Embedded-atom Potential Research Articles

Molecular dynamics study of the scratching property of the tetrahedral amorphous carbon coating on the piston ring

In order to reduce friction and wear of the piston ring-cylinder liner system of the internal combustion engine, the tetrahedral amorphous carbon (ta-C) coating on the piston ring is considered. The scratching properties of the ta-C coating and diamond ball are studied by molecular dynamics simulation. The atomic configuration, surface morphology, RMS roughness, friction force, coefficient of friction, wear rate, and normal stress of the ta-C coating are analysed under different scratching depths, substrate temperatures, and scratching velocities. The interatomic interactions are described using the second nearest-neighbour modified embedded-atom method potential, as well as Tersoff potential and Lennard-Jones potential. The simulation results show that the ta-C coating exhibits excellent scratching properties. The scratching depth has a significant effect on the scratching property of the ta-C coating, while the substrate temperature and scratching velocity have a relatively small effect.

Reactive scattering of H2 on Cu(111) at 925K: Effective Hartree potential vs sudden approximation.

We present new quantum dynamical results for the reactive scattering of hydrogen molecules from a Cu(111) surface at a surface temperature of 925K. Reaction, scattering, and diffraction probabilities are compared for results obtained using both an effective Hartree potential (EfHP) and a sudden approximation approach, implemented through the static corrugation model (SCM), to include surface temperature effects. Toward this goal, we show how the SRP48 DFT-functional and an embedded atom potential perform when used to calculate copper lattice constants and thermal expansion coefficients based on lattice dynamics calculations within the quasi-harmonic approximation. The so-calculated phonons are then used in the EfHP approach to replace the normal modes of a fictitious copper cluster used in earlier work. We find that both the EfHP and SCM approaches correctly predict the reaction probability curve broadening effect when the surface temperature is increased. Similarly, results for rovibrationally elastic scattering appear to be improved, predominantly for the SCM model. The behavior of the EfHP results appears to remain much closer to that of a Born-Oppenheimer static surface approach, which excludes any surface temperature effects. Finally, for the diffraction, we show very clear attenuation effects for the SCM approach, significantly decreasing specular diffraction probabilities at 925K surface temperature. These results demonstrate that state-of-the-art theoretical models are able to reproduce strictly quantum mechanical scattering effects with a sudden approximation model and open up interesting opportunities for further comparisons to experimental diffraction results.

Atomistic and continuum Ascertainment of The crack tip stress fields in anisotropic elastic cubic media

The article provides a comparative analysis of stresses associated with the crack tip in an anisotropic elastic medium with cubic crystalline symmetry of elastic properties under mixed loading conditions obtained by two fundamentally different approaches: atomistic simulations and continuum fracture mechanics methods. The atomistic modelling approach is premised on the application of the molecular dynamics (MD) method implemented in the open source code program Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The continuum mechanics approach is based on the classical elasticity theory of anisotropic media, in which the mechanical fields associated with the crack tip are represented by the crack tip stress and displacement series expansions generalizing the well-known classical asymptotical presentation of M. Williams to the case of anisotropic media. Using the MD method, a large series of computations of the loading of monocrystalline copper and aluminum plates with a face-centered cubic crystal lattice weakened by a central crack applying the embedded atom potential (EAM) was implemented. MD modeling is aimed at determining the atomic stresses and strains near the crack tip. The computed atomic stresses were compared with the stress field determined by the continuum elasticity theory of anisotropic media for crystal lattices with cubic symmetry of elastic properties. A comparative analysis was carried out for the angular dependencies of the stress and strain tensor components at various selected distances from the crack tip for the entire range of mixed deformation forms starting from pure tensile loading and ending with forms close to pure transverse shear. It is ascertained that the crack tip fields determined on the basis of two fundamentally different approaches, precisely, discrete and continuum, are completely consistent with each other. It is established that mathematical methods of continuum fracture mechanics can be applied to describe stress, strain and displacement fields at the atomic level.

