Machine Learning Force Fields Research Articles

Exploring fracture of H-BN and graphene by neural network force fields

Extreme mechanical processes such as strong lattice distortion and bond breakage during fracture often lead to catastrophic failure of materials and structures. Understanding the nucleation and growth of cracks is challenged by their multiscale characteristics spanning from atomic-level structures at the crack tip to the structural features where the load is applied. Atomistic simulations offer ‘first-principles’ tools to resolve the progressive microstructural changes at crack fronts and are widely used to explore the underlying processes of mechanical energy dissipation, crack path selection, and dynamic instabilities (e.g. kinking, branching). Empirical force fields developed based on atomic-level structural descriptors based on atomic positions and the bond orders do not yield satisfying predictions of fracture, especially for the nonlinear, anisotropic stress–strain relations and the energy densities of edges. High-fidelity force fields thus should include the tensorial nature of strain and the energetics of bond-breaking and (re)formation events during fracture, which, unfortunately, have not been taken into account in either the state-of-the-art empirical or machine-learning force fields. Based on data generated by density functional theory calculations, we report a neural network-based force field for fracture (NN-F3) constructed by using the end-to-end symmetry preserving framework of deep potential—smooth edition (DeepPot-SE). The workflow combines pre-sampling of the space of strain states and active-learning techniques to explore the transition states at critical bonding distances. The capability of NN-F3 is demonstrated by studying the rupture of hexagonal boron nitride (h-BN) and twisted bilayer graphene as model problems. The simulation results elucidate the roughening physics of fracture defined by the lattice asymmetry in h-BN, explaining recent experimental findings, and predict the interaction between cross-layer cracks in twisted graphene bilayers, which leads to a toughening effect.

Accurate Quantum Monte Carlo Forces for Machine-Learned Force Fields: Ethanol as a Benchmark.

Quantum Monte Carlo (QMC) is a powerful method to calculate accurate energies and forces for molecular systems. In this work, we demonstrate how we can obtain accurate QMC forces for the fluxional ethanol molecule at room temperature by using either multideterminant Jastrow-Slater wave functions in variational Monte Carlo or just a single determinant in diffusion Monte Carlo. The excellent performance of our protocols is assessed against high-level coupled cluster calculations on a diverse set of representative configurations of the system. Finally, we train machine-learning force fields on the QMC forces and compare them to models trained on coupled cluster reference data, showing that a force field based on the diffusion Monte Carlo forces with a single determinant can faithfully reproduce coupled cluster power spectra in molecular dynamics simulations.

Understanding the Role of 1/2 ⟨110⟩ Dislocations in Deformation Mechanisms of Single-Crystal High-Entropy Carbide Ceramics from Machine Learning Force Field Simulations

Understanding the Role of 1/2 ⟨110⟩ Dislocations in Deformation Mechanisms of Single-Crystal High-Entropy Carbide Ceramics from Machine Learning Force Field Simulations

Machine learning-aided first-principles calculations of redox potentials

We present a method combining first-principles calculations and machine learning to predict the redox potentials of half-cell reactions on the absolute scale. By applying machine learning force fields for thermodynamic integration from the oxidized to the reduced state, we achieve efficient statistical sampling over a broad phase space. Furthermore, through thermodynamic integration from machine learning force fields to potentials of semi-local functionals, and from semi-local functionals to hybrid functionals using Δ-machine learning, we refine the free energy with high precision step-by-step. Utilizing a hybrid functional that includes 25% exact exchange (PBE0), this method predicts the redox potentials of the three redox couples, Fe3+/Fe2+, Cu2+/Cu+, and Ag2+/Ag+, to be 0.92, 0.26, and 1.99 V, respectively. These predictions are in good agreement with the best experimental estimates (0.77, 0.15, 1.98 V). This work demonstrates that machine-learned surrogate models provide a flexible framework for refining the accuracy of free energy from coarse approximation methods to precise electronic structure calculations, while also facilitating sufficient statistical sampling.

Polarization-driven band topology evolution in twisted MoTe2 and WSe2

Motivated by recent experimental observations of opposite Chern numbers in R-type twisted MoTe2 and WSe2 homobilayers, we perform large-scale density-functional-theory calculations with machine learning force fields to investigate moiré band topology across a range of twist angles in both materials. We find that the Chern numbers of the moiré frontier bands change sign as a function of twist angle, and this change is driven by the competition between moiré ferroelectricity and piezoelectricity. Our large-scale calculations, enabled by machine learning methods, reveal crucial insights into interactions across different scales in twisted bilayer systems. The interplay between atomic-level relaxation effects and moiré-scale electrostatic potential variation opens new avenues for the design of intertwined topological and correlated states, including the possibility of mimicking higher Landau level physics in the absence of magnetic field.

