### Browsing by Author "Fan, Zheyong"

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Item Barbalinardo et al. Reply(American Physical Society, 2022-06-24) Barbalinardo, Giuseppe; Chen, Zekun; Dong, Haikuan; Fan, Zheyong; Donadio, Davide; University of California Davis; Multiscale Statistical and Quantum Physics; Department of Applied PhysicsItem Combining linear-scaling quantum transport and machine-learning molecular dynamics to study thermal and electronic transports in complex materials(Institute of Physics Publishing, 2024-06-19) Fan, Zheyong; Xiao, Yang; Wang, Yanzhou; Ying, Penghua; Chen, Shunda; Dong, Haikuan; Department of Applied Physics; Multiscale Statistical and Quantum Physics; Bohai University; Department of Applied Physics; Tel Aviv University; George Washington UniversityWe propose an efficient approach for simultaneous prediction of thermal and electronic transport properties in complex materials. Firstly, a highly efficient machine-learned neuroevolution potential (NEP) is trained using reference data from quantum-mechanical density-functional theory calculations. This trained potential is then applied in large-scale molecular dynamics simulations, enabling the generation of realistic structures and accurate characterization of thermal transport properties. In addition, molecular dynamics simulations of atoms and linear-scaling quantum transport calculations of electrons are coupled to account for the electron-phonon scattering and other disorders that affect the charge carriers governing the electronic transport properties. We demonstrate the usefulness of this unified approach by studying electronic transport in pristine graphene and thermoelectric transport properties of a graphene antidot lattice, with a general-purpose NEP developed for carbon systems based on an extensive dataset.Item Efficient Calculation of the Lattice Thermal Conductivity by Atomistic Simulations with Ab Initio Accuracy(WILEY-V C H VERLAG GMBH, 2022-02) Brorsson, Joakim; Hashemi, Arsalan; Fan, Zheyong; Fransson, Erik; Eriksson, Fredrik; Ala-Nissila, Tapio; Krasheninnikov, Arkady V.; Komsa, Hannu Pekka; Erhart, Paul; Department of Applied Physics; Multiscale Statistical and Quantum Physics; Chalmers University of TechnologyHigh-order force constant expansions can provide accurate representations of the potential energy surface relevant to vibrational motion. They can be efficiently parametrized using quantum mechanical calculations and subsequently sampled at a fraction of the cost of the underlying reference calculations. Here, force constant expansions are combined via the hiphive package with GPU-accelerated molecular dynamics simulations via the GPUMD package to obtain an accurate, transferable, and efficient approach for sampling the dynamical properties of materials. The performance of this methodology is demonstrated by applying it both to materials with very low thermal conductivity (Ba8Ga16Ge30, SnSe) and a material with a relatively high lattice thermal conductivity (monolayer-MoS2). These cases cover both situations with weak (monolayer-MoS2, SnSe) and strong (Ba8Ga16Ge30) pho renormalization. The simulations also enable to access complementary information such as the spectral thermal conductivity, which allows to discriminate the contribution by different phonon modes while accounting for scattering to all orders. The software packages described here are made available to the scientific community as free and open-source software in order to encourage the more widespread use of these techniques as well as their evolution through continuous and collaborative development.Item Energetics and structure of grain boundary triple junctions in graphene(2017-07-06) Hirvonen, Petri; Fan, Zheyong; Ervasti, Mikko M.; Harju, Ari; Elder, Ken R.; Ala-Nissilä, Tapio; Department of Applied Physics; Oakland UniversityGrain 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.Item Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon(2018-03-26) Dong, Haikuan; Fan, Zheyong; Shi, Libin; Harju, Ari; Ala-Nissila, Tapio; Department of Applied Physics; Centre of Excellence in Quantum Technology, QTF; Multiscale Statistical and Quantum Physics; Bohai UniversityMolecular 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.Item GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations(American Institute of Physics, 2022-09-21) Fan, Zheyong; Wang, Yanzhou; Ying, Penghua; Song, Keke; Wang, Junjie; Wang, Yong; Zeng, Zezhu; Xu, Ke; Lindgren, Eric; Rahm, J. Magnus; Gabourie, Alexander J.; Liu, Jiahui; Dong, Haikuan; Wu, Jianyang; Chen, Yue; Zhong, Zheng; Sun, Jian; Erhart, Paul; Su, Yanjing; Ala-Nissila, Tapio; Department of Applied Physics; Multiscale Statistical and Quantum Physics; Multiscale Statistical and Quantum Physics; Harbin Institute of Technology; University of Science and Technology Beijing; Nanjing University; The University of Hong Kong; Xiamen University; Chalmers University of Technology; Stanford University; Bohai UniversityWe present our latest advancements of machine-learned