Elastic Waves & Phonon Dispersion

Parameters

1D diatomic chain: Two atoms per unit cell with masses m₁ and m₂.

Dispersion: ω²= K(m₁+m₂)/(m₁m₂) ± K√[(m₁+m₂)²−4m₁m₂sin²(ka/2)]/(m₁m₂)

Acoustic branch (−): atoms move in phase. Optical branch (+): atoms out of phase. Gap opens when m₁≠m₂.