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Difference between revisions of "Bravais-Miller indices"

From Online Dictionary of Crystallography

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== 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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In case of hexagonal or rhombohedral lattices, 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  
  
 
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Revision as of 14:09, 12 June 2016

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

Definition

In case of hexagonal or rhombohedral lattices, 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

Miller indices
Weber indices