Integral reflection conditions

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(Definition: D centred cell)
 
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<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td></tr>
<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td></tr>
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<td> ''h'' + ''k'' + ''l'' = 3''n''</td> <td>D centred</td> <td> ''D''</td></tr>
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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:

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
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:
h, k, l all odd or all

even (‘unmixed’)
all-face centred F
h + k + l = 3n rhombohedrally

centred, obverse

setting (standard)
R (hexagonal axes)
hk + l = 3n rhombohedrally

centred, reverse

setting
hk = 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