Phonon lifetime and thermal conductivity in amorphous solids

✍ Scribed by K. Handrich

• Publisher: John Wiley and Sons
• Year: 1983
• Tongue: English
• Weight: 336 KB
• Volume: 116
• Category: Article
• ISSN: 0370-1972
• DOI: 10.1002/pssb.2221160214

✦ Synopsis

Abstract

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.