Difference between revisions of "Integral reflection conditions"
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| + | <font color="blue">Conditions de réflexion intégrales</font> (''Fr''). <font color="red">Integrale Auslöschungen</font> (''Ge''). <font color="green">Ausencias integrales</font> (''Sp''). | ||
| + | |||
== Definition == | == Definition == | ||
| − | The integral reflections are the general [[reflection conditions]] | + | The integral reflections are the general [[reflection conditions]] appearing when a [[centred lattices|multiple (non-primitive) cell]] is used to describe the [[Bravais lattice]] of a crystal. They are given in the table below: |
<table border cellspacing=0 cellpadding=5 align=center> | <table border cellspacing=0 cellpadding=5 align=center> | ||
| − | + | <caption align=top> '''Integral reflection conditions for centred lattices.''' </caption> | |
| − | + | <tr align=left> | |
| − | <th> Reflection<br> condition </th> | + | <th>Reflection<br> condition </th> |
| − | <th> Centring type of cell </th> | + | <th>Centring type of cell </th> |
<th>Centring symbol</th> | <th>Centring symbol</th> | ||
</tr> | </tr> | ||
| Line 15: | Line 17: | ||
</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
| − | <td>''h'' + ''k'' = 2''n''</td> <td>''C''-face centred</td> <td>''C''</ | + | <td>''h'' + ''k'' = 2''n''</td> <td>''C''-face centred</td> <td>''C''</td> |
</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
| − | <td>''k'' + ''l'' = 2''n''</td> <td>''A''-face centred</td> <td>''A''</ | + | <td>''k'' + ''l'' = 2''n''</td> <td>''A''-face centred</td> <td>''A''</td> |
</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
| Line 24: | Line 26: | ||
</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
| − | <td>''h'' + ''k'' + ''l'' = 2''n''</td> <td>body centred</td> <td>''I''</ | + | <td>''h'' + ''k'' + ''l'' = 2''n''</td> <td>body centred</td> <td>''I''</td> |
</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
| Line 30: | Line 32: | ||
''k'' + ''l'' = 2''n'' or:<br> | ''k'' + ''l'' = 2''n'' or:<br> | ||
''h'', ''k'', ''l'' all odd or all<br> | ''h'', ''k'', ''l'' all odd or all<br> | ||
| − | even (‘unmixed’)</td> <td>all-face centred</td> <td> ''F''</ | + | even (‘unmixed’)</td> <td>all-face centred</td> <td> ''F''</td> |
</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
<td> − ''h'' + ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br> | <td> − ''h'' + ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br> | ||
| + | centred, obverse<br> | ||
| + | setting (standard)</td> | ||
| + | <td rowspan=2>''R'' (hexagonal axes)</td></tr> | ||
| + | <tr align=left> | ||
| + | <td> ''h'' − ''k'' + ''l'' = 3''n''</td><td> rhombohedrally<br> | ||
centred, reverse<br> | centred, reverse<br> | ||
| − | setting </td | + | setting </td></tr> |
<tr align=left> | <tr align=left> | ||
| − | <td> ''h'' − ''k | + | <td> ''h'' − ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td></tr> |
| − | |||
| − | |||
| − | </tr> | ||
<tr align=left> | <tr align=left> | ||
| − | <td> ''h'' | + | <td> ''h'' + ''k'' + ''l'' = 3''n''</td> <td>D centred</td> <td> ''D''</td></tr> |
</table> | </table> | ||
| + | |||
| + | ==See also == | ||
| + | *Chapter 2.1.3.13 of ''International Tables for Crystallography, Volume A'', 6th edition | ||
| + | |||
| + | [[Category:X-rays]]<br> | ||
Latest revision as of 12:59, 27 August 2018
Conditions de réflexion intégrales (Fr). Integrale Auslöschungen (Ge). Ausencias integrales (Sp).
Definition
The integral reflections are the general reflection conditions appearing when a multiple (non-primitive) cell is used to describe the Bravais lattice of a crystal. They are given in the table below:
| 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 |
| h + k + l = 3n | D centred | D |
See also
- Chapter 2.1.3.13 of International Tables for Crystallography, Volume A, 6th edition