Application of Houston?s method to the calculation of the direction-dependent thermal conductivity in finite crystals at low temperatures

[+] Author and Article Information
Michel Kazan

Department of Physics, American University of Beirut, P.O. Box 11-0236, Riad El-Solh, Beirut 1107-2020, Lebanon

1Corresponding author.

ASME doi:10.1115/1.4036601 History: Received November 08, 2016; Revised April 21, 2017


Although atomistic simulations and first principles computation of harmonic normal modes and anharmonic forces are nowadays widely used to solve Boltzmann equation for phonons and accurately calculate the lattice thermal conductivity, there is still a need for analytical approximate models leading to reliable solutions to heat transport problems, particularly at low temperatures. The utmost need for such approximate models stems from the fact that most of the atomistic simulation techniques do not account for quantum mechanics effects occurring at low temperatures, and first principles computation requires very small mesh size to account for the excitation of only long wavelength phonons. This paper presents significant advances in the analytical calculation of the low temperature lattice thermal conductivity in finite crystals. It shows that an accurate prediction of the direction-dependent lattice thermal conductivity can be obtained at low temperatures when Houston’s method is used to account for the anisotropy of the Brillouin zone in the calculation of the phonon spectrum. It also provides an approach to predict from a spatial-dependent Boltzmann equation the rate at which phonons are scattered by the sample boundary in the presence of intrinsic scattering mechanisms, which is crucial for the calculation of the lattice thermal conductivity in finite crystals.

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