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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–Bravais index for HCP lattice. Crystallographic features of HCP systems, such as vectors and atomic plane families, can be described using a four-value Miller index notation ( hkil) in which the third index i denotes a degenerate but convenient component which is equal to −h − k.
Selection rules for the Miller indices Bravais lattices Example compounds Allowed reflections Forbidden reflections Simple cubic Po Any h, k, ℓ: None Body-centered cubic Fe, W, Ta, Cr h + k + ℓ = even h + k + ℓ = odd Face-centered cubic (FCC) Cu, Al, Ni, NaCl, LiH, PbS h, k, ℓ all odd or all even h, k, ℓ mixed odd and even Diamond FCC ...
Consider the scattering of a beam of wavelength by an assembly of particles or atoms stationary at positions , =, …,.Assume that the scattering is weak, so that the amplitude of the incident beam is constant throughout the sample volume (Born approximation), and absorption, refraction and multiple scattering can be neglected (kinematic diffraction).
In crystallography, a lattice plane of a given Bravais lattice is any plane containing at least three noncollinear Bravais lattice points. Equivalently, a lattice plane is a plane whose intersections with the lattice (or any crystalline structure of that lattice) are periodic (i.e. are described by 2d Bravais lattices). [1]
In order to employ this technique successfully, one must consider the observed point group symmetry of the measured faces and creatively apply the rule that "crystal morphologies are often combinations of simple (i.e. low multiplicity) forms where the individual faces have the lowest possible Miller indices for any given zone axis". This shall ...
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The seven lattice systems and their Bravais lattices in three dimensions. In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (), [1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by