Integral reflection conditions

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(Definition)
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<table border cellspacing=0 cellpadding=5 align=center>
<table border cellspacing=0 cellpadding=5 align=center>
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<caption align=top> '''Integral reflection conditions for centred lattices.''' </caption>
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<caption align=top> '''Integral reflection conditions for centred lattices.''' </caption>
  <tr align=left>
  <tr align=left>
<th> Reflection<br> condition </th>
<th> Reflection<br> condition </th>
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<td> &minus; ''h'' + ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
<td> &minus; ''h'' + ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
centred, reverse<br>
centred, reverse<br>
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setting </td><td rowspan=2>''R'' (hexagonal axes)</td>></tr>
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setting </td><td rowspan=2>''R'' (hexagonal axes)</td></tr>
<tr align=left>
<tr align=left>
<td> ''h'' &minus; ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
<td> ''h'' &minus; ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
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</tr>
</tr>
<tr align=left>
<tr align=left>
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<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonnally centred</td> <td> ''H''</td>
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<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td>
</table>
</table>

Revision as of 11:32, 29 March 2008

Definition

The integral reflections are the general reflection conditions due to the centring of cells. They are given in the table below:

<tr align=left> <td>k + l = 2n</td> <td>A-face centred</td> <td>A</th> </tr> <tr align=left> <td>l + h = 2n</td> <td>B-face centred</td> <td>B</td> </tr> <tr align=left> <td>h + k + l = 2n</td> <td>body centred</td> <td>I</th> </tr> <tr align=left> <td>h + k, h + l and
k + l = 2n or:
h, k, l all odd or all
even (‘unmixed’)</td> <td>all-face centred</td> <td> F</th> </tr> <tr align=left> <td> − h + k + l = 3n</td> <td> rhombohedrally
centred, reverse
setting </td><td rowspan=2>R (hexagonal axes)</td></tr> <tr align=left> <td> hk + l = 3n</td> <td> rhombohedrally
centred, obverse
setting (standard)</td> </tr> <tr align=left> <td> hk = 3n</td> <td>hexagonally centred</td> <td> H</td> </table>
Integral reflection conditions for centred lattices.
Reflection
condition
Centring type of cell Centring symbol
None Primitive P
R (rhombohedral axes)
h + k = 2n C-face centred C</th>