Dynamics of growing carbon nanotube interfaces probed by machine learning-enabled molecular simulations

Carbon nanotubes (CNTs), hollow cylinders of carbon, hold great promise for advanced technologies, provided their structure remains uniform throughout their length. Their growth takes place at high temperatures across a tube-catalyst interface. Structural defects formed during growth alter CNT properties. These defects are believed to form and heal at the tube-catalyst interface but an understanding of these mechanisms at the atomic-level is lacking. Here we present DeepCNT-22, a machine learning force field (MLFF) to drive molecular dynamics simulations through which we unveil the mechanisms of CNT formation, from nucleation to growth including defect formation and healing. We find the tube-catalyst interface to be highly dynamic, with large fluctuations in the chiral structure of the CNT-edge. This does not support continuous spiral growth as a general mechanism, instead, at these growth conditions, the growing tube edge exhibits significant configurational entropy. We demonstrate that defects form stochastically at the tube-catalyst interface, but under low growth rates and high temperatures, these heal before becoming incorporated in the tube wall, allowing CNTs to grow defect-free to seemingly unlimited lengths. These insights, not readily available through experiments, demonstrate the remarkable power of MLFF-driven simulations and fill long-standing gaps in our understanding of CNT growth mechanisms.

The Quasi-Plastic Deformation Mechanisms and Inverse Hall-Petch Relationship in Nanocrystalline Boron Carbide under Compression

Abstract Grain boundary (GB) plays a significant role in the deformation behaviors of nanocrystalline ceramics. Here, we investigate the compression behaviors of nanocrystalline boron carbide (n-B4C) with varying grain sizes, using molecular dynamics simulations with a machine-learning force field. The results reveal quasi-plastic deformation mechanisms in n-B4C: GB sliding, intergranular amorphization, and intragranular amorphization. GB sliding arises from the presence of the soft GBs, leading to intergranular amorphization. Intragranular amorphization arises from the interaction between grains with unfavorable orientations and the softened amorphous GBs, finally causing structural failure. Furthermore, the n-B4C models with varying grain sizes from 4.07 nm to 10.86 nm display an inverse Hall-Petch relationship due to the GB sliding mechanism. A higher strain rate in n-B4C often leads to higher yield strength, following a 2/3 power relationship. These deformation mechanisms are critical for the design of ceramics with superior mechanical properties.

Complexity of many-body interactions in transition metals via machine-learned force fields from the TM23 data set

This work examines challenges associated with the accuracy of machine-learned force fields (MLFFs) for bulk solid and liquid phases of d-block elements. In exhaustive detail, we contrast the performance of force, energy, and stress predictions across the transition metals for two leading MLFF models: a kernel-based atomic cluster expansion method implemented using sparse Gaussian processes (FLARE), and an equivariant message-passing neural network (NequIP). Early transition metals present higher relative errors and are more difficult to learn relative to late platinum- and coinage-group elements, and this trend persists across model architectures. Trends in complexity of interatomic interactions for different metals are revealed via comparison of the performance of representations with different many-body order and angular resolution. Using arguments based on perturbation theory on the occupied and unoccupied d states near the Fermi level, we determine that the large, sharp d density of states both above and below the Fermi level in early transition metals leads to a more complex, harder-to-learn potential energy surface for these metals. Increasing the fictitious electronic temperature (smearing) modifies the angular sensitivity of forces and makes the early transition metal forces easier to learn. This work illustrates challenges in capturing intricate properties of metallic bonding with current leading MLFFs and provides a reference data set for transition metals, aimed at benchmarking the accuracy and improving the development of emerging machine-learned approximations.

Simulating CO2 diffusivity in rigid and flexible Mg-MOF-74 with machine-learning force fields

The flexibility of metal–organic frameworks (MOFs) affects their gas adsorption and diffusion properties. However, reliable force fields for simulating flexible MOFs are lacking. As a result, most atomistic simulations so far have been carried out assuming rigid MOFs, which inevitably overestimates the gas adsorption energy. Here, we show that this issue can be addressed by applying a machine-learning potential, trained on quantum chemistry data, to atomistic simulations. We find that inclusion of flexibility is particularly important for simulating CO2 chemisorption in MOFs with coordinatively unsaturated metal sites. Specifically, we demonstrate that the diffusion of CO2 in a flexible Mg-MOF-74 structure is about one order of magnitude faster than in a rigid one, challenging the rigid-MOF assumption in previous simulations.

