Dispersion relation for a 1D diatomic lattice
A 1D diatomic chain has alternating masses M₁ and M₂ coupled by spring constant k. The dispersion relation has two branches:
The band gap opens at the Brillouin zone boundary q=π/a:
In the acoustic branch, M₁ and M₂ move in phase. In the optical branch, they move out of phase — this couples to light in ionic crystals.