Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation

Vazrik Chiloyan, Lingping Zeng, Samuel Huberman, Alexei A. Maznev, Keith A. Nelson, and Gang Chen
Phys. Rev. B 93, 155201 – Published 6 April 2016

Abstract

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying nondiffusive thermal transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring nondiffusive transport. By utilizing the known Fourier heat conduction solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating experiment, which is a useful tool for studying nondiffusive thermal transport and probing the MFP distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the nonuniversality of the suppression function used in the past, while providing a general approach to studying thermal properties in the nondiffusive regime.

  • Figure
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  • Received 24 November 2015
  • Revised 7 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.155201

©2016 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Vazrik Chiloyan1, Lingping Zeng1, Samuel Huberman1, Alexei A. Maznev2, Keith A. Nelson2, and Gang Chen1,*

  • 1Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 2Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *Corresponding author: gchen2@mit.edu

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Vol. 93, Iss. 15 — 15 April 2016

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