Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation
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Author(s)
Esfarjani, Keivan
Chen, Gang
Collins, Kimberlee C
Maznev, Alexei
Tian, Zhiting
Nelson, Keith Adam
Date Issued
September 2013
Journal
Journal of Applied Physics
Publisher
American Institute of Physics (AIP)
Citation
Collins, Kimberlee C. et al. “Non-Diffusive Relaxation of a Transient Thermal Grating Analyzed with the Boltzmann Transport Equation.” Journal of Applied Physics 114, 10 (September 2013): 104302 © 2013 AIP Publishing LLC
Version
Final published version
Abstract
The relaxation of an one-dimensional transient thermal grating (TTG) in a medium with phonon-mediated thermal transport is analyzed within the framework of the Boltzmann transport equation (BTE), with the goal of extracting phonon mean free path (MFP) information from TTG measurements of non-diffusive phonon transport. Both gray-medium (constant MFP) and spectrally dependent MFP models are considered. In the gray-medium approximation, an analytical solution is derived. For large TTG periods compared to the MFP, the model yields an exponential decay of grating amplitude with time in agreement with Fourier's heat diffusion equation, and at shorter periods, phonon transport transitions to the ballistic regime, with the decay becoming strongly non-exponential. Spectral solutions are obtained for Si and PbSe at 300 K using phonon dispersion and lifetime data from density functional theory calculations. The spectral decay behaviors are compared to several approximate models: a single MFP solution, a frequency-integrated gray-medium model, and a "two-fluid" BTE solution. We investigate the utility of using the approximate models for the reconstruction of phonon MFP distributions from non-diffusive TTG measurements.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1063/1.4820572
