Nat. We show the phonon lifetimes (q)=[(q)s]1 as a function of the energy (q)s for La2Zr2O7 [at a temperature of 200K (a), 800K (b), and 1300K (c)], and for CsPbBr3 [at a temperature of 50K (d), 225K (e), and 350K (f)]. In crystals, heat carriers propagate and scatter particlelike as described by Peierlss formulation of the Boltzmann transport equation for phonon wave packets. Going over to a Fokker-Planck description, we Boltzmann Phonon mean free paths (MFP) in La2Zr2O7 and CsPbBr3. Improved Callaway model for lattice thermal conductivity. (b) Numerical results for the spatial distribution of heat flux deviation, plotted in logarithmic scale \(\mathrm{lg}|({\boldsymbol{q}}-{{\boldsymbol{q}}}_{0})/{\boldsymbol{q}}|\). The coherences conductivities (Cxx) are blue. Phys. This research project contributed to the state-of-the-art in two ways: (1) by developing and demonstrating a calibration-free simple methodology to compute intrinsic phonon scattering (Normal and Umklapp processes) time scales with the inclusion of optical phonons, and (2) by developing a suite of numerical algorithms for solution of the BTE for phonons. On the other hand, when \(\eta \) is negligible, we recover the normal diffusive heat transport governed by Fourier law. impurities. This item is part of a JSTOR Collection. Morelli, D. T.; Heremans, J. P.; Slack, G. A. Fugallo, Giorgia; Lazzeri, Michele; Paulatto, Lorenzo, Fan, Xiaofeng; Zheng, W. T.; Kuo, Jer-Lai. Both normal (N) and resistive (R) scattering processes conserve total energy, giving, while only the N-process obeys crystal momentum conservation, giving, To get the equation governing the dynamics of the conserved quantity, we multiply by \(\hslash {\omega }_{s{\bf{k}}}\), integrate over k and sum over the phonon index on both sides of Eq. This paper elucidates how quantum wave-particle duality emerges in thermal transport, discussing how particlelike and wavelike heat-transport mechanisms can emerge and coexist, and providing a quantitative criterion to assess their relative strength and the crossover between the regimes where one or the other dominates. The quadratic dispersion of ZA modes have frequency dependent phonon group velocity, i.e., \({v}_{g}\propto k\), and k-independent constant density of states. Effect of the phase convention on the thermal conductivity of La2Zr2O7. the first step, we determine the corresponding MEP projector so that, for any given , there holds. Phys. 12, we have solved Eq. The inclusion of quadratic phonon mode changes its coefficients. We illustrate the general method of Chapman Our results also illustrate the universal transport behaviors of hydrodynamics, independent of the type of quasi-particles and their microscopic interactions. CAS Vibrational properties and heat conduction mechanisms in La2Zr2O7. All the three transport coefficients can be divided into contributions from the linear and quadratic phonon modes, respectively. 105, Issue 10, Journal of Applied Physics, Vol. Black, total conductivity from Eq. Nucl. (a)Group velocity of acoustic modes in graphene. WebThe purpose of this note is to clarify the solution of the non-local Peierls Boltzmann equation found by Hua and Lindsay (Phys. (a) 24, 1163, https://doi.org/10.1002/pssa.2210240102 (1974). VanGessel, Francis; Peng, Jie; Chung, Peter W. Yang, Xiuxian; Dai, Zhenhong; Zhao, Yinchang, Smith, Brandon; Lindsay, Lucas; Kim, Jaehyun, Pandey, Tribhuwan; Polanco, Carlos A.; Lindsay, Lucas, Simoncelli, Michele; Marzari, Nicola; Cepellotti, Andrea, DeAngelis, Freddy; Muraleedharan, Murali Gopal; Moon, Jaeyun, Plata, Jose J.; Nath, Pinku; Usanmaz, Demet, Yuan, Kunpeng; Sun, Zhehao; Zhang, Xiaoliang, - Physical Review. The heat current flow within the ribbon can be obtained from the solutions. : Condens. 120, Issue 2, Physical Review Letters, Vol. They acknowledge financial support from National Natural Science Foundation of China (Grant No. Jackson, H. E., Walker, C. T. & McNelly, T. F. Second sound in naf. The yellow region below the Ioffe-Regel limit represents overdamped phonons, which require full spectral-function approaches [78, 79] to be described correctly. Use of the American Physical Society websites and journals implies that 1(c). The 1st term on the left hand side (LHS) is the hydrodynamic term due to viscosity. In this scenario, bulk thermal conductivity values, which are experimentally determined by inversion of the Fourier law itself, cannot be used for analysis. 1(c). B 102, This is the case for the Debye model. We discuss the conditions determining the relative strength of particlelike and wavelike conduction mechanisms, showing that in the intermediate case of complex crystals with ultralow thermal conductivity these can be equally relevant. A.; Simak, S. I. Regner, Keith T.; Sellan, Daniel P.; Su, Zonghui, Cepellotti, Andrea; Fugallo, Giorgia; Paulatto, Lorenzo. Weathers, Annie; Carrete, Jess; DeGrave, John P. Mizokami, Keiyu; Togo, Atsushi; Tanaka, Isao, Fugallo, Giorgia; Rousseau, Benoit; Lazzeri, Michele. 