Difference between revisions of "Reflection conditions"
From Online Dictionary of Crystallography
BrianMcMahon (talk | contribs) m |
BrianMcMahon (talk | contribs) m (Style edits to align with printed edition) |
||
| Line 58: | Line 58: | ||
<table border cellspacing=0 cellpadding=5 align=center> | <table border cellspacing=0 cellpadding=5 align=center> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>Type of reflection</th><th>Reflection condition</th> <th>Glide vector</th><th>Glide plane</th> </tr> |
<tr> <td rowspan=4>0''kl''</td> <td>''k'' = 2 ''n''</td> <td>'''b'''/2</td><td> ''b''</td></tr> | <tr> <td rowspan=4>0''kl''</td> <td>''k'' = 2 ''n''</td> <td>'''b'''/2</td><td> ''b''</td></tr> | ||
<tr> | <tr> | ||
| Line 68: | Line 68: | ||
</table> | </table> | ||
| − | The zonal reflection conditions are listed in Table 2. | + | The zonal reflection conditions are listed in Table 2.1.3.7 of ''International Tables for Crystallography, Volume A'', 6th edition. |
| − | *''Screw axes'' | + | |
| + | *''Screw axes'' | ||
The resulting conditions apply only to one-dimensional sets of reflections, ''i.e.'' reciprocal-lattice rows containing the origin (such as ''h''00, 0''k''0, 00''l''). They are called ''[[serial reflection conditions]]''. For instance, for a screw axis parallel to [001], the reflection conditions are: | The resulting conditions apply only to one-dimensional sets of reflections, ''i.e.'' reciprocal-lattice rows containing the origin (such as ''h''00, 0''k''0, 00''l''). They are called ''[[serial reflection conditions]]''. For instance, for a screw axis parallel to [001], the reflection conditions are: | ||
<table border cellspacing=0 cellpadding=5 align=center> | <table border cellspacing=0 cellpadding=5 align=center> | ||
<tr> | <tr> | ||
| − | <th> | + | <th>Type of reflection</th><th>Reflection condition</th> <th>Screw vector</th><th>Screw axis</th> </tr> |
<tr> <td rowspan=2>00''l''</td> <td>''l'' = 2 ''n''</td> <td>'''c'''/2</td><td> 2<sub>1</sub>; 4<sub>2</sub></td></tr> | <tr> <td rowspan=2>00''l''</td> <td>''l'' = 2 ''n''</td> <td>'''c'''/2</td><td> 2<sub>1</sub>; 4<sub>2</sub></td></tr> | ||
<tr> | <tr> | ||
| Line 85: | Line 86: | ||
</table> | </table> | ||
| − | The serial reflection conditions are listed in Table 2. | + | The serial reflection conditions are listed in Table 2.1.3.7 of ''International Tables for Crystallography, Volume A'', 6th edition. |
(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. | (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. | ||
| Line 91: | Line 92: | ||
==See also == | ==See also == | ||
| − | Section 1.6.4 of ''International Tables | + | Section 1.6.4 of ''International Tables for Crystallography, Volume A'', 6th edition |
[[Category:X-rays]]<br> | [[Category:X-rays]]<br> | ||
Revision as of 16:22, 16 May 2017
Conditions de réflexion (Fr). Condizioni di diffrazione (It). 消滅則 (Ja).
Definition
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
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.
| Reflection condition |
Centring type of cell | Centring symbol |
|---|---|---|
| None | Primitive | P R (rhombohedral axes) |
| h + k = 2n | C-face centred | C |
| k + l = 2n | A-face centred | A |
| l + h = 2n | B-face centred | B |
| h + k + l = 2n | body centred | I |
| h + k, h + l and k + l = 2n or: | all-face centred | F |
| − h + k + l = 3n | rhombohedrally centred, obverse |
R (hexagonal axes) |
| h − k + l = 3n | rhombohedrally centred, reverse | |
| h − k = 3n | hexagonally centred | H |
- 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 2.1.3.7 of International Tables for Crystallography, Volume A, 6th edition.
- 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 [001], 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 2.1.3.7 of International Tables for Crystallography, Volume A, 6th edition.
(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 1.6.4 of International Tables for Crystallography, Volume A, 6th edition