potentials (MLPs) based on the neuroevolution potential (NEP) framework introduced in Fan et al. [Phys. Rev. B 104, 104309 (2021)] and their implementation in the open-source package gpumd. We increase the accuracy of NEP models both by improving the radial functions in the atomic-environment descriptor using a linear combination of Chebyshev basis functions and by extending the angular descriptor with some four-body and five-body contributions as in the atomic cluster expansion approach. We also detail our efficient implementation of the NEP approach in graphics processing units as well as our workflow for the construction of NEP models and demonstrate their application in large-scale atomistic simulations. By comparing to state-of-the-art MLPs, we show that the NEP approach not only achieves above-average accuracy but also is far more computationally efficient. These results demonstrate that the gpumd package is a promising tool for solving challenging problems requiring highly accurate, large-scale atomistic simulations. To enable the construction of MLPs using a minimal training set, we propose an active-learning scheme based on the latent space of a pre-trained NEP model. Finally, we introduce three separate Python packages, viz., gpyumd, calorine, and pynep, that enable the integration of gpumd into Python workflows.Item Grain extraction and microstructural analysis method for two-dimensional poly and quasicrystalline solids(2018-10-16) Hirvonen, Petri; La Boissonière, Gabriel Martine; Fan, Zheyong; Achim, Cristian; Provatas, Nikolas; Elder, Ken R.; Ala-Nissilä, Tapio; Centre of Excellence in Quantum Technology, QTF; McGill University; University of Concepción; Oakland University; Department of Applied PhysicsWhile the microscopic structure of defected solid crystalline materials has significant impact on their physical properties, efficient and accurate determination of a given polycrystalline microstructure remains a challenge. In this paper, we present a highly generalizable and reliable variational method to achieve this goal for two-dimensional crystalline and quasicrystalline materials. The method is benchmarked and optimized successfully using a variety of large-scale systems of defected solids, including periodic structures and quasicrystalline symmetries to quantify their microstructural characteristics, e.g., grain size and lattice misorientation distributions. We find that many microstructural properties show universal features independent of the underlying symmetries.Item Heat transport across graphene/hexagonal-BN tilted grain boundaries from phase-field crystal model and molecular dynamics simulations(American Institute of Physics, 2021-12-21) Dong, Haikuan; Hirvonen, Petri; Fan, Zheyong; Qian, Ping; Su, Yanjing; Ala-Nissila, Tapio; Centre of Excellence in Quantum Technology, QTF; University of Science and Technology Beijing; Department of Applied PhysicsWe study the interfacial thermal conductance of grain boundaries (GBs) between monolayer graphene and hexagonal boron nitride (h-BN) sheets using a combined atomistic approach. First, realistic samples containing graphene/h-BN GBs with different tilt angles are generated using the phase-field crystal model developed recently [P. Hirvonen et al., Phys. Rev. B 100, 165412 (2019)] that captures slow diffusive relaxation inaccessible to molecular dynamics (MD) simulations. Then, large-scale MD simulations using the efficient GPUMD package are performed to assess heat transport and rectification properties across the GBs. We find that lattice mismatch between the graphene and h-BN sheets plays a less important role in determining the interfacial thermal conductance as compared to the tilt angle. In addition, we find no significant thermal rectification effects for these GBs.Item Homogeneous nonequilibrium molecular dynamics method for heat transport and spectral decomposition with many-body potentials(American Physical Society, 2019-02-28) Fan, Zheyong; Dong, Haikuan; Harju, Ari; Ala-Nissilä, Tapio; Department of Applied Physics; Centre of Excellence in Quantum Technology, QTF; Multiscale Statistical and Quantum Physics; Bohai UniversityThe 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)PYLAAG0375-960110.1016/0375-9601(82)90748-4] 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.Item Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids(AMERICAN INSTITUTE OF PHYSICS, 2019-12-21) Li, Zhen; Xiong, Shiyun; Sievers, Charles; Hu, Yue; Fan, Zheyong; Wei, Ning; Bao, Hua; Chen, Shunda; Donadio, Davide; Ala-Nissila, Tapio; Department of Applied Physics; Centre of Excellence in Quantum Technology, QTF; Multiscale Statistical and Quantum Physics; Northwest Agriculture and Forestry University; Soochow University; University of California, Davis; Shanghai Jiao Tong UniversityNonequilibrium molecular dynamics (NEMD) has been extensively used to study thermal transport at various length scales in many materials. In this method, two local thermostats at different temperatures are used to generate a nonequilibrium