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Difference between revisions of "Integral reflection conditions"

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<font color="blue">Conditions de réflexion intégrales</font> (''Fr''). <font color="red">Integrale Auslöschungen</font> (''Ge''). <font color="green">Ausencias integrales</font> (''Sp'').
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== Definition ==
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The integral reflections are the general [[reflection conditions]] appearing when a [[centred lattices|multiple (non-primitive) cell]] is used to describe the [[Bravais lattice]] of a crystal. They are given in the table below:
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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>
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<caption align=top> '''Integral reflection conditions for centred lattices.''' </caption>
<tr align=left>
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<tr align=left>
<th> Reflection<br> condition </th>
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<th>Reflection<br> condition </th>
<th> Centring type of cell </th>
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<th>Centring type of cell </th>
 
<th>Centring symbol</th>
 
<th>Centring symbol</th>
 
</tr>
 
</tr>
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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''</th>
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<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''</th>
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<td>''k'' + ''l'' = 2''n''</td> <td>''A''-face centred</td> <td>''A''</td>
 
</tr>
 
</tr>
 
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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''</th>
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<td>''h'' + ''k'' + ''l'' = 2''n''</td> <td>body centred</td> <td>''I''</td>
 
</tr>
 
</tr>
 
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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''</th>
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even (‘unmixed’)</td> <td>all-face centred</td> <td> ''F''</td>
 
</tr>
 
</tr>
 
<tr align=left>
 
<tr align=left>
 
<td> &minus; ''h'' + ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
 
<td> &minus; ''h'' + ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
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centred, obverse<br>
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setting (standard)</td>
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<td rowspan=2>''R'' (hexagonal axes)</td></tr>
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<tr align=left>
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<td> ''h'' &minus; ''k'' + ''l'' = 3''n''</td><td> rhombohedrally<br>
 
centred, reverse<br>
 
centred, reverse<br>
setting </td><td rowspan=2>''R'' (hexagonal axes)</td>></tr>
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setting </td></tr>
 
<tr align=left>
 
<tr align=left>
<td> ''h'' &minus; ''k'' + ''l'' = 3''n''</td> <td> rhombohedrally<br>
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<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td></tr>
centred, obverse<br>
 
setting (standard)</td>
 
</tr>
 
 
<tr align=left>
 
<tr align=left>
<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonnally centred</td> <td> ''H''</td>
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<td> ''h'' + ''k'' + ''l'' = 3''n''</td> <td>D centred</td> <td> ''D''</td></tr>
 
</table>
 
</table>
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==See also ==
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*Chapter 2.1.3.13 of ''International Tables for Crystallography, Volume A'', 6th edition
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[[Category:X-rays]]<br>

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