Reciprocal lattice

Summary

Let $\Lambda$ be a Bravais lattice. Its reciprocal lattice is the set of wave vectors $k$ for which the plane wave $e^{i k \cdot x}$ has every period in $\Lambda$. It is again a lattice, and it is the dual lattice of $\Lambda$ scaled by $2\pi$. Functions with the periodicity of the crystal expand as Fourier series over the reciprocal lattice. In diffraction experiments the sharp peaks occur at points of the reciprocal lattice.