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

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 propose a direct approach to calculating the effective thermal conductivity from the BTE. We reveal 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.

Authors:
 [1];  [1];  [1];  [1];  [1];  [1]
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  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Solid-State Solar-Thermal Energy Conversion Center (S3TEC); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1371459
Alternate Identifier(s):
OSTI ID: 1245886
Grant/Contract Number:  
SC0001299; FG02-09ER46577; SC0001299/DE-FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 93; Journal Issue: 15; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; solar (photovoltaic); solar (thermal); solid state lighting; phonons; thermal conductivity; thermoelectric; defects; mechanical behavior; charge transport; spin dynamics; materials and chemistry by design; optics, synthesis (novel materials); synthesis (self-assembly); synthesis (scalable processing)

Citation Formats

Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., and Chen, Gang. Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation. United States: N. p., 2016. Web. doi:10.1103/PhysRevB.93.155201.
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Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., & Chen, Gang. Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation. United States. https://doi.org/10.1103/PhysRevB.93.155201
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Chiloyan, Vazrik, Zeng, Lingping, Huberman, Samuel, Maznev, Alexei A., Nelson, Keith A., and Chen, Gang. Wed . "Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation". United States. https://doi.org/10.1103/PhysRevB.93.155201. https://www.osti.gov/servlets/purl/1371459.
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@article{osti_1371459,
title = {Variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann transport equation},
author = {Chiloyan, Vazrik and Zeng, Lingping and Huberman, Samuel and Maznev, Alexei A. and Nelson, Keith A. and Chen, Gang},
abstractNote = {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 propose a direct approach to calculating the effective thermal conductivity from the BTE. We reveal 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.},
doi = {10.1103/PhysRevB.93.155201},
journal = {Physical Review B},
number = 15,
volume = 93,
place = {United States},
year = {Wed Apr 06 00:00:00 EDT 2016},
month = {Wed Apr 06 00:00:00 EDT 2016}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevB.93.155201
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Citation Metrics:
Cited by: 19 works
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Figures / Tables:

FIG. 1 FIG. 1: Effective thermal conductivity of silicon (a) and PbSe (b). Here the effective thermal conductivity is plotted to compare the variational technique with the exact numerical technique and various approximations. The variational technique for the full spectral BTE, both with the physical condition of Eq. (4) and with leastmore » squares optimization, demonstrates excellent agreement with the exact numerical solution.« less
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Works referenced in this record:

Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport
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    Works referencing / citing this record:

    Monte Carlo study of non-diffusive relaxation of a transient thermal grating in thin membranes
    journal, February 2016

    • Zeng, Lingping; Chiloyan, Vazrik; Huberman, Samuel
    • Applied Physics Letters, Vol. 108, Issue 6
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    Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials
    journal, October 2018

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    • Journal of Applied Physics, Vol. 124, Issue 16
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    Modeling ballistic phonon transport from a cylindrical electron beam heat source
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    Achieving high power factor and output power density in p-type half-Heuslers Nb 1-x Ti x FeSb
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    • He, Ran; Kraemer, Daniel; Mao, Jun
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    Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond
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    • Sanchez-Martinez, Miguel-Ángel; Alzina, Francesc; Oyarzo, Juan
    • Nanomaterials, Vol. 9, Issue 3
    • DOI: 10.3390/nano9030414

    Monte Carlo Study of Non-diffusive Relaxation of A Transient Thermal Grating in Thin Membranes
    text, January 2015

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