Space-time dependent thermal conductivity in nonlocal thermal transport
Abstract
Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1669763
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 10; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Lattice thermal conductivity; Phonons; Boltzmann theory
Citation Formats
Hua, Chengyun, and Lindsay, Lucas. Space-time dependent thermal conductivity in nonlocal thermal transport. United States: N. p., 2020.
Web. doi:10.1103/physrevb.102.104310.
Hua, Chengyun, & Lindsay, Lucas. Space-time dependent thermal conductivity in nonlocal thermal transport. United States. https://doi.org/10.1103/physrevb.102.104310
Hua, Chengyun, and Lindsay, Lucas. Wed .
"Space-time dependent thermal conductivity in nonlocal thermal transport". United States. https://doi.org/10.1103/physrevb.102.104310. https://www.osti.gov/servlets/purl/1669763.
@article{osti_1669763,
title = {Space-time dependent thermal conductivity in nonlocal thermal transport},
author = {Hua, Chengyun and Lindsay, Lucas},
abstractNote = {Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.},
doi = {10.1103/physrevb.102.104310},
journal = {Physical Review. B},
number = 10,
volume = 102,
place = {United States},
year = {Wed Sep 30 00:00:00 EDT 2020},
month = {Wed Sep 30 00:00:00 EDT 2020}
}
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Works referenced in this record:
Energy-Flux Operator for a Lattice
journal, October 1963
- Hardy, Robert J.
- Physical Review, Vol. 132, Issue 1
Temperature in a Peierls-Boltzmann treatment of nonlocal phonon heat transport
journal, August 2018
- Allen, Philip B.; Perebeinos, Vasili
- Physical Review B, Vol. 98, Issue 8
Unusual high thermal conductivity in boron arsenide bulk crystals
journal, July 2018
- Tian, Fei; Song, Bai; Chen, Xi
- Science, Vol. 361, Issue 6402
Ab initio thermal transport in compound semiconductors
journal, April 2013
- Lindsay, L.; Broido, D. A.; Reinecke, T. L.
- Physical Review B, Vol. 87, Issue 16
Variational Calculation of the Thermal Conductivity of Germanium
journal, February 1969
- Hamilton, R. A. H.; Parrott, J. E.
- Physical Review, Vol. 178, Issue 3
Deviational simulation of phonon transport in graphene ribbons with ab initio scattering
journal, October 2014
- Landon, Colin D.; Hadjiconstantinou, Nicolas G.
- Journal of Applied Physics, Vol. 116, Issue 16
Observation of second sound in graphite at temperatures above 100 K
journal, March 2019
- Huberman, S.; Duncan, R. A.; Chen, K.
- Science, Vol. 364, Issue 6438
Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation
journal, September 2013
- Collins, Kimberlee C.; Maznev, Alexei A.; Tian, Zhiting
- Journal of Applied Physics, Vol. 114, Issue 10
Phonon Boltzmann Equation and Second Sound in Solids
journal, August 1970
- Hardy, Robert J.
- Physical Review B, Vol. 2, Issue 4
Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films
journal, May 2015
- Hua, Chengyun; Minnich, Austin J.
- Journal of Applied Physics, Vol. 117, Issue 17
An enhanced Fourier law derivable from the Boltzmann transport equation and a sample application in determining the mean-free path of nondiffusive phonon modes
journal, September 2014
- Ramu, Ashok T.; Ma, Yanbao
- Journal of Applied Physics, Vol. 116, Issue 9
Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge
journal, February 2010
- Ward, A.; Broido, D. A.
- Physical Review B, Vol. 81, Issue 8
Derivation and calculation of complementary variational principles for the lattice thermal conductivity
journal, August 1976
- Srivastava, G. P.
- Journal of Physics C: Solid State Physics, Vol. 9, Issue 16
Nonlocal theory of thermal conductivity
journal, July 1988
- Mahan, G. D.; Claro, Francisco
- Physical Review B, Vol. 38, Issue 3
Ultrahigh thermal conductivity in isotope-enriched cubic boron nitride
journal, January 2020
- Chen, Ke; Song, Bai; Ravichandran, Navaneetha K.
