Decomposition of coherent and incoherent phonon conduction in superlattices and random multilayers (original) (raw)
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Phonon thermal conductivity by non-local non-equilibrium molecular dynamics
arXiv: Materials Science, 2014
Non-equilibrium (NE) molecular dynamics (MD), or NEMD, gives a "direct" simulation of thermal conductivity kappa. Heat H(x) is added and subtracted in equal amounts at different places x. After steady state is achieved, the temperature T(x) is found by averaging over finite sections. Usually the aim is to extract a value of dT/dx from a place distant from sources and sinks of heat. This yields an effective kappa(L) for the thermal conductivity, L being the system size. The result is then studied as a function of L, to extract the bulk limit kappa. Here instead, our heat is H(x)~sin(qx), where q=2pi/L. This causes a steady-state temperature T_0 + Delta T sin(2pi x/L). A thermal conductivity kappa(q) is extracted, which is well converged at the chosen q (or L). Bulk conductivity kappa requires taking the q to 0 limit. The method is tested for liquid and crystalline argon. One advantage is reduced computational noise at a given total MD run time. Another advantage is that kap...
We demonstrate the existence of a coherent transport of thermal energy in superlattices by introducing a microscopic definition of the phonon coherence length. A criterion is provided to distinguish the coherent transport regime from diffuse interface scattering and discuss how these can be specifically controlled by several physical parameters. Our approach provides a convenient framework for the interpretation of previous thermal conductivity measurements and calculations; it also paves the way for the design of a new class of thermal interface materials.
Coherent Phonon Heat Conduction in Superlattices
Science, 2012
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Size effects in thermal conduction by phonons
Physical Review B, 2014
Heat transport in nanoscale systems is both hard to measure microscopically, and hard to interpret. Ballistic and diffusive heat flow coexist, adding confusion. This paper looks at a very simple case: a nanoscale crystal repeated periodically. This is a popular model for simulation of bulk heat transport using classical molecular dynamics (MD), and is related to transient thermal grating experiments. Nanoscale effects are seen in perhaps their simplest form. The model is solved by an extension of standard quasiparticle gas theory of bulk solids. Both structure and heat flow are constrained by periodic boundary conditions. Diffusive transport is fully included, while ballistic transport by phonons of long mean free path is diminished in a specific way. Heat current J(x) and temperature gradient ∇T (x) have a non-local relationship, via κ(x − x), over a distance |x − x | determined by phonon mean free paths. In MD modeling of bulk conductivity, finite computer resources limit system size. Long mean free paths, comparable to the scale of heating and cooling, cause undesired finite-size effects that have to be removed by extrapolation. The present model allows this extrapolation to be quantified. Calculations based on the Peierls-Boltzmann equation, using a generalized Debye model, show that extrapolation involves fractional powers of 1/L. It is also argued that heating and cooling should be distributed sinusoidally (ė ∝ cos(2πx/L)) to improve convergence of numerics.
2009
Phonon transport in superlattices is investigated using anharmonic and quasi-harmonic lattice dynamics calculations. Within the lattice dynamics framework, we develop a method for predicting the properties of both coherent and incoherent phonons. The method is implemented for test systems consisting of Stillinger-Weber silicon-germanium superlattices. In these systems the mode dependent frequencies, heat capacities, group velocities, transmission coefficients, and relaxation times of the phonons are computed and used to predict the thermal conductivity. We relate changes in the superlattice structure (e.g., period length and interface roughness) to the predicted phonon properties and, for each structure, identify the phonon modes that dominate thermal transport.
Computer Physics Communications
MCBTE solves the linearized Boltzmann transport equation for phonons in three-dimensions using a variance-reduced Monte Carlo solution approach. The algorithm is suited for both transient and steady-state analysis of thermal transport in structured materials with size features in the nanometer to hundreds of microns range. The code is portable and integrated with both first-principles density functional theory calculations and empirical relations for the input of phonon frequency, group velocity, and mean free path required for calculating the thermal properties. The program outputs spaceand time-resolved temperature and heat flux for the transient study. For the steady-state simulations, the frequency-resolved contribution of phonons to temperature and heat flux is written to the output files, thus allowing the study of cumulative thermal conductivity as a function of phonon frequency or mean free path. We provide several illustrative examples, including ballistic and quasi-ballistic thermal transport, the thermal conductivity of thin films and periodic nanostructures, to demonstrate the functionality and to benchmark our code against available theoretical/analytical/computational results from the literature. Moreover, we parallelize the code using the Mat-* Corresponding author.