steady state with a constant heat flux. Conventionally, the thermal conductivity of a finite system is calculated as the ratio between the heat flux and the temperature gradient extracted from the linear part of the temperature profile away from the local thermostats. Here, we show that, with a proper choice of the thermostat, the nonlinear part of the temperature profile should actually not be excluded in thermal transport calculations. We compare NEMD results against those from the atomistic Green's function method in the ballistic regime and those from the homogeneous nonequilibrium molecular dynamics method in the ballistic-to-diffusive regime. These comparisons suggest that in all the transport regimes, one should directly calculate the thermal conductance from the temperature difference between the heat source and sink and, if needed, convert it into the thermal conductivity by multiplying it with the system length. Furthermore, we find that the Langevin thermostat outperforms the Nosé-Hoover (chain) thermostat in NEMD simulations because of its stochastic and local nature. We show that this is particularly important for studying asymmetric carbon-based nanostructures, for which the Nosé-Hoover thermostat can produce artifacts leading to unphysical thermal rectification.Item Inter-layer and intra-layer heat transfer in bilayer/monolayer graphene van der Waals heterostructure(2018-06-06) Rajabpour, Ali; Fan, Zheyong; Vaez Allaei, S. Mehdi; Imam Khomeini International University; Centre of Excellence in Quantum Technology, QTF; University of Tehran; Department of Applied PhysicsVan der Waals heterostructures have exhibited interesting physical properties. In this paper, heat transfer in hybrid coplanar bilayer/monolayer (BL-ML) graphene, as a model layered van der Waals heterostructure, was studied using non-equilibrium molecular dynamics (MD) simulations. The temperature profile and inter- and intra-layer heat fluxes of the BL-ML graphene indicated that, there is no fully developed thermal equilibrium between layers and the drop in the average temperature profile at the step-like BL-ML interface is not attributable to the effect of Kapitza resistance. By increasing the length of the system up to 1 μm in the studied MD simulations, the thermally non-equilibrium region was reduced to a small area near the step-like interface. All MD results were compared to a continuum model and a good match was observed between the two approaches. Our results provide a useful understanding of heat transfer in nano- and micro-scale layered materials and van der Waals heterostructures.Item Interpretation of apparent thermal conductivity in finite systems from equilibrium molecular dynamics simulations(American Physical Society, 2021-01-19) Dong, Haikuan; Xiong, Shiyun; Fan, Zheyong; Qian, Ping; Su, Yanjing; Ala-Nissila, Tapio; Department of Applied Physics; Multiscale Statistical and Quantum Physics; Centre of Excellence in Quantum Technology, QTF; Soochow University; University of Science and Technology BeijingWe propose a way to properly interpret the apparent thermal conductivity obtained for finite systems using equilibrium molecular dynamics simulations (EMD) with fixed or open boundary conditions in the transport direction. In such systems the heat current autocorrelation function develops negative values after a correlation time which is proportional to the length of the simulation cell in the transport direction. Accordingly, the running thermal conductivity develops a maximum value at the same correlation time and eventually decays to zero. By comparing EMD with nonequilibrium molecular dynamics (NEMD) simulations, we conclude that the maximum thermal conductivity from EMD in a system with domain length 2L is equal to the thermal conductivity from NEMD in a system with domain length L. This facilitates the use of nonperiodic-boundary EMD for thermal transport in finite samples in close correspondence to NEMD.Item Methodology Perspective of Computing Thermal Transport in Low-Dimensional Materials and Nanostructures: The Old and the New(2018) Zhou, Yanguang; Fan, Zheyong; Qin, Guangzhao; Yang, Jia Yue; Ouyang, Tao; Hu, Ming; Department of Applied Physics; RWTH Aachen University; XiangTan UniversityDemands for engineering thermal transport properties are ever increasing for a wide range of modern micro-and nanodevices and materials-based energy technologies. In particular, there is a severe situation due to the rapid progress in the synthesis and processing of materials and devices with structural characteristic length on the nanometer scales, which are comparable or even smaller than the intrinsic length scales (such as mean free path and wavelength) of basic energy carriers (such as phonons, electrons, and photons). Although advanced approaches for controlling the electronic and photonic transport have been proposed in the past decades, progress on controlling lattice vibrations (i.e., the phonons) is still far behind. Gaps between the fundamental understandings of the behavior