Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach

Isaeva, Leyla; Barbalinardo, Giuseppe; Donadio, Davide; Baroni, Stefano

doi:10.1038/s41467-019-11572-4

Cited by 172 publications

(194 citation statements)

References 30 publications

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“…These experimental observations have been accompanied by several pioneering efforts aimed at providing a quantitative description of heat hydrodynam-out any fitting parameter, deriving all quantities from first-principles, to accurately describe the thermal properties of many bulk crystals [22,[27][28][29][30][31][32][33][34][35][36], provided phonon branches remain well separated [37,38].…”

Section: Introductionmentioning

confidence: 99%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

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Heat conduction in dielectric crystals originates from the propagation of atomic vibrational waves, whose microscopic dynamics is well described by linearized or generalized phonon Boltzmann transport. Recently, it was shown that the thermal conductivity can be resolved exactly and in a closed form as a sum over relaxons, i.e. the collective phonon excitations that are eigenvectors of Boltzmann equation's scattering matrix [Cepellotti and Marzari, Phys. Rev. X 6, 041013 (2016)]. Relaxons have a well-defined parity and only odd relaxons contribute to the thermal conductivity. Here, we show that the complementary set of even relaxons determines another quantity -the thermal viscosity -that enters into the description of heat transport in the hydrodynamic regime, where dissipation of crystal momentum by Umklapp scattering phases out. We also show how the thermal viscosity and conductivity parametrize two novel viscous heat equations -two coupled equations for the local temperature and drift velocity fields -which represent the thermal counterpart of the Navier-Stokes equations of hydrodynamics in the linear, laminar regime. These viscous heat equations are derived from a coarse-graining of the linearized Boltzmann transport equation for phonons, and encompass both limits of Fourier's law or second sound for strong or weak Umklapp dissipation, respectively. Last, we introduce the Fourier deviation number, a dimensionless parameter that quantifies the steady-state deviations from Fourier's law due to hydrodynamic effects. We showcase these findings in a test case of a complex-shaped device made of silicon or diamond. This formulation generalizes rigorously Fourier's heat equation, and extends the reach of microscopic computational techniques to characterize the fundamental parameters governing heat conduction. * michele.simoncelli@epfl.ch ics. Sussmann and Thellung [12], starting from the linearized BTE (LBTE) in absence of momentumdissipating (Umklapp) phonon-phonon scattering events, derived mesoscopic equations in terms of temperature and phonon drift velocity, the thermal counterpart of pressure and fluid velocity in liquids. Further advances came from Gurzhi [13,14] and Guyer & Krumhansl [15,16] who, including the effect of weak crystal momentum dissipation, obtained equations for damped second sound and Poiseuille heat flow. Among early works, we also mention the discussions on phonon hydrodynamics using approaches different from the LBTE of Refs. [17,18]. While correctly capturing the qualitative features of phonon hydrodynamics, all the theoretical investigations mentioned above are heuristic, e.g. they assume simplified phonon dispersion relations (either power-law [13,14] or linear isotropic [12,15,16]), or neglect momentum dissipation. A more rigorous and general formulation -albeit valid only in the hydrodynamic regime of weak Umklapp scattering -was introduced by Hardy, who extended the discussion of second sound [19] and, together with Albers, of Poiseuille flow in terms of mesoscopic transport equations...

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Section: Introductionmentioning

confidence: 99%

Generalization of Fourier’s Law into Viscous Heat Equations

2020

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“…In simple crystals the thermal conductivity (κ) can be well understood within the phonon-gas model (PGM) 1 . However, for amorphous materials [2][3][4] , defective crystals 5 , anharmonic crystals 6 , and -as we show here -crystals with complex structures, the PGM is incomplete. The thermal conductivity of all solids spans roughly five orders of magnitude ( Figure 1a).…”

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confidence: 58%

“…3.29 to 3.31 of Ref. 12 ), and was recently made tractable in a lattice dynamical context by Simoncelli et al 6 and Isaeva et al 4 . Hardy's heat current operator is commonly used along with the Green-Kubo method to extract κ from molecular dynamics (MD) simulations.…”

Section: Resultsmentioning

confidence: 94%

“…4. The diffuson channel, κ diff represents the diffusion of thermal energy through quasi-degenerate normal modes 4 , or normal mode mixing (also referred to as coherences 6 ). Normal mode mixing and κ diff can be understood through the concept of band folding which we schematically show for one dimension in Figure 1b.…”

