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arXiv · 1511.08989

A 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·Gang Chen
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Abstract

The phonon Boltzmann transport equation (BTE) is a powerful tool for studying non-diffusive 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 non-diffusive transport. By utilizing the known Fourier 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 (TTG) experiment, which is a useful tool for studying non-diffusive thermal transport and probing the mean free path (MFP) distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the non-universality of the suppression function used in the past, while providing a general approach to studying thermal properties in the non-diffusive regime.

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Vazrik Chiloyan, Lingping Zeng, Samuel Huberman, Alexei A. Maznev, Keith A. Nelson, Gang Chen. 2015-11-29. A Variational Approach to Extracting the Phonon Mean Free Path Distribution from the Spectral Boltzmann Transport Equation. https://doi.org/10.1103/physrevb.93.155201

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