 Reciprocal lattice vector

A reciprocal lattice vector $\mathbf{G}$ has the displayed property for every direct lattice vector $\mathbf{R}$. Thus $e^{i\mathbf{G}\cdot \mathbf{R}}=1$. Fourier components of a lattice-periodic potential carry these wavevectors and couple plane-wave electronic states whose momenta differ by $\hslash \mathbf{G}$. This is the origin of the Bragg-plane mixing in a nearly-free electron model.