# Bravais-Miller indices

### From Online Dictionary of Crystallography

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

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 _{1}**,

**a**,

_{2}**a**) and one (

_{3}**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**is expressed as

_{3}**a**= -

_{3}**a**-

_{1}**a**. Analogously, the indices

_{2}*h*,

*k*,

*i*are cyclically permutable and related by

*h* + *k* + *i* = 0.