Phonon lifetime and thermal conductivity in amorphous solids

After a short discussion of the static structure factor S (κ) in the small angle region and the low‐temperature thermal conductivity χ( T ) of amorphous solids, a perturbation theory is developed, which yields the phonon lifetime τ κ and the thermal conductivity χ of a weakly and randomly inhomogeneous solid. It is shown that the strong increase of S (κ) for κ ⪅ 10 −2 Å −1 leads to τ κ ∽ κ and χ ∽ T 2 for T ⪅ 1 K. From S (κ) ≈ const. for κ ⪆ 10 −2 Å −1 it follows τ κ ∽ κ 4 (Rayleigh scattering). Thus phonons with wave vectors κ ⪆ 10 −2 Å −1 will be strongly scattered and will not contribute to the thermal conductivity. This is the reason for the plateau of χ for T ⪆ 1 K.