Miller Indexes

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.

References in periodicals archive ?
[17] discovered that nanorods of rutile Ti[O.sub.2] and [alpha]-Mn[O.sub.2] have the same equilibrium geometric morphologies, with a structure consisting mainly of {100} and {110} Miller indexes. Furthermore Hummer et al.
Upon closely analyzing their geometric structure, it is found that all the [alpha]-Mn[O.sub.2] nanorods and microfacets are composed of two Miller indexes, for example, the (110) and (100) microsurfaces.
In deep analysis, the microfacet and nanorod models are also composed of two Miller indexes, for example, (110) and (100) microsurfaces.
Analyzing their geometric morphologies, it is found that they are also composed by two Miller indexes, for example, the (110) and (100) microsurfaces.
Because all the nanorods and microfacets are composed of {100} and {110} Miller indexes, it can be assumed that their electronic structure originates from that of the (100) and (110) bulk surfaces.