Integral reflection conditions

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> h − k + l = 3n</td> <td> rhombohedrally
centred, obverse
setting (standard)</td> </tr> <tr align=left> <td> h − k = 3n</td> <td>hexagonally centred</td> <td> H</td> </table>

See also

Section 2.2.13.1 of International Tables of Crystallography, Volume A

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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>