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Theory of the Thermal Conductivity of Metals, Alloys, and Semiconductors, Part II.

Report Number: ASD TDR 62-74 Part 2
Author(s): John R. Madigan
Corporate Author: Borg-Warner Corporation
Laboratory: Directorate of Materials and Processes
Date of Publication: 1963-01
Pages: 42
Contract: AF 33(616)-7374
Project: 7360
Task: 736001
AD Number: AD0297505

Abstract:
The lattice thermal conductivity of simple alloys can be calculated by assuming that the only effects of alloying on the thermal conductivity can be represented by point defect scattering mechanisms. The scattering of phonons represented by point defects has an inverse relaxation time proportional to the fourth power of the frequency. The proportionality constant depends on the particular scattering mechanism considered. In simple substitutional alloys where one chemically similar element is substituted for another there are three scattering processes to be considered besides phonon-phonon scattering. Phonons are scattered. Phonons are scatteed by the fluctuation in mass, the change in force constants, and the lattice distortion caused by the impurity atom. The relaxation time for all these processes acting simultaneously has been derived.

The relaxation time for phonon-phonon scattering due to cubic anharmonic terms in the expansion of the potential energy of the crystal in the displacements of the atoms comprising the crystal from equilibrium is proportional to the inverse frequency squared. When the relaxation time for point defect scattering is combined with that for phonon-phonon scattering to obtain an effective relaxation time one may calculate the lattice thermal conductivity as a function of alloy composition. We hav done this for the case of Ge-Si alloys and find reasonable agreement with experiment.

The possibility of modifying the theory with the aid of ideas from nonequilibrium statistical mechanics is considered.

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