Effects of grain size and zirconium concentration on mechanical properties of nanocrystalline copper grain boundary doping

ABSTRACT Alloying nanocrystalline Cu (nc–Cu) with immiscible elements (i.e. Zr) is a promising approach for reducing microstructural instability and inhibiting grain growth. Understanding the relationship between the grain size, Zr concentration, deformation, and mechanical properties of the nc–Cu–Zr system is essential for practical applications. Molecular dynamics simulations based on the many-body embedded-atom potential were used for the related analysis from an atomistic point of view. The grain size of nc–Cu was varied from 3 to 9 nm and the Zr concentration was varied from 0% to 7%. The simulation results show that doping Zr atoms into an nc–Cu system enhances tensile strength and ductility, but weakens compressive and shear strengths. Doping 1% Zr into nc–Cu greatly increases both ultimate tensile strength and ultimate tensile strain; the increase is insignificant for higher Zr concentrations (2% to 7%). For a given Zr concentration, the relationship between ultimate tensile strength and grain size is unclear. Grain boundary sliding dominates the elastic deformation mechanism of the nc–Cu–Zr system under tensile, compressive, and shear tests. Tensile fracture occurs faster for an nc–Cu–Zr system with a larger grain size.

Transferring predictions of formation energy across lattices of increasing size*

In this study, we show the transferability of graph convolutional neural network (GCNN) predictions of the formation energy of the nickel-platinum solid solution alloy across atomic structures of increasing sizes. The original dataset was generated with the large-scale atomic/molecular massively parallel simulator using the second nearest-neighbor modified embedded-atom method empirical interatomic potential. Geometry optimization was performed on the initially randomly generated face centered cubic crystal structures and the formation energy has been calculated at each step of the geometry optimization, with configurations spanning the whole compositional range. Using data from various steps of the geometry optimization, we first trained our open-source, scalable implementation of GCNN called HydraGNN on a lattice of 256 atoms, which accounts well for the short-range interactions. Using this data, we predicted the formation energy for lattices of 864 atoms and 2048 atoms, which resulted in lower-than-expected accuracy due to the long-range interactions present in these larger lattices. We accounted for the long-range interactions by including a small amount of training data representative for those two larger sizes, whereupon the predictions of HydraGNN scaled linearly with the size of the lattice. Therefore, our strategy ensured scalability while reducing significantly the computational cost of training on larger lattice sizes.

Extracting free energies from local composition fluctuations in solids: A frequency distribution analysis of simulated atom probe data obtained by TAPSim

The present work proposes a novel methodology to extract direct thermodynamic information, i.e. Gibbs free energies, from local composition fluctuations found in atom probe data based on statistical mechanics. The proof-of-concept is demonstrated with an exemplary simulated Cu–Ni alloy, which has first been equilibrated using Monte Carlo techniques with an embedded-atom method potential and subsequently field evaporated by TAPSim. It is shown that the variance of the frequency distribution of the local composition on the reconstructed data reveals a systematic dependence on the size of the chosen spherical (sub-) volume used for the evaluation, but nevertheless the extrapolation to an infinitely large volume unveils a unique link to the curvature of the Gibbs free energy. Given the composition range is explored at several points, the Gibbs excess free energy of mixing could be recovered in a CALPHAD-style parametrization. This methodology promises to improve the accuracy of thermodynamic information (e.g. miscibility gap, mixing/demixing tendencies, critical solution temperature) from direct atom probe measurements.

The deposition properties of tetrahedral amorphous carbon coatings deposited on piston ring: Molecular dynamics simulation

The tetrahedral amorphous carbon (ta-C) coatings are deposited on piston rings to improve the tribological property of the piston ring-cylinder liner system of the internal combustion engines. The deposition parameters are optimized by molecular dynamics simulation to reduce the cost of coatings’ fabrication. The ta-C coatings with higher sp3 fraction, lower friction coefficient, and superior anti-wear properties are achieved by optimizing the incident energy and substrate temperature of carbon atoms. The second nearest-neighbor modified embedded-atom method potential and Tersoff potential are used to describe the interatomic interactions. The effects of the incident energy of the carbon atoms and substrate temperature on the deposition properties of the ta-C coatings are discussed. The numerical results show that the ta-C coatings with high sp3 fraction, high density, and good interface mixing are obtained, and the deposition properties of the ta-C coatings are improved.

