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Difference between revisions of "Integral reflection conditions"

From Online Dictionary of Crystallography

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<caption align=top> '''Integral reflection conditions for centred lattices.''' </caption>
 
<caption align=top> '''Integral reflection conditions for centred lattices.''' </caption>
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<th> Reflection<br> condition </th>
 
<th> Reflection<br> condition </th>
 
<th> Centring type of cell </th>
 
<th> Centring type of cell </th>
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<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>
 
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<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>
 
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<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>
 
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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>
 
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<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td>
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<td> ''h'' &minus; ''k'' = 3''n''</td> <td>hexagonally centred</td> <td> ''H''</td></tr>
 
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Section 2.2.13.1 of ''International Tables of Crystallography, Volume A''
 
Section 2.2.13.1 of ''International Tables of Crystallography, Volume A''
  
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[[Category:X-rays]]<br>
 
[[Category:X-rays]]<br>

Revision as of 14:12, 6 February 2012

Conditions de réflexion intégrales (Fr).

Definition

The integral reflections are the general reflection conditions due to the centring of cells. 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, reverse

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

centred, obverse

setting (standard)
hk = 3n hexagonally centred H

See also

Section 2.2.13.1 of International Tables of Crystallography, Volume A