Question

Explain weiss indices and Miller indices, why crystallographic planes are represented by Miller indices
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Answer 1

Answer:

Miller indices form a notation system in crystallography for planes in crystal (Bravais) lattices.

In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices. They are written (hkℓ), and denote the family of planes orthogonal to {\displaystyle h\mathbf {b_{1}} +k\mathbf {b_{2}} +\ell \mathbf {b_{3}} }h{\mathbf  {b_{1}}}+k{\mathbf  {b_{2}}}+\ell {\mathbf  {b_{3}}}, where {\displaystyle \mathbf {b_{i}} }{\mathbf  {b_{i}}} are the basis of the reciprocal lattice vectors (note that the plane is not always orthogonal to the linear combination of direct lattice vectors {\displaystyle h\mathbf {a_{1}} +k\mathbf {a_{2}} +\ell \mathbf {a_{3}} }h{\mathbf  {a_{1}}}+k{\mathbf  {a_{2}}}+\ell {\mathbf  {a_{3}}} because the lattice vectors need not be mutually orthogonal). By convention, negative integers are written with a bar, as in 3 for −3. The integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller indices are also used to designate reflections in X-ray crystallography. In this case the integers are not necessarily in lowest terms, and can be thought of as corresponding to planes spaced such that the reflections from adjacent planes would have a phase difference of exactly one wavelength (2π), regardless of whether there are atoms on all these planes or not.

Explanation: