Miller index

Notation system for crystal lattice planes

Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and l, the Miller indices. They are written (hkl), and denote the family of (parallel) lattice planes (of the given Bravais lattice) orthogonal to g h k ℓ = h b 1 + k b 2 + ℓ b 3 , {\displaystyle \mathbf {g} _{hk\ell }=h\mathbf {b} _{1}+k\mathbf {b} _{2}+\ell \mathbf {b} _{3},} where bi are the basis or primitive translation vectors of the reciprocal lattice for the given Bravais lattice.

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