Difference between revisions of "Integral reflection conditions"
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<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> | <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> | ||
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</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> | ||
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</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> | ||
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''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> | ||
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</tr> | </tr> | ||
<tr align=left> | <tr align=left> | ||
| − | <td> ''h'' − ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td> | + | <td> ''h'' − ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td></tr> |
</table> | </table> | ||
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Section 2.2.13.1 of ''International Tables of Crystallography, Volume A'' | Section 2.2.13.1 of ''International Tables of Crystallography, Volume A'' | ||
| − | |||
[[Category:X-rays]]<br> | [[Category:X-rays]]<br> | ||
Revision as of 14:12, 6 February 2012
Conditions de réflexion intégrales (Fr).
Definition
The integral reflections are the general reflection conditions due to the centring of cells. 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, reverse | R (hexagonal axes) |
| h − k + l = 3n | rhombohedrally centred, obverse |
|
| h − k = 3n | hexagonally centred | H |
See also
Section 2.2.13.1 of International Tables of Crystallography, Volume A