Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation
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-diffusi...
| Main Authors: | , , , , , |
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| Format: | Article |
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American Institute of Physics (AIP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/118931 https://orcid.org/0000-0001-7804-5418 https://orcid.org/0000-0002-3968-8530 |
| _version_ | 1826197758109810688 |
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| author | Esfarjani, Keivan Chen, Gang Collins, Kimberlee C Maznev, Alexei Tian, Zhiting Nelson, Keith Adam |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Esfarjani, Keivan Chen, Gang Collins, Kimberlee C Maznev, Alexei Tian, Zhiting Nelson, Keith Adam |
| author_sort | Esfarjani, Keivan |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T10:52:41Z |
| format | Article |
| id | mit-1721.1/118931 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T10:52:41Z |
| publishDate | 2018 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/1189312022-09-27T15:40:21Z Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation Esfarjani, Keivan Chen, Gang Collins, Kimberlee C Maznev, Alexei Tian, Zhiting Nelson, Keith Adam Massachusetts Institute of Technology. Department of Chemistry Massachusetts Institute of Technology. Department of Mechanical Engineering Collins, Kimberlee C Maznev, Alexei Tian, Zhiting Nelson, Keith Adam Chen, Gang 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. 2018-11-06T20:39:36Z 2018-11-06T20:39:36Z 2013-09 2013-06 2018-11-06T19:13:51Z Article http://purl.org/eprint/type/JournalArticle 0021-8979 1089-7550 http://hdl.handle.net/1721.1/118931 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 https://orcid.org/0000-0001-7804-5418 https://orcid.org/0000-0002-3968-8530 http://dx.doi.org/10.1063/1.4820572 Journal of Applied Physics 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. application/pdf American Institute of Physics (AIP) Other repository |
| spellingShingle | Esfarjani, Keivan Chen, Gang Collins, Kimberlee C Maznev, Alexei Tian, Zhiting Nelson, Keith Adam Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation |
| title | Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation |
| title_full | Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation |
| title_fullStr | Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation |
| title_full_unstemmed | Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation |
| title_short | Non-diffusive relaxation of a transient thermal grating analyzed with the Boltzmann transport equation |
| title_sort | non diffusive relaxation of a transient thermal grating analyzed with the boltzmann transport equation |
| url | http://hdl.handle.net/1721.1/118931 https://orcid.org/0000-0001-7804-5418 https://orcid.org/0000-0002-3968-8530 |
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