Research Papers: Micro/Nanoscale Heat Transfer

Diffusive Phonons in Nongray Nanostructures

[+] Author and Article Information
Giuseppe Romano

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139
e-mail: romanog@mit.edu

Alexie M. Kolpak

Department of Mechanical Engineering,
Massachusetts Institute of Technology,
77 Massachusetts Avenue,
Cambridge, MA 02139

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 16, 2017; final manuscript received June 12, 2018; published online October 8, 2018. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 141(1), 012401 (Oct 08, 2018) (5 pages) Paper No: HT-17-1610; doi: 10.1115/1.4040611 History: Received October 16, 2017; Revised June 12, 2018

Nanostructured semiconducting materials are promising candidates for thermoelectrics (TEs) due to their potential to suppress phonon transport while preserving electrical properties. Modeling phonon-boundary scattering in complex geometries is crucial for predicting materials with high conversion efficiency. However, the simultaneous presence of ballistic and diffusive phonons challenges the development of models that are both accurate and computationally tractable. Using the recently developed first-principles Boltzmann transport equation (BTE) approach, we investigate diffusive phonons in nanomaterials with wide mean-free-path (MFP) distributions. First, we derive the short MFP limit of the suppression function, showing that it does not necessarily recover the value predicted by standard diffusive transport, challenging previous assumptions. Second, we identify a Robin type boundary condition describing diffuse surfaces within Fourier's law, extending the validity of diffusive heat transport in terms of Knudsen numbers. Finally, we use this result to develop a hybrid Fourier/BTE approach to model realistic materials, obtaining good agreement with experiments. These results provide insight on thermal transport in materials that are within experimental reach and open opportunities for large-scale screening of nanostructured TE materials.

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Grahic Jump Location
Fig. 1

(a) For short Kns, the suppression function, S¯(Λ), reaches a plateau that is significantly lower than that calculated by the standard Fourier's law. Up to Kn ≈ 1, the isotropic suppression function, SISO(Λ)≈S¯(Λ), because the phonon distributions are isotropic. The diffusive suppression function, SD(Λ), reveals the breakdown of Fourier's law for Kn > 1. In the inset, the unit cell including a single circular pore and with periodicity L = 10 nm. (b) The coefficients B2(Λ) for a realistic, diffusive, and ballistic materials. The dotted line represents the characteristic length, Lc; (c) S(Λ) and (d) SISO (Λ) for the case of ballistic and diffusive materials. Realistic materials lie in the shaded regions. The curves for Si at T = 150, 200, 250, and 300 K are shown for comparison.

Grahic Jump Location
Fig. 2

(a) Normal thermal flux for different Kns at the hot and cold sides of the pore. (b) Temperature profile around the boundary of the pore for TB, as calculated by Eq. (4), as well as for high and low Kn phonons. The angles ϕ = –π and ϕ = 0 coincide with the directions x̂ and −x̂.

Grahic Jump Location
Fig. 3

(a) The effective thermal conductivity from calculations and experiments [14] and (b) the thermal flux profile. As expected, most of the heat travel along the space between pores along the temperature gradient. (c) The suppression function, S(Λ) and the diffusive suppression function, SD(Λ). (d) The MFP distribution in the porous material. The maximum allowed MFP is around 30 nm, i.e., the phonon neck represented by the pore–pore distance.



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