Lattice thermal conductivity of solid LiF based on machine learning force fields and the Green–Kubo approach

Lattice thermal conductivity of solid LiF based on machine learning force fields and the Green–Kubo approach

Low-index mesoscopic surface reconstructions of Au surfaces using Bayesian force fields

Metal surfaces have long been known to reconstruct, significantly influencing their structural and catalytic properties. Many key mechanistic aspects of these subtle transformations remain poorly understood due to limitations of previous simulation approaches. Using active learning of Bayesian machine-learned force fields trained from ab initio calculations, we enable large-scale molecular dynamics simulations to describe the thermodynamics and time evolution of the low-index mesoscopic surface reconstructions of Au (e.g., the Au(111)-‘Herringbone,’ Au(110)-(1 × 2)-‘Missing-Row,’ and Au(100)-‘Quasi-Hexagonal’ reconstructions). This capability yields direct atomistic understanding of the dynamic emergence of these surface states from their initial facets, providing previously inaccessible information such as nucleation kinetics and a complete mechanistic interpretation of reconstruction under the effects of strain and local deviations from the original stoichiometry. We successfully reproduce previous experimental observations of reconstructions on pristine surfaces and provide quantitative predictions of the emergence of spinodal decomposition and localized reconstruction in response to strain at non-ideal stoichiometries. A unified mechanistic explanation is presented of the kinetic and thermodynamic factors driving surface reconstruction. Furthermore, we study surface reconstructions on Au nanoparticles, where characteristic (111) and (100) reconstructions spontaneously appear on a variety of high-symmetry particle morphologies.

Exploring Li-Ion Transport Properties of Li3TiCl6: A Machine Learning Molecular Dynamics Study

We performed large-scale molecular dynamics simulations based on a machine-learning force field (MLFF) to investigate the Li-ion transport mechanism in cation-disordered Li3TiCl6 cathode at six different temperatures, ranging from 25°C to 100°C. In this work, deep neural network method and data generated by ab − initio molecular dynamics (AIMD) simulations were deployed to build a high-fidelity MLFF. Radial distribution functions, Li-ion mean square displacements (MSD), diffusion coefficients, ionic conductivity, activation energy, and crystallographic direction-dependent migration barriers were calculated and compared with corresponding AIMD and experimental data to benchmark the accuracy of the MLFF. From MSD analysis, we captured both the self and distinct parts of Li-ion dynamics. The latter reveals that the Li-ions are involved in anti-correlation motion that was rarely reported for solid-state materials. Similarly, the self and distinct parts of Li-ion dynamics were used to determine Haven’s ratio to describe the Li-ion transport mechanism in Li3TiCl6. Obtained trajectory from molecular dynamics infers that the Li-ion transportation is mainly through interstitial hopping which was confirmed by intra- and inter-layer Li-ion displacement with respect to simulation time. Ionic conductivity (1.06 mS/cm) and activation energy (0.29eV) calculated by our simulation are highly comparable with that of experimental values. Overall, the combination of machine-learning methods and AIMD simulations explains the intricate electrochemical properties of the Li3TiCl6 cathode with remarkably reduced computational time. Thus, our work strongly suggests that the deep neural network-based MLFF could be a promising method for large-scale complex materials.

An investigation of self-interstitial diffusion in α-zirconium by an on-the-fly machine learning force field

The on-the-fly machine learning force field approach, based on the Gaussian approximation potential and Bayesian error estimation, was used to study the diffusion of self-interstitial atoms in α-zirconium. Ab initio molecular dynamics simulations of lattice vibration and interstitial diffusion at different temperatures were employed to develop the force field. The radial and angular descriptors of the potential were further optimized to achieve better agreement with first-principles results. Subsequent long-term diffusion simulations were performed to assess the diffusion behavior based on the obtained force field. Tracer diffusion coefficients and diffusion anisotropy were studied at temperatures of 600–1200 K, and the Bayesian errors were estimated throughout the diffusion simulations. The mean and maximum estimated Bayesian errors of atomic force were approximately twice as large as those observed during the learning period. The basal diffusion was greatly favored compared to the interstitial diffusion along the c-axis, consistent with previous simulations based on first-principles results and classical potentials. The accuracy and applicability of the current on-the-fly machine learning approach were critically evaluated.

Data-Driven Discovery of Gas-Selective Organic Linkers in Metal-Organic Frameworks for the Separation of Ethylene and Ethane.

