Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit

Maznev, A. A.

doi:10.1103/PhysRevB.91.134306

Title: Boundary scattering of phonons: Specularity of a randomly rough surface in the small-perturbation limit

Journal Article · Tue Apr 28 00:00:00 EDT 2015 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.91.134306· OSTI ID:1370990

Maznev, A. A. ^[1]

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

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 4η²k² ,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 discovered to be proportional to η²k⁴L² , 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 imply 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.

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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

OSTI ID:: 1370990

Alternate ID(s):: OSTI ID: 1181141

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Vol. 91, Issue 13; Related Information: S3TEC partners with Massachusetts Institute of Technology (lead); Boston College; Oak Ridge National Laboratory; Rensselaer Polytechnic Institute; ISSN 1098-0121

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 47 works

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