Section: Resultsmentioning

confidence: 99%

“…Standard lattice dynamics (LD) (as computed by common computational suites such as phono3py 23 ), by design, only captures the phonon-gas channel. However, as we outline in Figure 1 the two-channel LD approach 4,6 captures vibrational heat conduction beyond the phonon-gas model. One benefit of the two-channel LD framework is that it can provide an intuitive physical picture which can help facilitate predictive materials design.…”

Section: Resultsmentioning

confidence: 99%

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Transition from Crystal-like to Amorphous-like Heat Conduction in Structurally-Complex Crystals

Hanus¹,

George²,

Wood³

et al. 2020

Preprint

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<pre>The physics of heat conduction puts practical </pre><pre>limits on many technological fields such as </pre><pre>energy production, storage, and conversion, as</pre><pre>well as high-power and high-frequency </pre><pre>electronics. Heat conduction in simple, </pre><pre>defect-free crystals is generally well </pre><pre>understood and seems to be well described by </pre><pre>the phonon-gas model (PGM), where phonon </pre><pre>wave-packets are viewed as heat carrying</pre><pre>particles which propagate their mean free </pre><pre>path before being scattered. It is widely</pre><pre>appreciated that the PGM does not describe </pre><pre>the full vibrational spectrum in amorphous </pre><pre>materials, since this picture likely breaks </pre><pre>down at higher frequencies. Furthermore, it </pre><pre>has been shown that the PGM also breaks down </pre><pre>in certain defective and anharmonic crystals,</pre><pre>not only in the amorphous limit. In this work, </pre><pre>in an attempt to bridge our understanding </pre><pre>between crystal-like (described by the PGM)</pre><pre>and amorphous-like heat conduction, we study </pre><pre>structurally-complex crystalline YB14(Mn,Mg)SB11 </pre><pre>experimentally using inelastic neutron </pre><pre>scattering and computationally using a </pre><pre>two-channel lattice dynamical approach. </pre><pre>One channel is the commonly considered PGM, </pre><pre>and the second we call the diffuson-channel </pre><pre>since it is mathematically the same mechanism </pre><pre>through which diffusons were defined. Our </pre><pre>results show that the diffuson-channel </pre><pre>dominates in YB14MnSb11 above 300 K, which is </pre><pre>a champion thermoelectric material above 800 K. </pre><pre>We demonstrate a method for the rational </pre><pre>design of amorphous-like heat conduction by </pre><pre>considering the energetic proximity phonon modes </pre><pre>and modifying them through chemical means.</pre>

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Diffuson‐Dominated and Ultra Defect‐Tolerant Two‐Channel Thermal Transport in Hybrid Halide Perovskites

Cai,

Lin,

Ahmadian‐Yazdi

et al. 2023

Adv Funct Materials

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Organic‐inorganic hybrid halide perovskites show a unique two‐channel thermal transport through propagons and diffusons, largely affecting other energy carriers for opto‐ and thermoelectric applications. Taking CH3NH3PbI3 as a prototype, the impact of iodine vacancy point defects on the two‐channel thermal transport is investigated using theoretical calculations and experimental validations. This work finds that iodine vacancies suppress the thermal transport in the propagon channel significantly, but less in the diffuson channel. This results in a weaker reduction of the total thermal conductivity (TC) than that predicted by the classical Klemens model. The TC reduction in the diffuson channel is mainly attributed to the declined vibrational density of states. Moreover, low‐frequency diffusons transformed from propagons compensate the reduction of TC in the diffuson channel, resulting in a dominant contribution from the diffuson channel to the total TC, which is 55% to 85% for 0% to 6% vacancy concentration. CH3NH3PbI3 also shows ultra‐defect‐tolerant diffusonic thermal transport, ≈1–2 orders of magnitude lower than diamond in the defect sensitivity factor. This work shows both scientific insights into the new two‐channel thermal transport mechanism in complex material systems with disorder, and technological significance on halide perovskites for solar cell, light‐emitting diode, thermoelectric, and memristor applications.

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Modeling heat transport in crystals and glasses from a unified lattice-dynamical approach

Cited by 172 publications

References 30 publications

Generalization of Fourier’s Law into Viscous Heat Equations

Generalization of Fourier’s Law into Viscous Heat Equations

Transition from Crystal-like to Amorphous-like Heat Conduction in Structurally-Complex Crystals

Diffuson‐Dominated and Ultra Defect‐Tolerant Two‐Channel Thermal Transport in Hybrid Halide Perovskites

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