Effect of Interlayer Bonding on Superlubric Sliding of Graphene Contacts: A Machine-Learning Potential Study.

Surface defects and their mutual interactions are anticipated to affect the superlubric sliding of incommensurate layered material interfaces. Atomistic understanding of this phenomenon is limited due to the high computational cost of ab initio simulations and the absence of reliable classical force-fields for molecular dynamics simulations of defected systems. To address this, we present a machine-learning potential (MLP) for bilayer defected graphene, utilizing state-of-the-art graph neural networks trained against many-body dispersion corrected density functional theory calculations under iterative configuration space exploration. The developed MLP is utilized to study the impact of interlayer bonding on the friction of bilayer defected graphene interfaces. While a mild effect on the sliding dynamics of aligned graphene interfaces is observed, the friction coefficients of incommensurate graphene interfaces are found to significantly increase due to interlayer bonding, nearly pushing the system out of the superlubric regime. The methodology utilized herein is of general nature and can be adapted to describe other homogeneous and heterogeneous defected layered material interfaces.

Combining linear-scaling quantum transport and machine-learning molecular dynamics to study thermal and electronic transports in complex materials.

We 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.

Indentation Depth-Dependent Hardness of Metal-Organic Framework Crystals: The Effect of Local Amorphization Induced by Indentation.

The hardness of metal-organic frameworks (MOFs) is an important mechanical property metric measuring their resistance to the permanent plastic deformation. The hardness of most MOFs measured from nanoindentation experiments usually exhibits the similar unique indentation depth dependence feature, the mechanism of which still remains unclear. In order to explain the effect of the indentation depth on the hardness of MOFs, we conducted nanoindentation simulations on HKUST-1 by using reactive molecular dynamics simulations. Our simulations reveal that the HKUST-1 material near the indenter can transform from the parent crystalline phase to a new amorphous phase due to the high pressure generated, while its counterpart far from the indenter remains in the crystalline phase. By considering the crystalline-amorphous interface in the energy analysis of MOFs, we derived an analytical expression of the hardness at different indentation depths. It is found that the interface effect can greatly increase the hardness of MOFs, as observed in nanoindentation simulations. Moreover, the proposed analytical expression can well explain the indentation depth-dependent hardness of many MOF crystals measured in nanoindentation experiments. Overall, this work can provide a better understanding of the indentation depth dependence of the hardness of MOFs.

Combining the D3 dispersion correction with the neuroevolution machine-learned potential.

Machine-learned potentials (MLPs) have become a popular approach of modeling interatomic interactions in atomistic simulations, but to keep the computational cost under control, a relatively short cutoff must be imposed, which put serious restrictions on the capability of the MLPs for modeling relatively long-ranged dispersion interactions. In this paper, we propose to combine the neuroevolution potential (NEP) with the popular D3 correction to achieve a unified NEP-D3 model that can simultaneously model relatively short-ranged bonded interactions and relatively long-ranged dispersion interactions. We show that improved descriptions of the binding and sliding energies in bilayer graphene can be obtained by the NEP-D3 approach compared to the pure NEP approach. We implement the D3 part into thegpumdpackage such that it can be used out of the box for many exchange-correlation functionals. As a realistic application, we show that dispersion interactions result in approximately a 10% reduction in thermal conductivity for three typical metal-organic frameworks.

The thermoelastic properties of monolayer covalent organic frameworks studied by machine-learning molecular dynamics.

