/4||d|
The zonal reflection conditions are listed in Table 22.214.171.124 of International Tables of Crystallography, Volume A.
- Screw axes.
The resulting conditions apply only to one-dimensional sets of reflections, i.e. reciprocal-lattice rows containing the origin (such as h00, 0k0, 00l). They are called serial reflection conditions. For instance, for a screw axis parallel to , the reflection conditions are:
|type of reflection||reflection condition||screw vector||screw axis|
|00l||l = 2 n||c/2||21; 42|
|l = 4 n||c/4||41; 43|
|000l||l = 2 n||c/2||63|
|l = 3 n||c/3||41; 31; 32; 62; 64|
|l = 6 n||c/6||61;65|
The serial reflection conditions are listed in Table 126.96.36.199 of International Tables of Crystallography, Volume A.
(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.
Section 1.6.4 of International Tables of Crystallography, Volume A, 6th edition