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Phonon lifetime and thermal conductivity in amorphous solids
Author(s) -
Handrich K.
Publication year - 1983
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221160214
Subject(s) - thermal conductivity , phonon , amorphous solid , condensed matter physics , thermal , phonon scattering , plateau (mathematics) , rayleigh scattering , scattering , materials science , perturbation (astronomy) , conductivity , thermal conduction , physics , thermodynamics , optics , chemistry , quantum mechanics , crystallography , mathematics , mathematical analysis
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.