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

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

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

Charge-Transfer-Driven Nonplanar Adsorption of F₄TCNQ Molecules on Epitaxial Graphene

π-conjugated organic molecules tend to adsorb in a planar configuration on graphene irrespective of their charge state. In contrast, here we demonstrate charging-induced strong structural relaxation of tetrafluoro­tetracyano­quinodimethane (F₄TCNQ) on epitaxial graphene on Ir(111) (G/Ir(111)). The work function modulation over the graphene moiré unit cell causes site-selective charging of F₄TCNQ. Upon charging, the molecule anchors to the face-centered cubic sites of the G/Ir(111) moiré through one or two cyano groups. The reaction is reversible and can be triggered on a single molecule by moving it between different adsorption sites. We introduce a model taking into account the trade-off between tilt-induced charging and reduced van der Waals interactions, which provides a general framework for understanding charging-induced structural relaxation on weakly interacting substrates. In addition, we argue that the partial sp³ rehybridization of the underlying graphene and the possible bonding mechanism between the cyano groups and the graphene substrate are also relevant for the complete understanding of the experiments. These results provide insight into molecular charging on graphene, and they are directly relevant for potential device applications where the use of molecules has been suggested for doping and band structure engineering

Molecular Self-Assembly on Graphene on SiO₂ and h‑BN Substrates

One of the suggested ways of controlling the electronic properties of graphene is to establish a periodic potential modulation on it, which could be achieved by self-assembly of ordered molecular lattices. We have studied the self-assembly of cobalt phthalocyanines (CoPc) on chemical vapor deposition (CVD) grown graphene transferred onto silicon dioxide (SiO₂) and hexagonal boron nitride (h-BN) substrates. Our scanning tunneling microscopy (STM) experiments show that, on both substrates, CoPc forms a square lattice. However, on SiO₂, the domain size is limited by the corrugation of graphene, whereas on h-BN, single domain extends over entire terraces of the underlying h-BN. Additionally, scanning tunneling spectroscopy (STS) measurements suggest that CoPc molecules are doped by the substrate and that the level of doping varies from molecule to molecule. This variation is larger on graphene on SiO₂ than on h-BN. These results suggest that graphene on h-BN is an ideal substrate for the study of molecular self-assembly toward controlling the electronic properties of graphene by engineered potential landscapes

Electronic States at the Graphene–Hexagonal Boron Nitride Zigzag Interface

The electronic properties of graphene edges have been predicted to depend on their crystallographic orientation. The so-called zigzag (ZZ) edges haven been extensively explored theoretically and proposed for various electronic applications. However, their experimental study remains challenging due to the difficulty in realizing clean ZZ edges without disorder, reconstructions, or the presence of chemical functional groups. Here, we propose the ZZ-terminated, atomically sharp interfaces between graphene and hexagonal boron nitride (BN) as experimentally realizable, chemically stable model systems for graphene ZZ edges. Combining scanning tunneling microscopy and numerical methods, we explore the structure of graphene–BN interfaces and show them to host localized electronic states similar to those on the pristine graphene ZZ edge

Kapitza thermal resistance across individual grain boundaries in graphene

We study heat transport across individual grain boundaries in suspended monolayer graphene using extensive classical molecular dynamics (MD) simulations. We construct bicrystalline graphene samples containing grain boundaries with symmetric tilt angles using the two-dimensional phase field crystal method and then relax the samples with MD. The corresponding Kapitza resistances are then computed using nonequilibrium MD simulations. We find that the Kapitza resistance depends strongly on the tilt angle and shows a clear correlation with the average density of defects in a given grain boundary, but is not strongly correlated with the grain boundary line tension. We also show that quantum effects are significant in quantitative determination of the Kapitza resistance by applying the mode-by-mode quantum correction to the classical MD data. The corrected data are in good agreement with quantum mechanical Landauer-Butticker calculations