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Planes with different Miller indices in cubic crystals ... plane has a 3-fold symmetry: it remains unchanged by a rotation of 1/3 (2 π /3 rad, 120°). The ...
If OA is divided into h parts, OB into k parts, and OC into l parts, the planes (a 1 b 1 c 1, a 2 b 2 c 2, etc.) are identified by the Miller indices (hkl). The diagram shows plane (243). [1] The law of rational indices is an empirical law in the field of crystallography concerning crystal structure. The law states that "when referred to three ...
The orientation of a plane with respect to the unit cell is most conveniently expressed in terms of Miller indices. For example, the set of Miller indices (110) describes the set of parallel planes (family of lattice planes) parallel to the z-axis and cutting the x- and the y-axis once, such that every unit cell is bisected by precisely one of ...
The Miller indices for a plane are integers with no common factors. Negative indices are indicated with horizontal bars, as in (1 2 3). In an orthogonal coordinate system for a cubic cell, the Miller indices of a plane are the Cartesian components of a vector normal to the plane. Considering only (hkℓ) planes intersecting one or more lattice ...
Miller index {h k ℓ} Cleavage forms parallel to crystallographic planes: [1] Basal, pinacoidal, or planar cleavage occurs when there is only one cleavage plane. Talc has basal cleavage. Mica (like muscovite or biotite) also has basal cleavage; this is why mica can be peeled into thin sheets.
If only two planes of atoms were diffracting, as shown in the Figure then the transition from constructive to destructive interference would be gradual as a function of angle, with gentle maxima at the Bragg angles. However, since many atomic planes are participating in most real materials, sharp peaks are typical. [5] [13]
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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 ...