View source for Bravais-Miller indices

<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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== 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 ('''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. 
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>
''h'' + ''k'' + ''i'' = 0
</center>

[[Image:MILLER-3.gif|center]]

== see also ==

[[Miller indices]]<br>
[[Weber indices]]

[[Category:Fundamental crystallography]]<br>
[[Category:Morphological crystallography]]