ATOMISTIC AND CONTINUAL DETERMINATION OF STRESS FIELDS AT A CRACK TIP IN ANISOTROPIC ENVIRONMENT WITH CUBIC SYSTEM

The article presents a comparative analysis of stresses associated with a crack tip in an anisotropic medium with cubic symmetry of elastic properties under mixed mode loading conditions, using two different approaches: atomistic and continuum approaches. The atomistic approach is based on the use of the molecular dynamics method implemented in the open source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The continuum approach is based on the classical theory of elasticity of anisotropic media, in which the mechanical fields associated with the crack tip are represented using series that generalize the well-known representation of M. Williams to the case of anisotropic media. Using the method of molecular dynamics, a large series of calculations of loading of single-crystal copper and aluminum plates with a face-centered crystal lattice, weakened by a central crack, was carried out using the embedded atom potential (EAM). Molecular dynamics modeling is aimed at determining atomistic stresses and strains near the crack tip. The calculated atomistic stresses were compared with the stress field determined by the continuum theory of elasticity of anisotropic media for crystal lattices with cubic symmetry of elastic properties. A comparative analysis was carried out for the angular dependences of the stress and strain tensor components at different distances from the crack tip for the entire range of mixed strain modes: from perfect normal tension to loadings close to perfect transverse shear. It is established that the fields found on the basis of two fundamentally different approaches (discrete and continuum) are fully consistent with each other. It is demonstrated that the mathematical methods of continuum fracture mechanics can be used to describe stress, strain, and displacement fields at the atomistic level.

Accuracy, Performance, and Transferability of Interparticle Potentials for Al–Cu Alloys: Comparison of Embedded Atom and Deep Machine Learning Models

In several recent years, a significant progress has been made in atomistic simulation of materials, involving the application of machine learning methods to constructing classical interatomic interaction potentials. These potentials are many-body functions with a large number of variable parameters whose values are optimized with the use of energies and forces calculated for various atomic configurations by ab initio methods. In the present paper a machine learning potential is developed on the basis of deep neural networks (DP) for Al–Cu alloys, and the accuracy and performance of this potential is compared with the embedded atom potential. The analysis of the results obtained implies that the DP provides a sufficiently high accuracy of calculation of the structural, thermodynamic, and transport properties of Al–Cu alloys in both solid and liquid states over the entire range of compositions and a wide temperature interval. The accuracy of the embedded atom model (EAM) in calculating the same properties is noticeably lower on the whole. It is demonstrated that the application of the potentials based on neural networks to the simulation on modern graphic processors allows one to reach a computational efficiency on the same order of magnitude as those of the embedded atom calculations, which at least four orders of magnitude higher than the computational efficiency of ab initio calculations. The most important result is that about the possibility of application of DP parameterized with the use of configurations corresponding to melts and perfect crystals to the simulation of structural defects in crystals and interphase surfaces.

An embedded-atom method interatomic potential for lithium-iron binary system and its applications in the liquid first wall system

Molecular dynamics simulations have been widely used to investigate the thermodynamic and structural properties of liquid lithium (Li) and solid substrates as the concept of liquid divertor of fusion devices becomes more and more popular. However, this kind of studies are limited by the complexity of constructing the interatomic potentials for alloy systems. In this work, a new interatomic potential based on the embedded-atom method (EAM) was developed for the Li-Fe (iron) binary system. The parameters of the potential were optimized based on the first-principles calculations and experimental results of the elemental and binary properties of Li-Fe system. Results show that the new potential provides good descriptions of the mechanical and thermal properties of solid α-Fe and liquid Li including the elastic moduli of α-Fe and the viscosity of liquid Li. Especially, the addition of the surface energies and interfacial adhesion work into the fitting database guarantees that the wetting properties of liquid Li on α-Fe surfaces are well predicted. The contact angle on {100} Fe surface was calculated to be 58.4° which agrees very well with the experimental results. The new potential was applied to simulate the tensile tests of Li-Fe alloy and the Li flow in an α-Fe capillary channel. Results suggest that this potential is suitable for simulations of a variety of processes such as the surface corrosion of α-Fe by liquid Li, and the wetting and spreading of liquid Li on α-Fe surfaces, which are of interests in the context of the development of liquid divertor in future fusion reactors.