- Science, Vol. 367, Issue 6477
Solution of the Linearized Phonon Boltzmann Equation
journal, August 1966
- Guyer, R. A.; Krumhansl, J. A.
- Physical Review, Vol. 148, Issue 2
almaBTE : A solver of the space–time dependent Boltzmann transport equation for phonons in structured materials
journal, November 2017
- Carrete, Jesús; Vermeersch, Bjorn; Katre, Ankita
- Computer Physics Communications, Vol. 220
Boltzmann Transport in Nanostructures as a Friction Effect
journal, July 2017
- Cepellotti, Andrea; Marzari, Nicola
- Nano Letters, Vol. 17, Issue 8
An alternative approach to efficient simulation of micro/nanoscale phonon transport
journal, October 2012
- Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.
- Applied Physics Letters, Vol. 101, Issue 15
Thermal Conductivity, Second Sound, and Phonon-Phonon Interactions in NaF
journal, February 1971
- Jackson, Howard E.; Walker, Charles T.
- Physical Review B, Vol. 3, Issue 4
Role of hydrodynamic viscosity on phonon transport in suspended graphene
journal, March 2018
- Li, Xun; Lee, Sangyeop
- Physical Review B, Vol. 97, Issue 9
Lowest‐Order Contribution to the Lattice Thermal Conductivity
journal, November 1965
- Hardy, Robert J.
- Journal of Mathematical Physics, Vol. 6, Issue 11
Perturbation Expansion for Lattice Thermal Conductivity
journal, November 1965
- Hardy, Robert J.; Swenson, Robert J.; Schieve, William C.
- Journal of Mathematical Physics, Vol. 6, Issue 11
Thermal Conductivity of Perfect Dielectric Crystals in the Absence of Umklapp Processes
journal, June 1963
- Sussmann, J. A.; Thellung, A.
- Proceedings of the Physical Society, Vol. 81, Issue 6
Importance of frequency-dependent grain boundary scattering in nanocrystalline silicon and silicon–germanium thermoelectrics
journal, November 2014
- Hua, Chengyun; Minnich, Austin J.
- Semiconductor Science and Technology, Vol. 29, Issue 12
Ab initio theory of the lattice thermal conductivity in diamond
journal, September 2009
- Ward, A.; Broido, D. A.; Stewart, Derek A.
- Physical Review B, Vol. 80, Issue 12
An iterative approach to the phonon Boltzmann equation in the theory of thermal conductivity
journal, July 1995
- Omini, M.; Sparavigna, A.
- Physica B: Condensed Matter, Vol. 212, Issue 2
High thermal conductivity in cubic boron arsenide crystals
journal, July 2018
- Li, Sheng; Zheng, Qiye; Lv, Yinchuan
- Science, Vol. 361, Issue 6402
ShengBTE: A solver of the Boltzmann transport equation for phonons
journal, June 2014
- Li, Wu; Carrete, Jesús; A. Katcho, Nebil
- Computer Physics Communications, Vol. 185, Issue 6
Direct Solution to the Linearized Phonon Boltzmann Equation
journal, June 2013
- Chaput, Laurent
- Physical Review Letters, Vol. 110, Issue 26
Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate
journal, August 2014
- Zeng, Lingping; Chen, Gang
- Journal of Applied Physics, Vol. 116, Issue 6
Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment
journal, August 2019
- Hua, Chengyun; Lindsay, Lucas; Chen, Xiangwen
- Physical Review B, Vol. 100, Issue 8
Thermal Conductivity, Second Sound, and Phonon Hydrodynamic Phenomena in Nonmetallic Crystals
journal, August 1966
- Guyer, R. A.; Krumhansl, J. A.
