# Integral reflection conditions

(Difference between revisions)
 Revision as of 07:13, 5 May 2006 (view source)← Older edit Revision as of 11:32, 29 March 2008 (view source) (→Definition)Newer edit → Line 4: Line 4: - '''Integral reflection conditions for centred lattices.''' + '''Integral reflection conditions for centred lattices.'''
Reflection
condition
Reflection
condition
− ''h'' + ''k'' + ''l'' = 3''n'' rhombohedrally
− ''h'' + ''k'' + ''l'' = 3''n'' rhombohedrally
centred, reverse
centred, reverse
- setting
''R'' (hexagonal axes)
''R'' (hexagonal axes)
''h'' − ''k'' + ''l'' = 3''n'' rhombohedrally
''h'' − ''k'' + ''l'' = 3''n'' rhombohedrally
Line 42: Line 42:
''h'' − ''k'' = 3''n'' hexagonnally centred ''H'' ''h'' − ''k'' = 3''n'' hexagonally centred ''H''
Line 35: Line 35: > + setting - +

## 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>