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Title: Onset of nondiffusive phonon transport in transient thermal grating decay

Abstract

The relaxation of a spatially sinusoidal temperature perturbation in a dielectric crystal at a temperature comparable to or higher than the Debye temperature is investigated theoretically. We assume that most phonons contributing to the specific heat have a mean free path (MFP) much shorter than the thermal transport distance and can be described by the thermal diffusion model. Low-frequency phonons that may have MFP comparable to or longer than the grating period are described by the Boltzmann transport equation. These low-frequency phonons are assumed to interact with the thermal reservoir of high-frequency phonons but not with each other. Within the single mode relaxation time approximation, an analytical expression for the thermal grating relaxation rate is obtained. We show that the contribution of “ballistic” phonons with long MFP to the effective thermal conductivity governing the grating decay is suppressed compared to their contribution to thermal transport at long distances. In conclusion, the reduction in the effective thermal conductivity in Si at room temperature is found to be significant at grating periods as large as 10 μm.

Authors:
 [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:
1386852
Grant/Contract Number:  
SC0001299; FG02-09ER46577
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 84; Journal Issue: 19; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 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

Maznev, Alexei A., Johnson, Jeremy A., and Nelson, Keith A. Onset of nondiffusive phonon transport in transient thermal grating decay. United States: N. p., 2011. Web. doi:10.1103/PhysRevB.84.195206.
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Maznev, Alexei A., Johnson, Jeremy A., & Nelson, Keith A. Onset of nondiffusive phonon transport in transient thermal grating decay. United States. https://doi.org/10.1103/PhysRevB.84.195206
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Maznev, Alexei A., Johnson, Jeremy A., and Nelson, Keith A. Mon . "Onset of nondiffusive phonon transport in transient thermal grating decay". United States. https://doi.org/10.1103/PhysRevB.84.195206. https://www.osti.gov/servlets/purl/1386852.
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@article{osti_1386852,
title = {Onset of nondiffusive phonon transport in transient thermal grating decay},
author = {Maznev, Alexei A. and Johnson, Jeremy A. and Nelson, Keith A.},
abstractNote = {The relaxation of a spatially sinusoidal temperature perturbation in a dielectric crystal at a temperature comparable to or higher than the Debye temperature is investigated theoretically. We assume that most phonons contributing to the specific heat have a mean free path (MFP) much shorter than the thermal transport distance and can be described by the thermal diffusion model. Low-frequency phonons that may have MFP comparable to or longer than the grating period are described by the Boltzmann transport equation. These low-frequency phonons are assumed to interact with the thermal reservoir of high-frequency phonons but not with each other. Within the single mode relaxation time approximation, an analytical expression for the thermal grating relaxation rate is obtained. We show that the contribution of “ballistic” phonons with long MFP to the effective thermal conductivity governing the grating decay is suppressed compared to their contribution to thermal transport at long distances. In conclusion, the reduction in the effective thermal conductivity in Si at room temperature is found to be significant at grating periods as large as 10 μm.},
doi = {10.1103/PhysRevB.84.195206},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 19,
volume = 84,
place = {United States},
year = {Mon Nov 28 00:00:00 EST 2011},
month = {Mon Nov 28 00:00:00 EST 2011}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevB.84.195206
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Cited by: 79 works
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Figures / Tables:

FIG. 1 FIG. 1: (Color online) Correction factor A vs the product of the grating wave number and phonon mean free path. The solid curve was calculated according to Eq. (18) while the dashed curve was obtained from the “stitching model,” Eq. (23).
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      Figures / Tables found in this record:

      FIG. 1 (p. 5)figure
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      TABLE I (p. 6)table
      TABLE I (p. 6)table
      FIG. 2 (p. 7)figure
      FIG. 2 (p. 7)figure
      FIG. 3 (p. 7)figure
      FIG. 3 (p. 7)figure
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