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Miller–Bravais indices. With hexagonal and rhombohedral lattice systems, it is possible to use the Bravais–Miller system, which uses four indices (h k i ℓ) that obey the constraint h + k + i = 0. Here h, k and ℓ are identical to the corresponding Miller indices, and i is a redundant index.
Miller indices of a plane (hkl) and a direction [hkl].The intercepts on the axes are at a/ h, b/ k and c/ l. The International Union of Crystallography (IUCr) gives the following definition: "The law of rational indices states that the intercepts, OP, OQ, OR, of the natural faces of a crystal form with the unit-cell axes a, b, c are inversely proportional to prime integers, h, k, l.
Miller projection with 1,000 km indicatrices of distortion. The Miller cylindrical projection is a modified Mercator projection , proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4 ⁄ 5 , projected according to Mercator, and then the result is multiplied by 5 ⁄ 4 to retain scale along the equator. [ 1 ]
If, on the other hand, the Miller indices are not relative prime, the family of planes defined by them is not a family of lattice planes, because not every plane of the family then intersects lattice points. [2] Conversely, planes that are not lattice planes have aperiodic intersections with the lattice called quasicrystals; this is known as a ...
In a haxagonal system hkl miller indices are enough to define a plane or a direction, however, You will prefer to use four hkil indices, because this way equivalent planes/directions will have similar indices. E.g. the unit cell defines 3 lattice unit vectors a, b, and c. Between a and b there is a 120° angle.
Download QR code; In other projects Appearance. move to sidebar hide ... Example of crystallographic planes and Miller indices for a cubic structure: Date: 30 ...
Download QR code; In other projects Appearance. ... English: Definition of the Miller indices of a plane. Français : Définition des indices de Miller d'un plan.
The attitude of a lattice plane is the orientation of the line normal to the plane, [12] and is described by the plane's Miller indices. In three-space a family of planes (a series of parallel planes) can be denoted by its Miller indices (hkl), [13] [14] so the family of planes has an attitude common to all its constituent planes.