Elastic Waves & Phonon Dispersion
Parameters
Spring constant (K):
1.00
Mass ratio (m₂/m₁):
1.00
Lattice spacing (a):
1.00
Excitation wavenumber:
0.50
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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.