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

Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel; Maznev, Alexei A.; Nelson, Keith A.; Chen, Gang

doi:10.1103/PhysRevB.93.155201

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

Journal Article · Wed Apr 06 00:00:00 EDT 2016 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.93.155201· OSTI ID:1371459

Chiloyan, Vazrik ^[1]; Zeng, Lingping ^[1]; Huberman, Samuel ^[1]; Maznev, Alexei A. ^[1]; Nelson, Keith A. ^[1]; Chen, Gang ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: 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 Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0001299; FG02-09ER46577; SC0001299/DE-FG02-09ER46577

OSTI ID:: 1371459

Alternate ID(s):: OSTI ID: 1245886

Journal Information:: Physical Review B, Vol. 93, Issue 15; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 19 works

Citation information provided by
Web of Science

References (27)

Determining Phonon Mean Free Paths from Observations of Quasiballistic Thermal Transport Minnich, A. J. Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.205901	journal	November 2012
Measuring Phonon Mean Free Path Distributions by Probing Quasiballistic Phonon Transport in Grating Nanostructures Zeng, Lingping; Collins, Kimberlee C.; Hu, Yongjie Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep17131	journal	November 2015
Quasi-ballistic thermal transport from nanoscale interfaces observed using ultrafast coherent soft X-ray beams Siemens, Mark E.; Li, Qing; Yang, Ronggui Nature Materials, Vol. 9, Issue 1 https://doi.org/10.1038/nmat2568	journal	November 2009
Instrumentation of broadband frequency domain thermoreflectance for measuring thermal conductivity accumulation functions Regner, K. T.; Majumdar, S.; Malen, J. A. Review of Scientific Instruments, Vol. 84, Issue 6 https://doi.org/10.1063/1.4808055	journal	June 2013
Thermal Conductivity Spectroscopy Technique to Measure Phonon Mean Free Paths Minnich, A. J.; Johnson, J. A.; Schmidt, A. J. Physical Review Letters, Vol. 107, Issue 9 https://doi.org/10.1103/PhysRevLett.107.095901	journal	August 2011
On the use of variational methods for solving Boltzmann equations involving non-Hermitian operators Ah-Sam, L. E. G.; Jensen, H. H�jgaard; Smith, H. Journal of Statistical Physics, Vol. 3, Issue 1 https://doi.org/10.1007/BF01012184	journal	January 1971
Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate Zeng, Lingping; Chen, Gang Journal of Applied Physics, Vol. 116, Issue 6 https://doi.org/10.1063/1.4893299	journal	August 2014
Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation Collins, Kimberlee C.; Maznev, Alexei A.; Tian, Zhiting Journal of Applied Physics, Vol. 114, Issue 10 https://doi.org/10.1063/1.4820572	journal	September 2013
Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films Hua, Chengyun; Minnich, Austin J. Journal of Applied Physics, Vol. 117, Issue 17 https://doi.org/10.1063/1.4919432	journal	May 2015
Variational Treatment of High-Frequency Transport Problems in Solids Hindley, N. K.; Garcia-Moliner, F. Physical Review, Vol. 140, Issue 1A https://doi.org/10.1103/PhysRev.140.A343	journal	October 1965
Non-diffusive thermal transport in GaAs at micron length scales Johnson, Jeremy A.; Eliason, Jeffrey K.; Maznev, Alexei A. Journal of Applied Physics, Vol. 118, Issue 15 https://doi.org/10.1063/1.4933285	journal	October 2015
Multidimensional quasiballistic thermal transport in transient grating spectroscopy Minnich, A. J. Physical Review B, Vol. 92, Issue 8 https://doi.org/10.1103/PhysRevB.92.085203	journal	August 2015
Nonlocal and Nonequilibrium Heat Conduction in the Vicinity of Nanoparticles Chen, G. Journal of Heat Transfer, Vol. 118, Issue 3 https://doi.org/10.1115/1.2822665	journal	August 1996
Analysis of heat flow in layered structures for time-domain thermoreflectance Cahill, David G. Review of Scientific Instruments, Vol. 75, Issue 12 https://doi.org/10.1063/1.1819431	journal	December 2004
Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G. Physical Review B, Vol. 84, Issue 20 https://doi.org/10.1103/PhysRevB.84.205331	journal	November 2011
Analytical Green's function of the multidimensional frequency-dependent phonon Boltzmann equation Hua, Chengyun; Minnich, Austin J. Physical Review B, Vol. 90, Issue 21 https://doi.org/10.1103/PhysRevB.90.214306	journal	December 2014
Spectral mapping of thermal conductivity through nanoscale ballistic transport Hu, Yongjie; Zeng, Lingping; Minnich, Austin J. Nature Nanotechnology, Vol. 10, Issue 8 https://doi.org/10.1038/nnano.2015.109	journal	June 2015
An alternative approach to efficient simulation of micro/nanoscale phonon transport Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G. Applied Physics Letters, Vol. 101, Issue 15 https://doi.org/10.1063/1.4757607	journal	October 2012
Spectral Phonon Transport Properties of Silicon Based on Molecular Dynamics Simulations and Lattice Dynamics Henry, Asegun S.; Chen, Gang Journal of Computational and Theoretical Nanoscience, Vol. 5, Issue 2 https://doi.org/10.1166/jctn.2008.2454	journal	February 2008
A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency Hoogeboom-Pot, Kathleen M.; Hernandez-Charpak, Jorge N.; Gu, Xiaokun Proceedings of the National Academy of Sciences, Vol. 112, Issue 16 https://doi.org/10.1073/pnas.1503449112	journal	March 2015
Direct Measurement of Room-Temperature Nondiffusive Thermal Transport Over Micron Distances in a Silicon Membrane Johnson, Jeremy A.; Maznev, A. A.; Cuffe, John Physical Review Letters, Vol. 110, Issue 2 https://doi.org/10.1103/PhysRevLett.110.025901	journal	January 2013
Broadband phonon mean free path contributions to thermal conductivity measured using frequency domain thermoreflectance Regner, Keith T.; Sellan, Daniel P.; Su, Zonghui Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2630	journal	March 2013
Onset of nondiffusive phonon transport in transient thermal grating decay Maznev, A. A.; Johnson, Jeremy A.; Nelson, Keith A. Physical Review B, Vol. 84, Issue 19 https://doi.org/10.1103/PhysRevB.84.195206	journal	November 2011
Reconstructing phonon mean-free-path contributions to thermal conductivity using nanoscale membranes Cuffe, John; Eliason, Jeffrey K.; Maznev, A. A. Physical Review B, Vol. 91, Issue 24 https://doi.org/10.1103/PhysRevB.91.245423	journal	June 2015
Transport regimes in quasiballistic heat conduction Hua, Chengyun; Minnich, Austin J. Physical Review B, Vol. 89, Issue 9 https://doi.org/10.1103/PhysRevB.89.094302	journal	March 2014
Examining thermal transport through a frequency-domain representation of time-domain thermoreflectance data Collins, Kimberlee C.; Maznev, Alexei A.; Cuffe, John Review of Scientific Instruments, Vol. 85, Issue 12 https://doi.org/10.1063/1.4903463	journal	December 2014
Microscale Heat Conduction in Dielectric Thin Films Majumdar, A. Journal of Heat Transfer, Vol. 115, Issue 1 https://doi.org/10.1115/1.2910673	journal	February 1993

