Dispersion Physics
Monatomic:
ω(k) = 2√(κ/m)|sin(ka/2)|
Linear near k=0 (acoustic)
Zone boundary: k = ±π/a
Diatomic (2 atoms/cell):
Two branches per polarization:
• Acoustic: atoms move together
• Optical: atoms move opposite
Gap at zone boundary:
Δω = 2|κ₁-κ₂|/√(Mm)
Phonons carry heat. Dispersion determines group velocity vg = dω/dk and thermal properties.