Boundary scattering of thermal phonons in thin solid films is typically analyzed using Fuchs-Sondheimer theory, which provides a simple equation to calculate the reduction of thermal conductivity as a function of the film thickness. However, this widely used equation is not applicable to highly anisotropic solids like graphite because it assumes the phonon dispersion is isotropic. Here, we derive a generalization of the Fuchs-Sondheimer equation for solids with arbitrary dispersion relations and examine its predictions for graphite. We find that the isotropic equation vastly overestimates the boundary scattering that occurs in thin graphite films due to the highly anisotropic group velocity, and that graphite can maintain its high in-plane thermal conductivity even in thin films with thicknesses as small as 10 nm.
This content will become publicly available on February 19, 2025
Nanocrystalline silicon can have unique thermal transport and mechanical properties governed by its constituent grain microstructure. Here, we use phonon ray-tracing and molecular dynamics simulations to demonstrate the largely tunable thermomechanical behaviors with varying grain sizes (a0) and aspect ratios (ξ). Our work shows that, by selectively increasing the grain size along the heat transfer direction while keeping the grain area constant, the in-plane lattice thermal conductivity (kx) increases more significantly than the cross-plane lattice thermal conductivity (ky) due to anisotropic phonon–grain boundary scattering. While kx generally increases with increasing ξ, a critical value exists for ξ at which kx reaches its maximum. Beyond this transition point, further increases in ξ result in a decrease in kx due to substantial scattering of low-frequency phonons with anisotropic grain boundaries. Moreover, we observe reductions in the elastic and shear modulus with decreasing grain size, and this lattice softening leads to significant reductions in phonon group velocity and thermal conductivity. By considering both thermal and mechanical size effects, we identify two distinct regimes of thermal transport, in which anisotropic phonon–grain boundary scattering becomes more appreciable at low temperatures and lattice softening becomes more pronounced at high temperatures. Through phonon spectral analysis, we attribute the significant thermal conductivity anisotropy in nanograined silicon to grain boundary scattering of low-frequency phonons and the softening-driven thermal conductivity reduction to Umklapp scattering of high-frequency phonons. These findings offer insights into the manipulation of thermomechanical properties of nanocrystalline silicon via microstructure engineering, carrying profound implications for the development of future nanomaterials.
more » « less- Award ID(s):
- 1935371
- PAR ID:
- 10541837
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 124
- Issue:
- 8
- ISSN:
- 0003-6951
- Subject(s) / Keyword(s):
- Molecular dynamics Thermal conductivity Thermal transport Thermomechanical analysis Nanomaterials
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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