Homogeneous nonequilibrium molecular dynamics method for heat transport and spectral decomposition with many-body potentials

The standard equilibrium Green-Kubo and nonequilibrium molecular dynamics (MD) methods for computing thermal transport coefficients in solids typically require relatively long simulation times and large system sizes. To this end, we revisit here the homogeneous nonequilibrium MD method by Evans [Phys. Lett. A 91, 457 (1982)] and generalize it to many-body potentials that are required for more realistic materials modeling. We also propose a method for obtaining spectral conductivity and phonon mean free path from the simulation data. This spectral decomposition method does not require lattice dynamics calculations and can find important applications in spatially complex structures. We benchmark the method by calculating thermal conductivities of three-dimensional silicon, two-dimensional graphene, and a quasi-one-dimensional carbon nanotube and show that the method is about one to two orders of magnitude more efficient than the Green-Kubo method. We apply the spectral decomposition method to examine the long-standing dispute over thermal conductivity convergence vs. divergence in carbon nanotubes

Heat transport in pristine and polycrystalline single-layer hexagonal boron nitride

We use a phase field crystal model to generate large-scale bicrystalline and polycrystalline single-layer hexagonal boron nitride (h-BN) samples and employ molecular dynamics (MD) simulations with the Tersoff many-body potential to study their heat transport properties. The Kapitza thermal resistance across individual h-BN grain boundaries is calculated using the inhomogeneous nonequilibrium MD method. The resistance displays strong dependence on the tilt angle, the line tension and the defect density of the grain boundaries. We also calculate the thermal conductivity of pristine h-BN and polycrystalline h-BN with different grain sizes using an efficient homogeneous nonequilibrium MD method. The in-plane and the out-of-plane (flexural) phonons exhibit different grain size scalings of the thermal conductivity in polycrystalline h-BN and the extracted Kapitza conductance is close to that of large-tilt-angle grain boundaries in bicrystals

Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon

© 2018 American Physical Society. Molecular dynamics (MD) simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three-dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it to the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity

Energetics and structure of grain boundary triple junctions in graphene

© 2017 The Author(s). Grain boundary triple junctions are a key structural element in polycrystalline materials. They are involved in the formation of microstructures and can influence the mechanical and electronic properties of materials. In this work we study the structure and energetics of triple junctions in graphene using a multiscale modelling approach based on combining the phase field crystal approach with classical molecular dynamics simulations and quantum-mechanical density functional theory calculations. We focus on the atomic structure and formation energy of the triple junctions as a function of the misorientation between the adjacent grains. We find that the triple junctions in graphene consist mostly of five-fold and seven-fold carbon rings. Most importantly, in addition to positive triple junction formation energies we also find a significant number of orientations for which the formation energy is negative

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

Two-dimensional materials have unusual phonon spectra due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components, corresponding to in-plane and out-of-plane phonon dynamics, respectively. This decomposition allows for direct computation of the corresponding thermal conductivity components in two-dimensional materials. We apply this decomposition to study heat transport in suspended graphene, using both equilibrium and nonequilibrium molecular dynamics simulations. We show that the flexural component is responsible for about two-thirds of the total thermal conductivity in unstrained graphene, and the acoustic flexural component is responsible for the logarithmic divergence of the conductivity when a sufficiently large tensile strain is applied

Thermal transport in MoS2 from molecular dynamics using different empirical potentials

Thermal properties of molybdenum disulfide (MoS2) have recently attracted attention related to fundamentals of heat propagation in strongly anisotropic materials, and in the context of potential applications to optoelectronics and thermoelectrics. Multiple empirical potentials have been developed for classical molecular dynamics (MD) simulations of this material, but it has been unclear which provides the most realistic results. Here, we calculate lattice thermal conductivity of single- and multilayer pristine MoS2 by employing three different thermal transport MD methods: equilibrium, nonequilibrium, and homogeneous nonequilibrium ones. We mainly use the Graphics Processing Units Molecular Dynamics code for numerical calculations, and the Large-scale Atomic/Molecular Massively Parallel Simulator code for crosschecks. Using different methods and computer codes allows us to verify the consistency of our results and facilitate comparisons with previous studies, where different schemes have been adopted. Our results using variants of the Stillinger-Weber potential are at odds with some previous ones and we analyze the possible origins of the discrepancies in detail. We show that, among the potentials considered here, the reactive empirical bond order (REBO) potential gives the most reasonable predictions of thermal transport properties as compared to experimental data. With the REBO potential, we further find that isotope scattering has only a small effect on thermal conduction in MoS2 and the in-plane thermal conductivity decreases with increasing layer number and saturates beyond about three layers. We identify the REBO potential as a transferable empirical potential for MD simulations of MoS2 which can be used to study thermal transport properties in more complicated situations such as in systems containing defects or engineered nanoscale features. This work establishes a firm foundation for understanding heat transport properties of MoS2 using MD simulations

Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models

© 2016 American Physical Society. We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further used to study their mechanical, thermal, or electronic properties. By fitting to quantum-mechanical density functional theory (DFT) calculations, we show that the PFC approach is able to predict realistic formation energies and defect structures of grain boundaries. We provide an in-depth comparison of the formation energies between PFC, DFT, and molecular dynamics (MD) calculations. The DFT and MD calculations are initialized using atomic configurations extracted from PFC ground states. Finally, we use the PFC approach to explicitly construct large realistic polycrystalline samples and characterize their properties using MD relaxation to demonstrate their quality

Spectral decomposition of thermal conductivity: Comparing velocity decomposition methods in homogeneous molecular dynamics simulations

The design of applications, especially those based on heterogeneous integration, must rely on detailed knowledge of material properties, such as thermal conductivity (TC). To this end, multiple methods have been developed to study TC as a function of vibrational frequency. Here, we compare three spectral TC methods based on velocity decomposition in homogenous molecular dynamics simulations: Green-Kubo modal analysis (GKMA), the spectral heat current (SHC) method, and a method we propose called homogeneous nonequilibrium modal analysis (HNEMA). First, we derive a convenient per-atom virial expression for systems described by general many-body potentials, enabling compact representations of the heat current, each velocity decomposition method, and other related quantities. Next, we evaluate each method by calculating the spectral TC for carbon nanotubes, graphene, and silicon. We show that each method qualitatively agrees except at optical phonon frequencies, where a combination of mismatched eigenvectors and a large density of states produces artificial TC peaks for modal analysis (MA) methods. Our calculations also show that the HNEMA and SHC methods converge much faster than the GKMA method, with the SHC method being the most computationally efficient. Finally, we demonstrate that our MA implementation in the Graphics Processing Units Molecular Dynamics code on a single graphics processing unit is over 1000 times faster than the existing implementation in the Large-scale Atomic/Molecular Massively Parallel Simulator code on one central processing unit

Thermal conductivity reduction in carbon nanotube by fullerene encapsulation: A molecular dynamics study

Single-walled carbon nanotubes (SWCNTs) in their pristine form have high thermal conductivity whose further improvement has attracted a lot of interest. Some theoretical studies have suggested that the thermal conductivity of a (10,10) SWCNT is dramatically enhanced by C60 fullerene encapsulation. However, recent experiments on SWCNT bundles show that fullerene encapsulation leads to a reduction rather than an increase in thermal conductivity. Here, we employ three different molecular dynamics methods to study the influence of C60 encapsulation on heat transport in a (10,10) SWCNT. All the three methods consistently predict a reduction of the thermal conductivity of (10,10) SWCNT upon C60 encapsulation by 20% - 30%, in agreement with experimental results on bundles of SWCNTs. We demonstrate that there is a simulation artifact in the Green-Kubo method which gives anomalously large thermal conductivity from artificial convection. Our results show that the C60 molecules conduct little heat compared to the outer SWCNT and reduce the phonon mean free paths of the SWCNT by inducing extra phonon scattering. We also find that the thermal conductivity of a (10,10) SWCNT monotonically decreases with increasing filling ratio of C60 molecules

Structure and pore size distribution in nanoporous carbon

We study the structural and mechanical properties of nanoporous (NP) carbon materials by extensive atomistic machine-learning (ML) driven molecular dynamics (MD) simulations. To this end, we retrain a ML Gaussian approximation potential (GAP) for carbon by recalculating the a-C structural database of Deringer and Csányi adding van der Waals interactions. Our GAP enables a notable speedup and improves the accuracy of energy and force predictions. We use the GAP to thoroughly study the atomistic structure and pore-size distribution in computational NP carbon samples. These samples are generated by a melt-graphitization-quench MD procedure over a wide range of densities (from 0.5 to 1.7 g/cm3) with structures containing 131072 atoms. Our results are in good agreement with experimental data for the available observables and provide a comprehensive account of structural (radial and angular distribution functions, motif and ring counts, X-ray diffraction patterns, pore characterization) and mechanical (elastic moduli and their evolution with density) properties. Our results show relatively narrow pore-size distributions, where the peak position and width of the distributions are dictated by the mass density of the materials. Our data allow further work on computational characterization of NP carbon materials, in particular for energy-storage applications, as well as suggest future experimental characterization of NP carbon-based materials.</p