Metal-organic frameworks (MOFs) are potential candidates for gas-selective adsorbents for the separation of an ethylene/ethane mixture. To accelerate material discovery, high-throughput computational screening is a viable solution. However, classical force fields, which were widely employed in recent studies of MOF adsorbents, have been criticized for their failure to cover complicated interactions such as those involving π electrons. Herein, we demonstrate that machine learning force fields (MLFFs) trained on quantum-chemical reference data can overcome this difficulty. We have constructed a MLFF to accurately predict the adsorption energies of ethylene and ethane on the organic linkers of MOFs and discovered that the π electrons from both the ethylene molecule and the aromatic rings in the linkers could substantially influence the selectivity for gas adsorption. Four kinds of MOF linkers are identified as having promise for the separation of ethylene and ethane, and our results could also offer a new perspective on the design of MOF building blocks for diverse applications.

Hyper‐Elastic Deformation via Martensitic Phase Transformation in Cadmium Telluride

Cadmium telluride (CdTe) is a highly promising material for photovoltaics (PV) and photodetectors due to its light‐absorbing properties. However, efficient design and use of flexible devices require a deep understanding of its atomic‐level deformation mechanism. Herein, uniaxial compression deformation of CdTe monocrystalline with varying crystal orientations is investigated using molecular dynamics (MD) with a newly developed machine‐learning force field (ML‐FF), alongside in‐situ micropillar compression experiments. The findings reveal that CdTe bulk deformation is dominated by reversible martensitic phase transformation, whereas CdTe pillar deformation is primarily driven by dislocation nucleation and movement. CdTe monocrystals possess exceptional super‐recoverable deformation along the <100> orientation due to hyper‐elastic processes induced by martensitic transformation. This discovery not only sheds light on the peculiarities observed in micropillar experimental measurements, but also provides pivotal insights into the fundamental deformation behaviors of CdTe and similar II–VI compounds under various stress conditions. These insights are crucial for the innovative design and enhanced functionality of future flexible electronic devices.

Accurate machine learning force fields via experimental and simulation data fusion

Machine Learning (ML)-based force fields are attracting ever-increasing interest due to their capacity to span spatiotemporal scales of classical interatomic potentials at quantum-level accuracy. They can be trained based on high-fidelity simulations or experiments, the former being the common case. However, both approaches are impaired by scarce and erroneous data resulting in models that either do not agree with well-known experimental observations or are under-constrained and only reproduce some properties. Here we leverage both Density Functional Theory (DFT) calculations and experimentally measured mechanical properties and lattice parameters to train an ML potential of titanium. We demonstrate that the fused data learning strategy can concurrently satisfy all target objectives, thus resulting in a molecular model of higher accuracy compared to the models trained with a single data source. The inaccuracies of DFT functionals at target experimental properties were corrected, while the investigated off-target properties were affected only mildly and mostly positively. Our approach is applicable to any material and can serve as a general strategy to obtain highly accurate ML potentials.

Insights into Lithium Sulfide Glass Electrolyte Structures and Ionic Conductivity via Machine Learning Force Field Simulations.

Sulfide-based solid electrolytes (SEs) are important for advancing all-solid-state batteries (ASSBs), primarily due to their high ionic conductivities and robust mechanical stability. Glassy SEs (GSEs) comprising mixed Si and P glass formers are particularly promising for their synthesis process and their ability to prevent lithium dendrite growth. However, to date, the complexity of their glassy structures hinders a complete understanding of the relationships between their structures and properties. This study introduces a new machine learning force field (ML-FF) tailored for lithium sulfide-based GSEs, enabling the exploration of their structural characteristics, mechanical properties, and lithium ionic conductivities. Using molecular dynamic (MD) simulations with this ML-FF, we explore the glass structures in varying compositions, including binary Li2S-SiS2 and Li2S-P2S5 as well as ternary Li2S-SiS2-P2S5. Our simulations yielded consistent results in terms of density, elastic modulus, radial distribution functions, and neutron structure factors compared to DFT and experimental work. Our findings reveal distinct local environments for Si and P within these glasses, with most Si atoms in edge-sharing configurations in Li2S-SiS2 and a mix of corner- and edge-sharing tetrahedra in the ternary Li2S-SiS2-P2S5 composition. For lithium ionic conductivity at 300 K, the 50Li2S-50SiS2 glass displayed the lowest conductivity at 2.1 mS/cm, while the 75Li2S-25P2S5 composition exhibited the highest conductivity at 3.6 mS/cm. The ternary glass showed a conductivity of 2.6 mS/cm, sitting between the two. Moreover, an in-depth analysis of lithium ion diffusion over the MD trajectory in the ternary glass demonstrated a significant correlation between diffusion pathways and the rotational dynamics of nearby SiS4 or PS4 tetrahedra. The ML-FF developed in this study provides an important tool for exploring a broad spectrum of solid-state and mixed former sulfide-based electrolytes.

