Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit
Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small-perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the specularity red...
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| Format: | Article |
| Language: | English |
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American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/96839 |
| _version_ | 1826199259487141888 |
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| author | Maznev, Alexei |
| author2 | Massachusetts Institute of Technology. Department of Chemistry |
| author_facet | Massachusetts Institute of Technology. Department of Chemistry Maznev, Alexei |
| author_sort | Maznev, Alexei |
| collection | MIT |
| description | Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small-perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the specularity reduction is given by 4η[superscript 2]k[superscript 2], where η is the rms roughness and k is the acoustic wave vector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is found to be proportional to η[superscript 2]k[superscript 4]L[superscript 2], with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of L. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering. |
| first_indexed | 2024-09-23T11:16:55Z |
| format | Article |
| id | mit-1721.1/96839 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:16:55Z |
| publishDate | 2015 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/968392022-10-01T02:32:53Z Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit Maznev, Alexei Massachusetts Institute of Technology. Department of Chemistry Maznev, Alexei Scattering of normally incident longitudinal and transverse acoustic waves by a randomly rough surface of an elastically isotropic solid is analyzed within the small-perturbation approach. In the limiting case of a large correlation length L compared with the acoustic wavelength, the specularity reduction is given by 4η[superscript 2]k[superscript 2], where η is the rms roughness and k is the acoustic wave vector, which is in agreement with the well-known Kirchhoff approximation result often referred to as Ziman's equation [J. M. Ziman, Electrons and Phonons (Clarendon Press, Oxford, 1960)]. In the opposite limiting case of a small correlation length, the specularity reduction is found to be proportional to η[superscript 2]k[superscript 4]L[superscript 2], with the fourth power dependence on frequency as in Rayleigh scattering. Numerical calculations for a Gaussian autocorrelation function of surface roughness connect these limiting cases and reveal a maximum of diffuse scattering at an intermediate value of L. This maximum becomes increasingly pronounced for the incident longitudinal wave as the Poisson's ratio of the medium approaches 1/2 as a result of increased scattering into transverse and Rayleigh surface waves. The results indicate that thermal transport models using Ziman's formula are likely to overestimate the heat flux dissipation due to boundary scattering, whereas modeling interface roughness as atomic disorder is likely to underestimate scattering. United States. Dept. of Energy. Office of Science (Solid-State Solar-Thermal Energy Conversion Center Award DE-SC0001299) 2015-04-29T13:22:04Z 2015-04-29T13:22:04Z 2015-04 2015-03 2015-04-28T22:00:21Z Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/96839 Maznev, A. A. "Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit." Phys. Rev. B 91, 134306 (April 2015). © 2015 American Physical Society en http://dx.doi.org/10.1103/PhysRevB.91.134306 Physical Review B 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. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Maznev, Alexei Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit |
| title | Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit |
| title_full | Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit |
| title_fullStr | Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit |
| title_full_unstemmed | Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit |
| title_short | Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit |
| title_sort | boundary scattering of phonons specularity of a randomly rough surface in the small perturbation limit |
| url | http://hdl.handle.net/1721.1/96839 |
| work_keys_str_mv | AT maznevalexei boundaryscatteringofphononsspecularityofarandomlyroughsurfaceinthesmallperturbationlimit |