Acoustic Phonon Thermal Conductivity

Material

Debye temperature Θ_D (K): 645 Sound velocity v_s (m/s ×10³): 9.0 Grain size / defect ℓ₀ (nm): 100

Temperature (K): 300

κ at T (W/m·K):–

C_v (J/m³·K):–

ℓ_mfp (nm):–

T/Θ_D:–

Debye model C_v → 3Nk_B (Dulong-Petit) above Θ_D.
Umklapp scattering: ℓ ∝ e^(Θ_D/2T) at low T.
Boundary: ℓ = min(ℓ_umklapp, ℓ_boundary).
κ ∝ T³ at T≪Θ_D, κ ∝ 1/T above.