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Difference between revisions of "Bravais-Miller indices"

From Online Dictionary of Crystallography

(see also: Weber indices)
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<font color="blue">Indices de Bravais-Miller</font>(''Fr''). <font color="green">Indices de Bravais-Miller</font> (''Sp''). <font color="black"> Indici di Bravais-Miller </font>(''It''). <Font color="purple"> ブラベー・ミラー指数</font> (''Ja'')
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<font color="blue">Indices de Bravais-Miller</font> (''Fr''). <font color="black">Indici di Bravais-Miller</font> (''It''). <font color="purple">ブラベー・ミラー指数</font> (''Ja''). <font color="green">Indices de Bravais-Miller</font> (''Sp'').
  
 
<Font color="black">  
 
<Font color="black">  
 
== Definition ==
 
== Definition ==
  
The Bravais-Miller indices are used in the case of hexagonal lattices. In that case, one uses four axes, '''a<sub>1</sub>''', '''a<sub>2</sub>''', '''a<sub>3</sub>''', '''c''' and four [[Miller indices]], (''hkil''), where ''h'', ''k'', ''i'', ''l'' are prime integers inversely proportional to the intercepts ''OP'', ''OQ'', ''OS'', ''OR'' of a plane of the family with the four axes. The indices ''h'', ''k'', ''i'' are cyclically permutable and related by  
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For trigonal and hexagonal crystals, it is useful to use a reference built on four axes, three in the plane normal to the unique axis ('''a<sub>1</sub>''', '''a<sub>2</sub>''', '''a<sub>3</sub>''') and one ( '''c''') for the unique axis. Consequently, four indices of lattice planes (''hkil'') are used, called  the '''Bravais-Miller indices'''. Here ''h'', ''k'', ''i'', ''l'' are integers inversely proportional to the intercepts of a plane of the family with the four axes.
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Only two of the three axes in a plane are linearly independent:  '''a<sub>3</sub>''' is expressed as '''a<sub>3</sub>''' = -'''a<sub>1</sub>'''-'''a<sub>2</sub>'''. Analogously, the indices ''h'', ''k'', ''i'' are cyclically permutable and related by  
  
 
<center>
 
<center>
''h'' + ''k'' + ''i'' = 0
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''h'' + ''k'' + ''i'' = 0.
 
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== see also ==
 
== see also ==
  
[[Miller indices]]
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*[[Miller indices]]
[[Weber indices]]
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*[[Weber indices]]
  
 
[[Category:Fundamental crystallography]]<br>
 
[[Category:Fundamental crystallography]]<br>
 
[[Category:Morphological crystallography]]
 
[[Category:Morphological crystallography]]

Latest revision as of 16:46, 9 November 2017

Indices de Bravais-Miller (Fr). Indici di Bravais-Miller (It). ブラベー・ミラー指数 (Ja). Indices de Bravais-Miller (Sp).

Definition

For trigonal and hexagonal crystals, it is useful to use a reference built on four axes, three in the plane normal to the unique axis (a1, a2, a3) and one ( c) for the unique axis. Consequently, four indices of lattice planes (hkil) are used, called the Bravais-Miller indices. Here h, k, i, l are integers inversely proportional to the intercepts of a plane of the family with the four axes. Only two of the three axes in a plane are linearly independent: a3 is expressed as a3 = -a1-a2. Analogously, the indices h, k, i are cyclically permutable and related by

h + k + i = 0.

MILLER-3.gif

see also