Phonon Dispersion — 1D Chain

Chain Parameters

Chain type: Mass ratio m₂/m₁: 2.0 Spring constant K₁: 1.0 Spring constant K₂: 0.4 Selected k (×π/a): 0.5

Selected k-point

k (π/a)—

ω_acoustic—

ω_optical—

v_group (acoustic)—

v_phase (acoustic)—

Diatomic chain has two phonon branches: the acoustic branch (ω→0 as k→0, both atoms move together) and optical branch (atoms move out of phase, couples to light). The gap at the zone boundary (k=π/a) is 2√(K/m₁) - 2√(K/m₂). Van Hove singularities occur where dω/dk=0 (zone boundary) — divergences in the density of states.