of the basic energy carriers at small scales and the technological demands still remain, particularly from a computer modeling point of view. Herewith, we give a perspective of the computational approaches for predicting the thermal transport properties of low-dimensional materials and nanostructures, which are mainly sorted into three categories: empirical molecular dynamics, anharmonic lattice dynamics based Boltzmann transport equation, and Landauer theory. The advantage and disadvantage of each method are discussed and some possible solutions are suggested. The discussion is focused on fully and accurately characterizing the mode-level phonon behavior, possible all-order phonon scattering process, and incorporation of realistic nanostructures. Moreover, emerging challenges of phonon coupling effects, such as electron-phonon, phonon-photon, and phonon-magnon coupling, are also discussed. We expect that this perspective will stimulate future research in computer modeling of micro-/nanoscale heat transfer beyond traditional phonons.Item Molecular dynamics simulations of heat transport using machine-learned potentials : A mini-review and tutorial on GPUMD with neuroevolution potentials(American Institute of Physics, 2024-04-28) Dong, Haikuan; Shi, Yongbo; Ying, Penghua; Xu, Ke; Liang, Ting; Wang, Yanzhou; Zeng, Zezhu; Wu, Xin; Zhou, Wenjiang; Xiong, Shiyun; Chen, Shunda; Fan, Zheyong; Department of Applied Physics; Centre of Excellence in Quantum Technology, QTF; Multiscale Statistical and Quantum Physics; Bohai University; Tel Aviv University; Chinese University of Hong Kong; Centre of Excellence in Quantum Technology, QTF; Institute of Science and Technology Austria; South China University of Technology; Peking University; Guangdong University of Technology; George Washington UniversityMolecular dynamics (MD) simulations play an important role in understanding and engineering heat transport properties of complex materials. An essential requirement for reliably predicting heat transport properties is the use of accurate and efficient interatomic potentials. Recently, machine-learned potentials (MLPs) have shown great promise in providing the required accuracy for a broad range of materials. In this mini-review and tutorial, we delve into the fundamentals of heat transport, explore pertinent MD simulation methods, and survey the applications of MLPs in MD simulations of heat transport. Furthermore, we provide a step-by-step tutorial on developing MLPs for highly efficient and predictive heat transport simulations, utilizing the neuroevolution potentials as implemented in the GPUMD package. Our aim with this mini-review and tutorial is to empower researchers with valuable insights into cutting-edge methodologies that can significantly enhance the accuracy and efficiency of MD simulations for heat transport studies.Item Multiscale modeling of polycrystalline graphene(2016-07-11) Hirvonen, Petri; Ervasti, Mikko M.; Fan, Zheyong; Jalalvand, Morteza; Seymour, Matthew; Vaez Allaei, S. Mehdi; Provatas, Nikolas; Harju, Ari; Elder, Ken R.; Ala-Nissilä, Tapio; Department of Applied Physics; Institute for Advanced Studies in Basic Sciences, Zanjan; McGill University; University of TehranWe 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.Item Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport(American Physical Society, 2021-09-18) Fan, Zheyong; Zeng, Zezhu; Zhang, Cunzhi; Wang, Yanzhou; Song, Keke; Dong, Haikuan; Chen, Yue; Ala-Nissila, Tapio; Department of Applied Physics; Centre of Excellence in Quantum Technology, QTF; Multiscale Statistical and Quantum Physics; The University of Hong Kong; University of Chicago; Multiscale Statistical and Quantum Physics; University of Science and Technology BeijingWe develop a neuroevolution-potential (NEP) framework for generating neural network-based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A descriptor of the atomic environment is constructed based on Chebyshev and Legendre polynomials. The method is implemented in graphic processing units within the open-source gpumd package, which can attain a computational speed over atom-step per second using one Nvidia Tesla V100. Furthermore, per-atom heat current is available in NEP, which paves the way for efficient and accurate MD simulations of heat transport in materials with strong phonon anharmonicity or spatial disorder, which usually cannot be accurately treated either with traditional empirical potentials or with perturbative methods.Item Nonlinear conductivity of a holographic superconductor under constant electric field(2017-02-23) Zeng, Hua Bi; Tian, Yu; Fan, Zheyong; Chen, Chiang Mei; Department of Applied Physics; Quantum Many-Body Physics; Bohai University; Shanghai Key Laboratory of High Temperature Superconductors; National Central UniversityThe dynamics of a two-dimensional superconductor under a constant electric field E is studied by using the gauge-gravity correspondence. The pair breaking current induced by E first increases to a peak value and then decreases to