Cited By (6)

Monte Carlo study of non-diffusive relaxation of a transient thermal grating in thin membranes Zeng, Lingping; Chiloyan, Vazrik; Huberman, Samuel Applied Physics Letters, Vol. 108, Issue 6 https://doi.org/10.1063/1.4941766	journal	February 2016
Tutorial: Time-domain thermoreflectance (TDTR) for thermal property characterization of bulk and thin film materials Jiang, Puqing; Qian, Xin; Yang, Ronggui Journal of Applied Physics, Vol. 124, Issue 16 https://doi.org/10.1063/1.5046944	journal	October 2018
Modeling ballistic phonon transport from a cylindrical electron beam heat source Wehmeyer, Geoff Journal of Applied Physics, Vol. 126, Issue 12 https://doi.org/10.1063/1.5115165	journal	September 2019
Achieving high power factor and output power density in p-type half-Heuslers Nb _1-x Ti _x FeSb He, Ran; Kraemer, Daniel; Mao, Jun Proceedings of the National Academy of Sciences, Vol. 113, Issue 48 https://doi.org/10.1073/pnas.1617663113	journal	November 2016
Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond Sanchez-Martinez, Miguel-Ángel; Alzina, Francesc; Oyarzo, Juan Nanomaterials, Vol. 9, Issue 3 https://doi.org/10.3390/nano9030414	journal	March 2019
Monte Carlo Study of Non-diffusive Relaxation of A Transient Thermal Grating in Thin Membranes Zeng, Lingping; Chiloyan, Vazrik; Huberman, Samuel arXiv https://doi.org/10.48550/arxiv.1512.03986	text	January 2015

Figures / Tables (4)

FIG. 1(p. 5)

FIG. 2(p. 5)

Similar Records

Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation

Journal Article · Tue Sep 10 00:00:00 EDT 2013 · Journal of Applied Physics · OSTI ID:1371459

Collins, Kimberlee C.; Maznev, Alexei A.; Tian, Zhiting; +3 more

Measuring phonon mean free path distributions by probing quasiballistic phonon transport in grating nanostructures

Journal Article · Fri Nov 27 00:00:00 EST 2015 · Scientific Reports · OSTI ID:1371459

Zeng, Lingping; Collins, Kimberlee C.; Hu, Yongjie; +8 more

Variational approach to solving the spectral Boltzmann transport equation in transient thermal grating for thin films

Journal Article · Mon Jul 11 00:00:00 EDT 2016 · Journal of Applied Physics · OSTI ID:1371459

Chiloyan, Vazrik; Zeng, Lingping; Huberman, Samuel; +3 more

Related Subjects

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)