Phonon interference and thermal conductance reduction in atomic-scale metamaterials

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Phonon interference and thermal conductance reduction in atomic-scale metamaterials

Haoxue Han, Lyudmila G. Potyomina, Alexandre A. Darinskii, Sebastian Volz, and Yuriy A. Kosevich

Phys. Rev. B 89, 180301(R) – Published 21 May 2014

Abstract

We introduce and model a three-dimensional (3D) atomic-scale phononic metamaterial producing two-path phonon interference antiresonances to control the heat flux spectrum. We show that a crystal plane partially embedded with defect-atom arrays can completely reflect phonons at the frequency prescribed by masses and interaction forces. We emphasize the predominant role of the second phonon path and destructive interference in the origin of the total phonon reflection and thermal conductance reduction in comparison with the Fano-resonance concept. The random defect distribution in the plane and the anharmonicity of atom bonds do not deteriorate the antiresonance. The width of the antiresonance dip can provide a measure of the coherence length of the phonon wave packet. All our conclusions are confirmed both by analytical studies of the equivalent quasi-1D lattice models and by numerical molecular dynamics simulations of realistic 3D lattices.

Received 12 December 2013
Revised 29 April 2014

DOI:https://doi.org/10.1103/PhysRevB.89.180301

Authors & Affiliations

Haoxue Han^1,2, Lyudmila G. Potyomina³, Alexandre A. Darinskii⁴, Sebastian Volz^1,2, and Yuriy A. Kosevich^1,2,5,*

¹CNRS, UPR 288 Laboratoire d'Energétique Moléculaire et Macroscopique, Combustion (EM2C), Grande Voie des Vignes, 92295 Châtenay-Malabry, France
²Ecole Centrale Paris, Grande Voie des Vignes, 92295 Châtenay-Malabry, France
³Department of Physics and Technology, National Technical University “Kharkiv Polytechnic Institute”, Frunze Street 21, Kharkiv 61002, Ukraine
⁴Institute of Crystallography, Russian Academy of Sciences, Leninskii Avenue 59, Moscow 119333, Russia
⁵Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygin Street 4, Moscow 119991, Russia

^*Corresponding author: yukosevich@gmail.com

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Issue

Vol. 89, Iss. 18 — 1 May 2014

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Images

Figure 1
(a) A phononic metamaterial with a FCC lattice containing a defect plane in which an impurity-atom array is embedded. The red and blue curve refer to the phonon path through the impurity atom bonds and through the host atom bonds, respectively. The presence of the two possible phonon paths can result in the “two-path phonon interference” antiresonance. The brown atoms are defect atoms and the green ones are the atoms of the host lattice. (b) The defect atoms have a periodic distribution with $f_{d} = 50 %$ . Randomly distributed defect atoms with (c) $f_{d} = 37.5 %$ and (d) 25 $%$ in the defect plane.
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Figure 2
Spectra of phonon energy transmission coefficient predicted by equivalent quasi-1D model (solid and dashed lines) and by MD simulations (symbols) of a 3D Ar metamaterial with planar defect containing heavy impurities, with mass $m = 3 m_{0}$ . Dashed-dotted line is the convolution of $α (ω)$ in Eq. (1) with a Gaussian WP with $l = 2 λ_{c}$ . Red, blue, and yellow symbols represent transmission of WP with $l = 20 λ_{c}$ through the two paths, one path with a single and two successive layers of defect atoms, respectively; green symbols represent transmission of WP with $l = 2 λ_{c}$ through two paths. Inset: Three possible quasi-1D lattice models describing phonon propagation through the lattice region containing the local defect. Black sticks between the atoms represent atom bonds. In the case of the Ar lattice, the coefficients in Eq. (1) are $ω_{R} = 1.0$ , $ω_{T} = 1.4$ , $ω_{\max} = 2.0$ , and $C = 0.25$ .
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Figure 3
(a) Spectra of phonon transmission coefficient $α$ of longitudinal acoustic mode in the phononic metamaterial, which consists of 2D array of periodically alternating isotopes with different mass ratio (MR) $m / m_{0}$ with $f_{d} = 50 %$ in a 3D Ar lattice. Black squares refer to $f_{d} = 100 %$ in the defect plane in comparison with the $f_{d} = 50 %$ case. Dashed lines are a guide to the eye. (b) Isotopic shift of the two-path phonon interference resonance versus the mass ratio $m / m_{0}$ . Symbols present the resonances from MD simulations of a 3D lattice and solid line shows the analytical prediction of the equivalent quasi-1D lattice model given by Eq. (2).
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Figure 4
(a) The temperature-dependent interfacial thermal conductance in a 3D Ar lattice across a defect plane $50 %$ -filled with periodic array of impurities (rectangles), a uniform defect plane with (pentagons) and without (circles) the second phonon path induced by non-nearest-neighbor bonds, in comparison with that of an atomic plane without defects (hexagons). (b) $α (ω)$ for a uniform defect plane with (pentagons) and without (circles) the second phonon path.
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Figure 5
(a) Two-path phonon interference antiresonance for both longitudinal and transverse phonons across a segregated Ge-defect layer (red squares and blue circles) plotted along with the nonresonant transmission across the uniform Ge-defect layer (open squares and circles) in a Si phononic metamaterial. (b) Evolution of the reflection resonance versus the increasing wave amplitude. (c) $α (ω)$ for a defect layer containing randomly dispersed Ge atoms with $f_{d} = 37.5 %$ and $25 %$ , compared with that of a defect layer containing $50 %$ of periodically alternating Ge atoms. The measured $α (ω)$ were averaged over different random distributions. (d) Resonance dip broadening in the limit of small filling fraction $f_{d} = 5 %$ for WP with a short coherence length ( $l = λ_{c}$ and $l = 2 λ_{c}$ , yellow and orange circles), in comparison with that of almost plane-wave WP ( $l = 20 λ_{c}$ , green circles).
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