Monte Carlo Simulation of Steady-State Microscale Phonon Heat Transport
Journal of Heat Transfer, 2008
Heat conduction in submicron crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The Monte Carlo method is effective in computing the solution of the BTE. These past years, transient Monte Carlo simulations have been developed, but they are generally memory demanding. This paper presents an alternative Monte Carlo method for analyzing heat conduction in such materials. The numerical scheme is derived from past Monte Carlo algorithms for steady-state radiative heat transfer and enables us to understand well the steady-state nature of phonon transport. Moreover, this algorithm is not memory demanding and uses very few iteration to achieve convergence. It could be computationally more advantageous than transient Monte Carlo approaches in certain cases. Similar to the famous Mazumder and Majumdar's transient algorithm (2001, "Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization," ASME J. Heat Transfer, 123, pp. 749-759), the dual polarizations of phonon propagation, the nonlinear dispersion relationships, the transition between the two polarization branches, and the nongray treatment of phonon relaxation times are accounted for. Scatterings by different mechanisms are treated individually, and the creation and/or destruction of phonons due to scattering is implicitly taken into account. The proposed method successfully predicts exact solutions of phonon transport across a gallium arsenide film in the ballistic regime and that across a silicon film in the diffusion regime. Its capability to model the phonon scattering by boundaries and impurities on the phonon transport has been verified. The current simulations agree well with the previous predictions and the measurement of thermal conductivity along silicon thin films and along silicon nanowires of widths greater than 22 nm. This study confirms that the dispersion curves and relaxation times of bulk silicon are not appropriate to model phonon propagation along silicon nanowires of 22 nm width.
Physical Review B, 2010
We use classical molecular dynamics to evaluate the thermal conductivity ͑T͒ from the heat-flux correlation ͗j͑0͒j͑t͒͘ for a two-dimensional Lennard-Jones triangular lattice. Our work, which follows Ladd, Moran, and Hoover ͓Phys. Rev. B 34, 5058 ͑1986͔͒, finds large deviations from the Eucken-Debye result ͑T͒ = A / T predicted by the phonon-gas model, even though phonon quasiparticles are fairly well defined. The main source of deviations comes from higher order ͑anharmonic͒ terms in the heat-flux operator j. By separating different orders of terms j = j ͑2͒ + j ͑3͒ +¯, we examine various separate contributions to ͑T͒Ϸ 22 + 23 +¯, both from the harmonic and the anharmonic heat fluxes. We find that 22 ͑T͒ϷA / T follows quasiparticle theory fairly well but important terms from 23 and 24 are independent of T in the classical ͑high T͒ limit. We use diagrammatic perturbation theory applied to the quantum Kubo formula, to check and explain the T dependence found numerically from anharmonic heat fluxes. We also demonstrate the importance of vertex correction in obtaining the correct quasiparticle coefficient of 1 / T.
Non-local phonon thermal conductivity and the ballistic to diffusive crossover
arXiv: Materials Science, 2016
The local Fourier relation between heat current to temperature gradient, J = -kdT/dr, does not hold on length scales shorter than carrier mean free paths. In insulating crystals, long phonon mean free paths enhance nonlocality of the kernel k(r,r') that relates a steady state heat current J(r) to remote temperature gradients dT(r')/dr'. If the system is spatially homogeneous, k(r,r') = k(r-r'), and in Fourier space, J(q) = -k(q)dT(q)/dr. A local relation has k(q) independent of q, or k(r-r')~delta(r-r'). In nanoscale systems, nonlocality, or equivalently, mixed ballistic/diffusive behavior, complicates heat transfer. Non-local information is starting to be measurable by modern sub-micron imaging methods. This paper derives the formula for k(q) from the Peierls-Boltzmann equation (PBE). There is a given applied thermal power P(k)=ikJ(k), which acts as a source term in the PBE. A new specific form of this source term is presented. Closed form results are ob...