Deposition of TiNi thin films on Ni(001) substrate using molecular dynamics simulation

This paper investigates the effect of incident energy and substrate temperature on the morphological and microstructural properties of TiNi thin films deposited on Ni substrate. The detailed analysis of surface morphology, the interface intermixing, density, and the voids in TiNi thin films was performed by molecular dynamics simulation combined with the second nearest-neighbor modified embedded-atom method interatomic potential (2 NN MEAM). The results indicate that higher incident energy and substrate temperature affect morphological properties of TiNi thin film. When the incident energy ranges from 0.1 to 10 eV, the surface roughness initially increases before eventually decreasing. Regarding the substrate temperature, the roughness decreases initially from 300 K to 700 K, but beyond 700 K, it begins to increase again. In addition, the interface mixing analysis was also affected by incident energy. It is found that, the thickness of the mixing interface was increased as the incident energy increase. This suggests that the growth mode changes from epitaxial to mixing. When the incident energy is higher than 10 eV, the diffusion rate of Ti atoms in the substrate layers is higher than that of Ni atoms. Conversely, at the surface of thin film, the concentration of Ni atoms is higher than that of Ti atoms. However, the substrate temperature has no significant effect on the change in interface thickness. The density of the TiNi thin films shows a significant dependence on the incident energy, but not affected by the substrate temperature. In addition, the result reveal that the increasing both the incident energy and the thickness of thin films reduces the concentration of voids and vacancies.

Parametrization of embedded-atom method potential for liquid lithium and lead-lithium eutectic alloy

Liquid lead-lithium eutectic remains as a promising candidate for various breeding-blanket designs in future nuclear-fusion technologies. The lack of a generalized theory of interatomic forces in the liquid state is reflected on the wide variety of proposed functional forms to describe interatomic interactions even in simple liquids. Computer simulations facilitate the study of liquid metal properties, due to mathematical and experimental challenges. A classical-MD EAM potential is parametrized using mechanical and non-mechanical (melting-point) properties to minimize the arbitrariness of functional forms, where the employed pair potential stems from the liquid-state theory to avoid the issue of the uniqueness of the potential. Enhanced performance is obtained for liquid density, energy, structure, diffusivity and shear viscosity of Li, and their temperature-dependencies. In a similar manner, reference experimental and ab initio MD data are used to parametrize a functional to describe Pb-Li pairwise interactions in liquid Pb-Li alloy, which is used with the derived EAM of liquid Li and a reference EAM of liquid Pb to investigate properties of liquid Pb-Li alloy. Enhanced transferability characteristics are obtained for low-in-lithium liquid Pb-Li melts, where Coulombic interactions are negligible. In specific, the exhibited behaviour of Li in liquid lead-lithium eutectic is consistent with findings from ab initio MD methods, and drastically different from predictions of previous C-MD studies which suggested a substantial segregation of Li atoms instead of dispersion. It is concluded that the functional form of the pair potential and its uniqueness influence both the pure liquid-metal properties and the validity of the potential transferability in multi-component systems, where a theoretical functional results in enhanced performance in pure and alloyed liquid systems.

Exploring the impact of cooling rates and pressure on fragility and structural transformations in iron monatomic metallic glasses: Insights from molecular dynamics simulations

In this study, we investigate Fe metallic glass under pressures from 0 to 20 GPa and cooling rates of 5 × 1012 to 1014 K/s using molecular dynamics (MD) simulations with an embedded-atom potential (EAM). Increasing pressure enhances brittleness, indicating a higher barrier energy for the glass transition. Higher pressures narrow the glass transition region, resulting in a shorter relaxation range. At pressures above 10 GPa, especially with a cooling rate of 5 × 1012 K/s, crystal nucleation is promoted, and short-range order strengthens, primarily body-centered cubic structure (bcc) clusters. Certain pressure-cooling rate combinations show significant increments. Pressure affects density and interatomic distance, while cooling rate changes have minimal effects.

Atomistic simulation of the effect of porosity on shock response of nanoporous gold.