54, Issue 2, Physical Review, Vol. (24) leads to divergent result. Article Going over to a Fokker-Planck description, we construct a self-consistent expansion around a model evolution equation. Boltzmann equation We consider the same ribbon at the same average temperature (\({T}_{0}=100\) K) as in Fig. Sellitto, A., Carlomagno, I. Lee, S., Broido, D., Esfarjani, K. & Chen, G. Hydrodynamic phonon transport in suspended graphene. 1 of Ref. Phys. WebThese data can be used with the Peierls- Boltzmann transport equation to calculate a spectral TC by 2469-9950/2021/103(20)/205421(11) 205421-1 2021 American Physical Society (1) there are two collision operators and which are simplified models of two different kinds of
Within the same expansion we obtain an equation for that function too. path of the traveling phonons is larger than the film thickness, thermodynamic equilibrium ceases to exist, and thus, the Fourier law of heat conduction is invalid. Rev. Phys. J. Zhaoli Guo or Jing-Tao L. Thermal Conductivity, Second Sound, and Phonon Hydrodynamic Phenomena in Nonmetallic. Phys. Since its inception nearly a decade ago, first-principles thermal transport has vastly expanded the range of materials examined, altered our physical intuition of phonon interactions and transport behaviors, provided deeper understanding of experiments, and accelerated the design of materials, Predictive methodologies for calculating lattice thermal transport and related properties have been recently developed and benchmarked successfully against measurements in a wide range of materials, from bulk to the nanoscale. Three regimes can be distinguished in a diagram reporting the phonon lifetime () as a function of the phonon frequency (). Ackerman, C. C., Bertman, B., Fairbank, H. A. Rev. 3(d)) directions, respectively. Restricting calculations to first-order perturbation approaches can overestimate optic phonon scattering rates by nearly three orders of magnitude. 4, Issue 4, Applied Physics Letters, Vol. Wang, J.-S., Wang, J. B 92, 115426, https://doi.org/10.1103/PhysRevB.92.115426 (2015). & Krumhansl, J. Phys. Bowker, New Providence, New Jersey The resulting equation has the form, It shares the same form as the electronic case in ref. C.Z. 10,11. 124, Issue 16, Journal of Applied Physics, Vol. the user has read and agrees to our Terms and Machida, Y. et al. 148, 778788, https://doi.org/10.1103/PhysRev.148.778 (1966). 2004 Society for Industrial and Applied Mathematics Exp(L), Exp(M), and Exp(S) refer to measurements [111] of xx in nanowires having, respectively, sections of 800380, 320390, and 300160nm2: their broad agreement supports the hypothesis of negligible finite-size boundary scattering [111]. [184]. We can also write \({\kappa }_{0}=\alpha C{v}_{g}^{2}{\tau }_{R}\), \(\eta =\beta {v}_{g}^{2}{\tau }_{N}\), \(\zeta =\alpha {v}_{g}^{2}{\tau }_{N}\), respectively, where \(\alpha ={C}_{L}/C\), \(\beta =9{E}_{L}\mathrm{/(8}\bar{E})\), with \(\bar{E}=\frac{3}{2}{E}_{L}+2{E}_{N}\). 1(b)]. 99, Issue 17, Physica B: Condensed Matter, Vol. 126, Issue 5, Nanoscale and Microscale Thermophysical Engineering, Vol. B 94, 155414, https://doi.org/10.1103/PhysRevB.94.155414 (2016). 12, 672676, https://doi.org/10.1038/nphys3667 (2016). In the meantime, to ensure continued support, we are displaying the site without styles 1(c), with the same dimensionless parameter . 112, Issue 17, Journal of Physics: Condensed Matter, Vol. The negative sign means heat flows opposite to the temperature gradient. On the right-hand side of
These equations can normally be derived from the microscopic equations of motion by considering physical quantities that are conserved during the inter-particle collisions, i.e., (crystal) momentum, energy or particle number. [106], Vassen etal. Rev. Phys. We take into account the out of plane quadratic phonon dispersion of the ZA mode, normally present in 2D materials. Phys. Google Scholar. The right hand side of Eq. Due to these limitations, studies on the hydrodynamic transport of quasi-particles in solid state system are scarce. international association for applied mathematics, and its publications Phys. Phonon Hydrodynamic Heat Conduction and Knudsen Minimum in Graphite. Model. In 1929, Peierls formulated the phonon Boltzmann transport equation to explain heat conduction in crystalline solids, discussing how quantized atomic vibrations mediated heat transport. Rev. One of the Bandurin, D. A. et al. At 200K (a)La2Zr2O7 is a simple crystal with interband spacings larger than the linewidths and PkC, while at 1300K it is a complex crystal with interband spacings smaller than the linewidths and PkC. CAS Rev. fails to describe heat conduction at low temperatures, where the evolution
