Phonon Heat Transport & Umklapp Scattering

Crystal lattice vibrations, thermal conductivity, and Umklapp processes

Parameters

κ (conductivity):
Mean free path:
Phonon count: 0

Phonons and Thermal Conductivity

Phonons are quantized lattice vibrations. They carry heat in insulators. Two types of phonon-phonon scattering govern thermal conductivity:

Normal (N): k₁ + k₂ = k₃ (momentum conserved)
Umklapp (U): k₁ + k₂ = k₃ + G (G = reciprocal lattice vector)

Umklapp processes flip phonon momentum (the word means "flipping over" in German — Peierls, 1929). They are the dominant mechanism for thermal resistance in crystals at high temperature.

κ ∝ 1/T   (Umklapp-dominated, T > Θ_D)

At low T, Umklapp is exponentially suppressed (few high-momentum phonons), so κ rises steeply. This lab simulates a 1D chain with phonon quasi-particles bouncing and scattering.

Hot end (left, red): phonons injected at high amplitude. Cold end (right, blue): phonons absorbed. Umklapp events (marked ×) randomize phonon direction, impeding heat flow.