Phonon Dispersion — Crystal Lattice
Acoustic & optical branches, group velocity, van Hove singularities
Lattice
1D Diatomic
2D Square
Mass ratio M₂/M₁:
2.0
Spring κ₁:
1.0
Probe k (×π/a):
0.5
Equations
ω²(k) = κ/μ ± κ√(1/μ² - 4sin²(ka)/M₁M₂)
Acoustic: ω→ vₛk (k→0)
Optical gap: ω₀=√(2κ/μ)
v_group = dω/dk
At probe k