Kinetic solutions of the Boltzmann-Peierls equation and its moment 71, 111, https://doi.org/10.1016/j.apm.2019.01.016 (2019). Shang, MY., Zhang, C., Guo, Z. et al. The results are plotted in Fig. The Einstein-Smoluchowski promeasure versus the Boltzmann Similar behavior of electrons in graphene and other 2D materials has received intense research focus very recently4,5,6,9,22,51. This is the so-called gray approximation. The points close to the diagonal 12 correspond to quasidegenerate vibrational eigenstates; the Allen-Feldman framework considers couplings only between these. The horizontal red lines show the mean square displacements (MSD) of the atoms. For quantitative analysis of specific materials, one needs to go beyond the gray approximation and consider the wave vector and branch dependence of \(\tau \), which is beyond the scope of present study. 117, Issue 2, Physica Status Solidi (a), Vol. SIAM Journal on Applied Mathematics 23, Issue 2, npj Computational Materials, Vol. Recently, it has been shown that these two conduction mechanisms emerge from a Wigner transport equation, which unifies and extends the Peierls-Boltzmann and Allen-Feldman formulations, allowing one to describe also complex crystals where particlelike and wavelike conduction mechanisms coexist. Google Scholar. The x and y directions are also shown. refer to [4] and [5]. Collision-dominated nonlinear hydrodynamics in graphene. Rev. The relative difference is rather small away from the two boundaries, especially around the vortices. You are using a browser version with limited support for CSS. In particular, calculations of interatomic force constants, integration methods, and construction. We show that our G-K equation can reasonably re-produce the main features of the hydrodynamic heat flow that we focus in this work. Li, X. 2023 American Physical Society. The suite of numerical algorithms includes Monte Carlo techniques and deterministic techniques based on the Discrete Ordinates Method and the Ballistic-Diffusive approximation of the BTE. While the ballistic phonon transport takes place in nanoscale ribbons, the hydrodynamic transport takes place in the microscale (See below for the estimation of length scale in graphene). The Peierls-Boltzmann transport equation for phonons is re-formulated and modified by means of sequences of transport and statistical postulates. It can be checked that, our results reduce to that of Debye model if we ignore the quadratic phonon mode. B 97, 094309, https://doi.org/10.1103/PhysRevB.97.094309 (2018). Here non-local thermal conductance/resistance means the temperature difference and the induced heat current (or vice versa) are separated in real space. Publishers note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The total conductivity (black) is given by the sum tot=P+C. Heat vortex in hydrodynamic phonon transport of two-dimensional materials. Green, Peierlss LBTE conductivity (P), which displays the universal T1 asymptotics (dashed line). Internet Explorer). In order to formulate better heat removal strategies and designs, it is first necessary to understand the fundamental mechanisms of heat transport in semiconductor thin films. Request Permissions, Published By: Society for Industrial and Applied Mathematics, Society for Industrial and Applied Mathematics. Macroscopic collective behavior emerges from microscopic many-body interactions between individual degrees of freedom comprising the system. and conserve the energy as well as the momentum, while the
Turkyilmazoglu, M. Latitudinally deforming rotating sphere. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Observation of second sound in graphite at temperatures above 100 k. Science 364, 375379, https://doi.org/10.1126/science.aav3548 (2019). The right side (RHS) of the G-K equation represents the effect of viscosity on the heat transport behavior. the university and industry smoother. Following ref. (33), we have considered only the zeroth order term of the heat current q. (c) Heat current loops (lines) and temperature distribution (color) due to the viscosity of the phonon gas as a signature of hydrodynamic heat transport. Thus, the cubic (super-linear) dependence of I on w can in principle be used as a signature of the Poiseuille flow. wrote the paper. and J.T.L. MATH Turkyilmazoglu, M. MHD natural convection in saturated porous media with heat generation/absorption and thermal radiation: closed-form solutions. Ballistic to diffusive crossover of heat flow in graphene ribbons. Lett. Heat current source and drain are attached to a graphene nano-ribbon. Here, the presence of quadratic dispersion makes vss temperature dependent, inherited from the different temperature dependence of CL and CN [see Fig. For electron transport, negative non-local resistance4, violation of Wiedemann-Franz law5 and large negative magnetoresistance21 have been experimentally observed and theoretically explained12,22,24,25,26. & L, J.-T. Quantum thermal transport in nanostructures.