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The best nanoparticle size distribution for minimum thermal conductivity.

Zhang H, Minnich AJ - Sci Rep (2015)

Bottom Line: Nanoparticles have long been demonstrated to reduce the thermal conductivity of crystals by scattering phonons, but most previous works assumed the nanoparticles to have a single size.Here, we use optimization methods to show that the best nanoparticle size distribution to scatter the broad thermal phonon spectrum is not a similarly broad distribution but rather several discrete peaks at well-chosen nanoparticle radii.For SiGe, the best size distribution yields a thermal conductivity below that of amorphous silicon.

View Article: PubMed Central - PubMed

Affiliation: Division of Engineering and Applied Science California Institute of Technology Pasadena,CA 91125.

ABSTRACT
Which sizes of nanoparticles embedded in a crystalline solid yield the lowest thermal conductivity? Nanoparticles have long been demonstrated to reduce the thermal conductivity of crystals by scattering phonons, but most previous works assumed the nanoparticles to have a single size. Here, we use optimization methods to show that the best nanoparticle size distribution to scatter the broad thermal phonon spectrum is not a similarly broad distribution but rather several discrete peaks at well-chosen nanoparticle radii. For SiGe, the best size distribution yields a thermal conductivity below that of amorphous silicon. Further, we demonstrate that a simplified distribution yields nearly the same low thermal conductivity and can be readily fabricated. Our work provides important insights into how to manipulate the full spectrum of phonons and will guide the design of more efficient thermoelectric materials.

No MeSH data available.


(a) Reduction in thermal conductivity per change in volume fraction of Ge, /dk/dx/, for various particle radii (R = 0.272 nm, 0.816 nm and 1.632 nm). The reduction in thermal conductivity achieved by adding more Ge defects decreases rapidly with increasing Ge concentration (b) Scattering rate of phonons by nanoparticles as a function of phonon frequency. Each circle indicates a particular phonon mode in the Brillouin zone from the DFT dispersion. Nanoparticles scatter phonons most effectively within a specific range of phonon frequencies. The Ge concentration for each radius is 1%.
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f3: (a) Reduction in thermal conductivity per change in volume fraction of Ge, /dk/dx/, for various particle radii (R = 0.272 nm, 0.816 nm and 1.632 nm). The reduction in thermal conductivity achieved by adding more Ge defects decreases rapidly with increasing Ge concentration (b) Scattering rate of phonons by nanoparticles as a function of phonon frequency. Each circle indicates a particular phonon mode in the Brillouin zone from the DFT dispersion. Nanoparticles scatter phonons most effectively within a specific range of phonon frequencies. The Ge concentration for each radius is 1%.

Mentions: To explain the observation of peaks in the optimal size distribution, we examine the response of the thermal conductivity as we progressively increase the mass defect concentration for a single nanoparticle size. Mathematically, we can express this quantity as /dk/dx/, or the change in thermal conductivity per increase in x. Figure 3a shows /dk/dx/ as function of x for nanoparticles of three different radii, based on the DFT dispersion. We observe that for given nanoparticles with fixed radius, the initial addition of nanoparticles results in a large drop in thermal conductivity, but that the addition of more nanoparticles has less and less of an effect as x increases.


The best nanoparticle size distribution for minimum thermal conductivity.

Zhang H, Minnich AJ - Sci Rep (2015)

(a) Reduction in thermal conductivity per change in volume fraction of Ge, /dk/dx/, for various particle radii (R = 0.272 nm, 0.816 nm and 1.632 nm). The reduction in thermal conductivity achieved by adding more Ge defects decreases rapidly with increasing Ge concentration (b) Scattering rate of phonons by nanoparticles as a function of phonon frequency. Each circle indicates a particular phonon mode in the Brillouin zone from the DFT dispersion. Nanoparticles scatter phonons most effectively within a specific range of phonon frequencies. The Ge concentration for each radius is 1%.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4355732&req=5

f3: (a) Reduction in thermal conductivity per change in volume fraction of Ge, /dk/dx/, for various particle radii (R = 0.272 nm, 0.816 nm and 1.632 nm). The reduction in thermal conductivity achieved by adding more Ge defects decreases rapidly with increasing Ge concentration (b) Scattering rate of phonons by nanoparticles as a function of phonon frequency. Each circle indicates a particular phonon mode in the Brillouin zone from the DFT dispersion. Nanoparticles scatter phonons most effectively within a specific range of phonon frequencies. The Ge concentration for each radius is 1%.
Mentions: To explain the observation of peaks in the optimal size distribution, we examine the response of the thermal conductivity as we progressively increase the mass defect concentration for a single nanoparticle size. Mathematically, we can express this quantity as /dk/dx/, or the change in thermal conductivity per increase in x. Figure 3a shows /dk/dx/ as function of x for nanoparticles of three different radii, based on the DFT dispersion. We observe that for given nanoparticles with fixed radius, the initial addition of nanoparticles results in a large drop in thermal conductivity, but that the addition of more nanoparticles has less and less of an effect as x increases.

Bottom Line: Nanoparticles have long been demonstrated to reduce the thermal conductivity of crystals by scattering phonons, but most previous works assumed the nanoparticles to have a single size.Here, we use optimization methods to show that the best nanoparticle size distribution to scatter the broad thermal phonon spectrum is not a similarly broad distribution but rather several discrete peaks at well-chosen nanoparticle radii.For SiGe, the best size distribution yields a thermal conductivity below that of amorphous silicon.

View Article: PubMed Central - PubMed

Affiliation: Division of Engineering and Applied Science California Institute of Technology Pasadena,CA 91125.

ABSTRACT
Which sizes of nanoparticles embedded in a crystalline solid yield the lowest thermal conductivity? Nanoparticles have long been demonstrated to reduce the thermal conductivity of crystals by scattering phonons, but most previous works assumed the nanoparticles to have a single size. Here, we use optimization methods to show that the best nanoparticle size distribution to scatter the broad thermal phonon spectrum is not a similarly broad distribution but rather several discrete peaks at well-chosen nanoparticle radii. For SiGe, the best size distribution yields a thermal conductivity below that of amorphous silicon. Further, we demonstrate that a simplified distribution yields nearly the same low thermal conductivity and can be readily fabricated. Our work provides important insights into how to manipulate the full spectrum of phonons and will guide the design of more efficient thermoelectric materials.

No MeSH data available.