what do you mean by miller indices
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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 reciprocal 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.
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 reciprocal 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.
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