- Physical Review, Vol. 148, Issue 2
Superdiffusive heat conduction in semiconductor alloys. II. Truncated Lévy formalism for experimental analysis
journal, February 2015
- Vermeersch, Bjorn; Mohammed, Amr M. S.; Pernot, Gilles
- Physical Review B, Vol. 91, Issue 8
Nonlocal theory for heat transport at high frequencies
journal, November 2014
- Koh, Yee Kan; Cahill, David G.; Sun, Bo
- Physical Review B, Vol. 90, Issue 20
Superdiffusive heat conduction in semiconductor alloys. I. Theoretical foundations
journal, February 2015
- Vermeersch, Bjorn; Carrete, Jesús; Mingo, Natalio
- Physical Review B, Vol. 91, Issue 8
Thermal Transport in Crystals as a Kinetic Theory of Relaxons
journal, October 2016
- Cepellotti, Andrea; Marzari, Nicola
- Physical Review X, Vol. 6, Issue 4
Analytical interpretation of nondiffusive phonon transport in thermoreflectance thermal conductivity measurements
journal, August 2014
- Regner, K. T.; McGaughey, A. J. H.; Malen, J. A.
- Physical Review B, Vol. 90, Issue 6
First-Principles Determination of Ultrahigh Thermal Conductivity of Boron Arsenide: A Competitor for Diamond?
journal, July 2013
- Lindsay, L.; Broido, D. A.; Reinecke, T. L.
- Physical Review Letters, Vol. 111, Issue 2, Article No. 025901
Efficient simulation of multidimensional phonon transport using energy-based variance-reduced Monte Carlo formulations
journal, November 2011
- Péraud, Jean-Philippe M.; Hadjiconstantinou, Nicolas G.
- Physical Review B, Vol. 84, Issue 20
Generalization of Fourier’s Law into Viscous Heat Equations
journal, January 2020
- Simoncelli, Michele; Marzari, Nicola; Cepellotti, Andrea
- Physical Review X, Vol. 10, Issue 1
Experimental observation of high thermal conductivity in boron arsenide
journal, July 2018
- Kang, Joon Sang; Li, Man; Wu, Huan
- Science, Vol. 361, Issue 6402
First Principles Peierls-Boltzmann Phonon Thermal Transport: A Topical Review
journal, April 2016
- Lindsay, Lucas
- Nanoscale and Microscale Thermophysical Engineering, Vol. 20, Issue 2
Ab initio variational approach for evaluating lattice thermal conductivity
journal, July 2013
- Fugallo, Giorgia; Lazzeri, Michele; Paulatto, Lorenzo
- Physical Review B, Vol. 88, Issue 4
Lattice thermal conductivity of silicon from empirical interatomic potentials
journal, July 2005
- Broido, D. A.; Ward, A.; Mingo, N.
- Physical Review B, Vol. 72, Issue 1
Thermal conductivity and phonon transport properties of silicon using perturbation theory and the environment-dependent interatomic potential
journal, September 2009
- Pascual-Gutiérrez, José A.; Murthy, Jayathi Y.; Viskanta, Raymond
- Journal of Applied Physics, Vol. 106, Issue 6
Transport regimes in quasiballistic heat conduction
journal, March 2014
- Hua, Chengyun; Minnich, Austin J.
- Physical Review B, Vol. 89, Issue 9
Phonon hydrodynamics in solids
journal, July 1974
- Beck, H.; Meier, P. F.; Thellung, A.
- Physica Status Solidi (a), Vol. 24, Issue 1
Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films
journal, May 2015
- Hua, Chengyun; Minnich, Austin J.
- Journal of Applied Physics, Vol. 117, Issue 17
Analytical Green's function of the multidimensional frequency-dependent phonon Boltzmann equation
journal, December 2014
- Hua, Chengyun; Minnich, Austin J.
- Physical Review B, Vol. 90, Issue 21
High thermal conductivity in cubic boron arsenide crystals
journal, July 2018
- Li, Sheng; Zheng, Qiye; Lv, Yinchuan
- Science, Vol. 361, Issue 6402