How momentum-flipping phonon collisions limit heat transport
Normal (N) process: k₁ + k₂ = k₃ — conserves momentum, no thermal resistance.
Umklapp (U) process: k₁ + k₂ = k₃ + G — reciprocal lattice vector G flips net momentum, creating thermal resistance.
Peierls (1929): κ ∝ τ/T. At high T:
τ_U ∝ e^(Θ_D/αT) → κ ∝ 1/T.
Callaway model: three-phonon scattering rate scales as T² exp(−Θ_D/2T) near and above the Debye temperature. Below T ≈ Θ_D/10: boundary scattering dominates (κ ∝ T³ from Bose-Einstein occupancy).
Diamond has κ ≈ 2200 W/m·K; lead ≈ 35 — Umklapp and mass disorder set the scale.