a constant value at late times, where the superconducting gap goes to zero, corresponding to a normal conducting phase. The peak value of the current is found to increase linearly with respect to the electric field. Moreover, the nonlinear conductivity, defined as an average of the conductivity in the superconducting phase, scales as similar to E-2/3 when the system is close to the critical temperature T-c, which agrees with predictions from solving the time-dependent Ginzburg-Landau equation. Away from T-c, the E-2/3 scaling of the conductivity still holds when E is large.Item Nonlinear transport in a two dimensional holographic superconductor(2016-06-16) Zeng, Hua Bi; Tian, Yu; Fan, Zheyong; Chen, Chiang Mei; Bohai University; Shanghai Key Laboratory of High Temperature Superconductors; Department of Applied Physics; National Central UniversityThe problem of nonlinear transport in a two-dimensional superconductor with an applied oscillating electric field is solved by the holographic method. The complex conductivity can be computed from the dynamics of the current for both the near- and nonequilibrium regimes. The limit of weak electric field corresponds to the near-equilibrium superconducting regime, where the charge response is linear and the conductivity develops a gap determined by the condensate. A larger electric field drives the system into a superconducting nonequilibrium steady state, where the nonlinear conductivity is quadratic with respect to the electric field. Increasing the amplitude of the applied electric field results in a far-from-equilibrium nonsuperconducting steady state with a universal linear conductivity of one. In the lower temperature regime we also find chaotic behavior of the superconducting gap, which results in a nonmonotonic field-dependent nonlinear conductivity.Item Nonperturbative phonon scatterings and the two-channel thermal transport in Tl3VSe4(American Physical Society, 2021-06-01) Zeng, Zezhu; Zhang, Cunzhi; Xia, Yi; Fan, Zheyong; Wolverton, Chris; Chen, Yue; Department of Applied Physics; Centre of Excellence in Quantum Technology, QTF; Multiscale Statistical and Quantum Physics; The University of Hong Kong; Northwestern UniversityWe study the role of nonperturbative phonon scattering in strongly anharmonic materials having ultralow lattice thermal conductivity with unusual temperature dependence. We take Tl3VSe4 as an example and investigate its lattice dynamics using perturbation theory (PT) up to the fourth order and molecular dynamics (MD) with a machine-learning potential. We find distinct differences of phonon linewidth between PT and MD in the whole Brillouin zone. The comparison between the theoretical phonon linewidths and experiments suggests that PT severely underestimates the phonon scatterings, even when the fourth-order anharmonicity is included. Moreover, we extend our calculations to higher temperatures and evaluate the two-channel thermal conductivity based on the unified theory developed by Simoncelli et al. [Nat. Phys. 15, 809 (2019)1745-247310.1038/s41567-019-0520-x]. We find a crucial coherence contribution to the total thermal conductivity at high temperatures. Our results pave the path for future studies of phonon properties and lattice thermal conductivities of strongly anharmonic crystals beyond the conventional PT realm.Item Phase-field crystal model for heterostructures(American Physical Society, 2019-10-16) Hirvonen, Petri; Heinonen, Vili; Dong, Haikuan; Fan, Zheyong; Elder, Ken R.; Ala-Nissila, Tapio; Centre of Excellence in Quantum Technology, QTF; Massachusetts Institute of Technology MIT; Bohai University; Oakland University; Department of Applied PhysicsAtomically thin two-dimensional heterostructures are a promising, novel class of materials with ground-breaking properties. The possibility of choosing many constituent components and their proportions allows optimization of these materials to specific requirements. The wide adaptability comes with a cost of large parameter space making it hard to experimentally test all the possibilities. Instead, efficient computational modeling is needed. However, large range of relevant time and length scales related to physics of polycrystalline materials poses a challenge for computational studies. To this end, we present an efficient and flexible phase-field crystal model to describe the atomic configurations of multiple atomic species and phases coexisting in the same physical domain. We extensively benchmark the model for two-dimensional binary systems in terms of their elastic properties and phase boundary configurations and their energetics. As a concrete example, we demonstrate modeling lateral heterostructures ofgraphene and hexagonal boron nitride. We consider both idealized bicrystals and large-scale systems with random phase distributions. We find consistent relative elastic moduli and lattice constants, as well as realistic continuous interfaces and faceted crystal shapes. Zigzag-oriented interfaces are observed to display the lowest formation energy.