On-the-fly machine learned force fields for the study of warm dense matter: Application to diffusion and viscosity of CH

We develop a framework for on-the-fly machine learned force field (MLFF) molecular dynamics (MD) simulations of warm dense matter (WDM). In particular, we employ an MLFF scheme based on the kernel method and Bayesian linear regression, with the training data generated from the Kohn–Sham density functional theory (DFT) using the Gauss spectral quadrature method, within which we calculate energies, atomic forces, and stresses. We verify the accuracy of the formalism by comparing the predicted properties of warm dense carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that ab initio MD simulations of WDM can be accelerated by up to three orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the diffusion coefficients and shear viscosity of CH at a density of 1 g/cm3 and temperatures in the range of 75 000–750 000 K. We find that the self- and inter-diffusion coefficients and the viscosity obey a power law with temperature, and that the diffusion coefficient results suggest a weak coupling between C and H in CH. In addition, we find agreement within standard deviation with previous results for C and CH but disagreement for H, demonstrating the need for ab initio calculations as presented here.

Atomic Diffusivities of Yttrium, Titanium and Oxygen Calculated by Ab Initio Molecular Dynamics in Molten 316L Oxide-Dispersion-Strengthened Steel Fabricated via Additive Manufacturing.

Oxide-dispersion-strengthened (ODS) steels have long been viewed as a prime solution for harsh environments. However, conventional manufacturing of ODS steels limits the final product geometry, is difficult to scale up to large components, and is expensive due to multiple highly involved, solid-state processing steps required. Additive manufacturing (AM) can directly incorporate dispersion elements (e.g., Y, Ti and O) during component fabrication, thus bypassing the need for an ODS steel supply chain, the scale-up challenges of powder processing routes, the buoyancy challenges associated with casting ODS steels, and the joining issues for net-shape component fabrication. In the AM process, the diffusion of the dispersion elements in the molten steel plays a key role in the precipitation of the oxide particles, thereby influencing the microstructure, thermal stability and high-temperature mechanical properties of the resulting ODS steels. In this work, the atomic diffusivities of Y, Ti, and O in molten 316L stainless steel (SS) as functions of temperature are determined by ab initio molecular dynamics simulations. The latest Vienna Ab initio Simulation Package (VASP) package that incorporates an on-the-fly machine learning force field for accelerated computation is used. At a constant temperature, the time-dependent coordinates of the target atoms in the molten 316L SS were analyzed in the form of mean square displacement in order to obtain diffusivity. The values of the diffusivity at multiple temperatures are then fitted to the Arrhenius form to determine the activation energy and the pre-exponential factor. Given the challenges in experimental measurement of atomic diffusivity at such high temperatures and correspondingly the lack of experimental data, this study provides important physical parameters for future modeling of the oxide precipitation kinetics during AM process.

Non-equilibrium nature of fracture determines the crack paths

Local kinetic processes during crack growth are non-equilibrium and discrete and thus cannot be resolved in the framework of continuum thermodynamics. Atomistic modeling using existing empirical or machine-learning force fields also fails to offer satisfactory solutions for the lack of sufficient accuracy in predicting the energetics of strong lattice distortion and edge cleavage during fracture. The problem is addressed here by using a high-fidelity neural network-based force field for fracture (NN-F3) that covers the space of strain states up to material failure and the non-equilibrium, intermediate states at the crack tip. Atomistic simulations using NN-F3 reveal spatial complexities from lattice-scale kinks to sample-scale crack patterns in 2D crystals such as graphene, which evolve along the process of crack growth. The non-uniform lattice distortion and undercoordination of cleaved edges at the crack front play critical roles in the fracture process. The fracture toughness by cleaving specific edges thus cannot be quantified by their energy densities with relaxed atomic-level structures, which, however, have been widely used in the literature. Instead, the fracture patterns, the critical stress intensity factors corresponding to the kinking events, and the energy densities of edges in the intermediate, unrelaxed states offer reasonable measures for the fracture resistance and its anisotropy, which can be determined from experimental or simulation data with the atomic-level resolution. The findings conform well with recent experimental observations.