Two-dimensional (2D) covalent organic frameworks (COFs) are emerging as promising 2D polymeric materials with broad applications owing to their unique properties, among which the mechanical properties are quite important for various applications. However, the mechanical properties of 2D COFs have not been systematically studied yet. Herein, a machine-learned neuroevolution potential (NEP) was developed to study the elastic properties of two representative monolayer 2D COFs, namely COF-1 and COF-5. The trained NEP enables one to study the elastic properties of 2D COFs in realistic situations (e.g., finite size and temperature) and possesses greatly improved computational efficiency when compared with density functional theory calculations. With the aid of the obtained NEP, molecular dynamics (MD) simulations together with a strain-fluctuation method were employed to evaluate the elastic constants of the considered 2D COFs at different temperatures. The elastic constants of COF-1 and COF-5 monolayers were found to decrease with an increase in the temperature, though they were almost isotropic irrespective of the temperature. The thermally induced softening of 2D COFs below a critical temperature was observed, which is mainly attributed to their inherent ripple configurations at finite temperatures, while above the critical temperature, the damping effect of anharmonic vibrations became the dominant factor. Based on the proposed mechanisms, analytical models were developed for capturing the temperature dependence of elastic constants, which were found to agree with the MD simulation results well. This work provides an in-depth insight into the thermoelastic properties of monolayer COFs, which can guide the development of 2D COF materials with tailored mechanical behaviors for enhancing their performance in various applications.

Sub-Micrometer Phonon Mean Free Paths in Metal-Organic Frameworks Revealed by Machine Learning Molecular Dynamics Simulations.

Metal-organic frameworks (MOFs) are a family of materials that have high porosity and structural tunability and hold great potential in various applications, many of which require a proper understanding of the thermal transport properties. Molecular dynamics (MD) simulations play an important role in characterizing the thermal transport properties of various materials. However, due to the complexity of the structures, it is difficult to construct accurate empirical interatomic potentials for reliable MD simulations of MOFs. To this end, we develop a set of accurate yet highly efficient machine-learned potentials for three typical MOFs, including MOF-5, HKUST-1, and ZIF-8, using the neuroevolution potential approach as implemented in the GPUMD package, and perform extensive MD simulations to study thermal transport in the three MOFs. Although the lattice thermal conductivity values of the three MOFs are all predicted to be smaller than 1 W/(m K) at room temperature, the phonon mean free paths (MFPs) are found to reach the sub-micrometer scale in the low-frequency region. As a consequence, the apparent thermal conductivity only converges to the diffusive limit for micrometer single crystals, which means that the thermal conductivity is heavily reduced in nanocrystalline MOFs. The sub-micrometer phonon MFPs are also found to be correlated with a moderate temperature dependence of thermal conductivity between those in typical crystalline and amorphous materials. Both the large phonon MFPs and the moderate temperature dependence of thermal conductivity fundamentally change our understanding of thermal transport in MOFs.

Accurate prediction of heat conductivity of water by a neuroevolution potential.

We propose an approach that can accurately predict the heat conductivity of liquid water. On the one hand, we develop an accurate machine-learned potential based on the neuroevolution-potential approach that can achieve quantum-mechanical accuracy at the cost of empirical force fields. On the other hand, we combine the Green-Kubo method and the spectral decomposition method within the homogeneous nonequilibrium molecular dynamics framework to account for the quantum-statistical effects of high-frequency vibrations. Excellent agreement with experiments under both isobaric and isochoric conditions within a wide range of temperatures is achieved using our approach.

Mechanical and thermal properties of graphyne-coated carbon nanotubes: a molecular dynamics simulation on one-dimensional all-carbon van der Waals heterostructures.

The mechanical and thermal properties of a hybrid nanotube consisting of a coaxial carbon nanotube (CNT) inside a graphyne nanotube (GNT), i.e., CNT@GNT, are investigated in this paper by using molecular dynamics simulations. The results show that the mechanical properties of CNT@GNT under uniaxial tension depend on the nanotube chirality of its components. Specifically, the Young's modulus of the CNT@GNT structure with an inner zigzag CNT is larger than that of its counterpart with an armchair CNT, while CNT@GNT with an armchair CNT and a zigzag GNT is found to possess the largest tensile strength and fracture strain. In addition, a unique fracture behavior of the successive rupture of its two components is observed in CNT@GNT. The thermal conductivity of CNT@GNT is found to be almost independent of the nanotube chirality of its components but increases as the length and diameter of the CNT@GNT increase. Moreover, strain engineering is shown as an effective avenue to modulate the thermal conductivity of CNT@GNT, which can be enhanced by tension but reduced by compression. The analysis of the phonon spectrum and spectral energy density demonstrates that this strain effect originates from changes of the phonon group velocity and phonon scattering in the strained CNT@GNT.

GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations.

We 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.

Delamination of MoS2/SiO2 interfaces under nanoindentation.

Molybdenum disulphide (MoS2) mounted on silicon dioxide (SiO2) constitutes the fundamental functional components of many nanodevices, but its mechanical properties, which are crucial for the device design and fabrication, remain almost unexplored. Here, the mechanical properties of the multilayer MoS2/SiO2 system are investigated via nanoindentation experiments and molecular dynamics simulations. In terms of the mechanical properties, a comparative study of MoS2/SiO2 and graphene/SiO2 systems is presented. The MoS2/SiO2 and graphene/SiO2 systems are found to possess comparable Young's modulus and hardness values, but their mechanical responses and failure modes under indentation are totally different. Interface delamination failure accompanied by ring-like through-thickness cracking is observed in the MoS2/SiO2 system with a relatively thin MoS2 layer, while no interface separation is found in indentation experiments for the graphene/SiO2 system using the same layer thickness. The different failure modes observed between the MoS2/SiO2 and graphene/SiO2 systems can be attributed to the comparable interface adhesion energy but very different bending stiffness values of the MoS2 and graphene components. Specifically, compared with graphene, the larger bending stiffness of MoS2 means that a larger bending force is experienced in the indentation process, overcoming the adhesion of the MoS2/SiO2 interface, which makes interface delamination much easier in the MoS2/SiO2 system.

Unusual Deformation and Fracture in Gallium Telluride Multilayers.

The deformation and fracture mechanism of two-dimensional (2D) materials are still unclear and not thoroughly investigated. Given this, mechanical properties and mechanisms are explored on example of gallium telluride (GaTe), a promising 2D semiconductor with an ultrahigh photoresponsivity and a high flexibility. Hereby, the mechanical properties of both substrate-supported and suspended GaTe multilayers were investigated through Berkovich-tip nanoindentation instead of the commonly used AFM-based nanoindentation method. An unusual concurrence of multiple pop-in and load-drop events in loading curve was observed. Theoretical calculations unveiled this concurrence originating from the interlayer-sliding mediated layers-by-layers fracture mechanism in GaTe multilayers. The van der Waals force dominated interlayer interactions between GaTe and substrates was revealed much stronger than that between GaTe interlayers, resulting in the easy sliding and fracture of multilayers within GaTe. This work introduces new insights into the deformation and fracture of GaTe and other 2D materials in flexible electronics applications.

Effects of interlayer interactions on the nanoindentation response of freely suspended multilayer gallium telluride.

Freestanding indentation is a widely used method to characterise the elastic properties of two-dimensional (2D) materials. However, many controversies and confusion remain in this field due to the lack of appropriate theoretical models in describing the indentation responses of 2D materials. Taking the multilayer gallium telluride (GaTe) as an example, in this paper we conduct a series of experiments and simulations to achieve a comprehensive understanding of its freestanding indentation behaviours. Specifically, the freestanding indentation experiments show that the elastic properties of the present multilayer GaTe with a relatively large thickness can only be extracted from the bending stage in the indentation process rather than the stretching stage widely utilised in the previous studies on thin 2D materials, since the stretching stage of thick 2D materials is inevitably accompanied with severe plastic deformations. In combination with existing continuum mechanical models and finite element simulations, an extremely small Young's modulus of multilayer GaTe is obtained from the nanoindentation experiments, which is two orders of magnitude smaller than the value obtained from first principles calculations. Our molecular dynamics (MD) simulations reveal that this small Young's modulus can be attributed to the significant elastic softening in the multilayer GaTe with increasing thickness and decreasing length. It is further revealed in MD simulations that this size-induced elastic softening originates from the synergistic effects of interlayer compression and interlayer shearing in the multilayer GaTe, both of which, however, are ignored in the existing indentation models. To consider these effects of interlayer interactions in the theoretical modelling of the freestanding indentation of multilayer GaTe, we propose here novel multiple-beam and multiple-plate models, which are found to agree well with MD results without any additional parameters fitting and thus can be treated as more precise theoretical models in characterising the freestanding indentation behaviours of 2D materials.