Nanoporous metals (NPMs) have a three-dimensional bicontinuous porous network structure that consists of interconnected nanoligaments. NPMs have the potential to effectively attenuate and dissipate the effects of impacts and blasts. Previous studies do not provide data on the possible effects of porosity at the nanoscale. Molecular dynamics simulations based on the embedded-atom method potential were performed using the open-source code LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). Nanoporous gold (NPG) absorbs shock energy first through the elastic-plastic deformation of ligaments and then through the collapse of ligaments. After the shock loading is relaxed, NPG with lower porosity has a higher amount of springback, and new voids tend to nucleate and grow at collapsed ligaments where the packing is looser. NPG with higher porosity has a better ability to resist the propagation of a shock wave and is subjected to a smaller stress effect.

New approaches to study of mismatched interfaces structure on low-index surfaces by molecular dynamics simulation

We used molecular dynamics simulations to study the structure of mismatched Al/Ni and Ag/Cu interfaces, considering low-index surfaces of the substrate. Embedded Atom Potentials are being employed to mimic atomic interactions between the different elements. The effect of the substrate orientation on the adlayer structure is investigated. The results showed that, on the (111) substrate, the adlayer presents a coincidence site lattice characterized by a rotation (labeled α) with respect to the substrate. This coincidence site lattice may contain dislocations and twin boundary that can be produced by the occurrence of a twin spirals (with opposite directions). To accommodate the adlayer deposition on the substrate, a slight shuffling of some atoms occurs in the substrate and leads to a rectangular structures producing a dislocation. Furthermore, on the (001) substrate, the accommodation of the triangular structure on the square lattice (substrate) is produced by a shift of some atomic rows producing a dislocation. But, the agglomeration of several square structures of 2d shape gives rise to a polycrystal delimited by a disclination forming grain boundaries and vacancies. However, the inward adsorption on the (110) substrate restricts the space of extension of adsorbed atoms, producing linear cracks. The relaxation of atoms adsorbed on these cracks change the linear shape of vacancies towards a staircase structure.

Transferability of Zr-Zr interatomic potentials

Tens of Zr inter-atomic potentials (force fields) have been developed to enable atomic-scale simulations of Zr alloys. These can provide critical insight in the in-reactor behaviour of nuclear fuel cladding and structural components exposed, but the results are strongly sensitive to the choice of potential. We provide a comprehensive comparison of 13 popular Zr potentials, and assess their ability to reproduce key physical, mechanical, structural and thermodynamic properties of Zr. We assess the lattice parameters, thermal expansion, melting point, volume-energy response, allotropic phase stability, elastic properties, and point defect energies, and compare them to experimental and ab-initio values. No potential was found to outperform all others on all aspects, but for every metric considered here, at least one potential was found to provide reliable results. Older embedded-atom method (EAM) potentials tend to excel in 2-3 metrics each, but at the cost of poorer transferability. The two highest-performing potentials overall, with complementary strengths and weaknesses, were the 2021 angular-dependent potential of Smirnova and Starikov (Comp. Mater. Sci. 197, 110581) and the 2019 embedded-atom method potential of Wimmer et al (J. Nucl. Mater. 532, 152055). All potentials trained through machine learning algorithms proved to have lower overall accuracy, and less transferability, than simpler and computationally faster potentials available. Point defect structures and energies is where the greatest divergence and least accuracy is observed. We created maps that will help modellers select the most suitable potential for a specific application, and which may help identify areas of improvement in future potentials.

The interplay between size, shape, and surface segregation in high-entropy nanoalloys.

