Bravais-Miller indices

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 (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

see also

Miller indices
Weber indices