Miller Indexes

(or crystallographic indexes), whole numbers that characterize the arrangement of crystal faces and their corresponding atomic planes within the crystal. Miller indexes are related to the length of the segments cut off by a plane across the three axes of the crystallographic system of coordinates. The lengths of segments cut off by any atomic plane of the crystal across the coordinate axes, which are expressed in lattice constants a, b, and c, are always whole numbers, p₁, p₂, and p₃. Reduction of the reciprocals of these numbers to a common denominator and removal of the denominator gives three whole numbers, h = p₂p₃, k = p₁p₃, and l = p₁p₂, which are the Miller indexes and are given within parentheses: (hkl). Negative Miller indexes indicate planes that intersect with negative directions of the coordinate axes. Miller indexes of a set of planes that are symmetrically equivalent to one another are given in braces: {hkl}

In addition to crystallography, Miller indexes are also used in X-ray diffraction analysis and electron and neutron diffraction analysis to denote the beams scattered by the corresponding atomic planes of the crystal.