The respective influences of particle shape and size on the energetic stability of five-component multimetallic nanoparticles have been computationally investigated for AlCuFeCrNi and AuCuPdNiCo mixtures at equiconcentration. Using available embedded-atom model potentials, exchange Monte Carlo simulations possibly assisted with systematic quenching, we explore tools to approach ideal phase equilibrium in such high-entropy nanoalloys. In particular, we show how deviations to ideal solid solution behaviors can be characterized using percolation analyses, and how the contribution of alloying fluctuations at finite temperature can be inferred to evaluate the entropy of mixing in such nonideal cases. An approximation to the entropy of mixing based on pair correlations only is also found to capture the behavior of the thermodynamical mixing entropy quite well, and can be used as an order parameter of mixing. While the AlCuFeCrNi mixture appears to mix reasonably well in all cases considered, cobalt and nickel segregate significantly in AuCuPdNiCo nanoparticles, deviating strongly from ideal random mixtures. A simple Gaussian regression model applied to a coarse distribution of concentrations is found to correctly predict conditions for optimising the mixing thermodynamical properties of the miscible AlCuFeCrNi nanoparticle.

Computational determination of a primary diffusion mode in [formula omitted]U-10Mo under irradiation

Low enriched uranium (< 20 %235U)-molybdenum (U-Mo) monolithic fuel is the primary candidate for high-performance research and test reactors and is in the process of being qualified to replace highly-enriched uranium (≥ 20 %235U) fuel. As part of the qualification process, it is critical to understand and predict the behavior of fission gas bubbles under irradiation, which affects fuel swelling and fuel failure. Mechanistic fuel models are being developed that can both reproduce the existing experimental data for fuel swelling, and be further applied to irradiation conditions beyond the experimental scope. Diffusion of species under irradiation conditions is an important parameter in the mechanistic fuel models; however, no temperature-relevant experimental diffusion data exists. In the present work, radiation-enhanced diffusion coefficients of U, Mo, and Xe in γU-10wt.%Mo were calculated in the temperature range between 300 K and 1400 K via rate-theory models and molecular dynamics simulations with an embedded-atom method interatomic potential for the U-Mo-Xe system. Accordingly, total diffusion coefficients under relevant irradiation conditions are determined using previously obtained intrinsic thermal diffusion and radiation-driven diffusion coefficients, as well as the newly calculated radiation-enhanced diffusion coefficients presented herein. Radiation-enhanced diffusion of U and Mo was dominant in the intermediate temperature range, whereas radiation-enhanced diffusion of Xe did not significantly contribute to total diffusion of Xe at the relevant fission rate densities. Radiation-enhanced diffusion of Xe became faster than both intrinsic thermal diffusion and radiation-driven diffusion at a fission rate density of 5×1022fiss/m3/s, which is higher than the typical fission rate density range in research reactors. The temperature regime where radiation-enhanced diffusion of each element dominated was dependent on the fission rate density. The total diffusion coefficients of U, Mo, and Xe, updated in this work, will be utilized as parameters in the mechanistic fuel models to help predict the behavior of fission gas bubbles under irradiation more accurately.

An embedded-atom method potential for studying the properties of Fe-Pb solid-liquid interface

A new interatomic potential for Fe-Pb binary system is developed in the framework of an embedded atom model using the force-matching method. Compared with the ab initio calculations and experiment values, the developed Fe-Pb EAM potential can accurately describe the ground state, defects and liquid properties of crystal and Fe-Pb solid-liquid interface, such as equation of state, vacancy and interstitial formation energies, adsorption and escape energies, melting point, radial distribution function and density at high temperature. High accuracy and feasibility of the developed Fe-Pb EAM potential can provide the further reliable studies on the corrosion behavior of liquid Pb on steels used in complicate environment of the irradiation, high temperature, pressure in nuclear reactors.

Molecular dynamic simulation of Cs corrosion in Cs oven for negative ion source applications

Molecular dynamic simulation is used to simulate the corrosion process of Fe or Ni in liquid Cs by Large-scale Atomic/Molecular Massively Parallel Simulator. The embedded-atom method potential is used to describe the interaction of Fe–Fe, Ni–Ni, and Cs–Cs, and Morse two-body potential is used to describe the Fe–Cs and Ni–Cs atomic interaction. Temperature is considered as a critical condition in this work. Results indicate that corrosion is easy to occur in the systems. The increase in temperature can help the process of Cs corrosion. Compared to the Ni–Cs system, the Fe–Cs system has a higher atomic concentration function. The radial distribution function shows that Cs atoms are dissolved into the substrates, but the Fe and Ni substrates are still crystalline structures. Moreover, Cs in Fe or Ni is still a liquid phase.