Narrow Low-Frequency Spectrum and Heat Management by Thermocrystals

By transforming heat flux from particle to wave phonon transport, we introduce a new class of engineered material to control thermal conduction. We show that rationally designed nanostructured alloys can lead to a fundamental new approach for thermal management, guiding heat as photonic and phononic crystals guide light and sound, respectively. Novel applications for these materials include heat waveguides, thermal lattices, heat imaging, thermo-optics, thermal diodes, and thermal cloaking.

Figure 1

Cumulative $\kappa$ as a function of frequency for (a) ${\mathrm{Si}}_{90}{\mathrm{Ge}}_{10}$ and (b) nanoparticle ${\mathrm{Si}}_{90}{\mathrm{Ge}}_{10}$. Blue lines correspond to bulk materials and red lines to thin film samples with thicknesses $t=1000$, 100, and $10\mu \mathrm{m}$, respectively. The cumulative $\kappa$ for bulk silicon is shown as reference. For ${\mathrm{Si}}_{90}{\mathrm{Ge}}_{10}$, $\kappa =20$, 18, 14, and $10\mathrm{W}/(\mathrm{m}°\mathrm{K})$ for bulk, $t=1000$, 100, and $10\mu \mathrm{m}$, respectively. For nanoparticle ${\mathrm{Si}}_{90}{\mathrm{Ge}}_{10}$, the numbers are $\kappa =7$, 5, 3.7, and $2.5\mathrm{W}/(\mathrm{m}°\mathrm{K})$.

Figure 2

(a) and (b) Yellow areas show the frequency gaps corresponding to the films patterned with a square arrangement of air cylinders (S1) [18] and with a complex but more effective design (S2) [35]. The lattice constants are 10 nm (right) and 20 nm (left). (c) Schematic of a thermocrystal made of a periodic array of air cylinders patterned on a nanostructured alloy film. (d) The corresponding phononic band diagram for a thermocrystal made of nanoparticle ${\mathrm{Si}}_{90}{\mathrm{Ge}}_{10}$ with cylinder radius $r/a=0.48$, where phonon frequencies are plotted versus the wave vector $\mathbf{k}$. The thermocrystals are designed such that the gap frequencies (yellow area) correspond to heat modes.

Figure 3

Schematics for thermocrystals opportunities and challenges (a) Heat waveguides: A waveguide is created in a triangular lattice of air rods (white). Hypersonic heat modes (yellow) can be guided along the channel. Color scheme shows the displacement field for a hypersonic wave propagating in the waveguide. (b) Thermal lattices: Point defects are introduced in a square lattice of air rods (black) [18]. Hypersonic heat modes can be localized around the defects. Color scheme shows time averaged displacement fields for confined modes. (c) Heat imaging: Schematic of a heat source and its image across a thermocrystal superlense. Negative refracted [37] hypersonic beams (black arrows) focus the point source (yellow) located on one side of the lens into a real image on the other side. (d) Thermo-optics: A point defect in a thermocrystal (missing cylinder) can localize both light and hypersonic heat modes and enhance light-heat interactions. Color scheme shows time averaged fields for localized photon (left) and phonon (right) modes. (e) Thermal diode: Schematic of a diode made of a diffraction structure and a periodic array of cylinders [42]. Hypersonic heat modes from the right have smaller transmission than those from the left. The system can provide thermal rectification through nonreciprocal phonon propagation. (f) Thermal cloaking: Acoustic pressure field for a cylindrical scatterer surrounded by a cloaking shell (adapted from Ref. 43). The development of metamaterials for elastic waves can lead to low temperature thermal cloaking.