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Concept# Reciprocal lattice

Summary

In physics, the reciprocal lattice represents the Fourier transform of another lattice. The direct lattice or real lattice is a periodic function in physical space, such as a crystal system (usually a Bravais lattice). The reciprocal lattice exists in the mathematical space of spatial frequencies, known as reciprocal space or k space, where \mathbf{k} refers to the wavevector.
In quantum physics, reciprocal space is closely related to momentum space according to the proportionality \mathbf{p} = \hbar \mathbf{k}, where \mathbf{p} is the momentum vector and \hbar is the reduced Planck constant. The reciprocal lattice of a reciprocal lattice is equivalent to the original direct lattice, because the defining equations are symmetrical with respect to the vectors in real and reciprocal space. Mathematically, direct and reciprocal lattice vectors represent covariant and contravariant vectors, respectively.
The reciprocal lattice is the

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