Embedded Atom Method Interatomic Potential Research Articles

Molecular dynamics simulation of the diffusion behaviour in Ti–Ag using diffusion couple method

The diffusion behaviour of the Ti–Ag system was investigated using classical molecular dynamics by simulating a diffusion couple at various temperatures. One bulk of the diffusion couple consisted of titanium atoms arranged in a hexagonal close-packed (hcp) structure, i.e., α-Ti, and the other consisted of silver atoms arranged in a face-centred cubic (fcc) structure. The modern second nearest-neighbour modified embedded-atom method (2NN-MEAM) interatomic potential was used. The mean square displacement (MSD) of Ti atoms diffusing into Ag and Ag atoms into α-Ti was recorded during the simulation. Diffusion coefficients were determined from the slopes of lines fit to linear regions of MSD dependence on time. The Arrhenius relation was used to determine the activation energy and the frequency of attempts. The activation energy of Ti was 0.61eV and frequency of attempts 1.90⋅10−8m2s−1. The determined activation energy of Ag and frequency of attempts were not considered reliable because the Ag diffusion coefficient did not grow exponentially with temperature. Ti atoms penetrated deeper and greater amounts into Ag than Ag into α-Ti and also had a greater diffusion coefficient at all temperatures. The results were compared with the available experimental data, and for these purposes, self-diffusion in α-Ti and Ag was further investigated. Finally, it was determined that Ag diffuses in α-Ti by hopping over interstitial positions and Ti in Ag via vacancies.

EFFECT OF VACANCIES AND VOID DEFECTS ON THE STRUCTURAL AND MECHANICAL BEHAVIOR OF TUNGSTEN UNDER HARSH TEMPERATURE AND PRESSURE CONDITIONS

The body-centered cubic transition metal tungsten is frequently used as a pressure calibration material at high temperatures and pressures due to its outstanding mechanical and thermal properties. In this study, molecular dynamics simulations were performed to investigate the behavior of tungsten under harsh temperature and pressure conditions and the impact of fundamental defects, particularly vacancies, and voids, on its physical, structural, and mechanical properties through their correlation with elastic constants. The study also covers mechanical stability, elastic properties, brittleness and ductility, and hardness. The simulations utilized two different embedded atom methods and one modified embedded atom method interatomic potentials. The results show that the fundamental structural characteristics and properties of pure tungsten crystal, including lattice constant, density, cohesive and vacancy formation energies, elastic constants, and moduli in the ground state for all three potentials, are in good agreement with previous experimental and theoretical calculations and results. The calculated results demonstrate that the elastic constants-related properties for defective structures also have the same trend as the perfect crystal. The presence of defects in the crystal causes a decrease in properties at all temperatures and pressures, directly correlated to the fraction of crystal defects. As the percentage of vacancies increases, a further reduction in the elastic constants is observed. Likewise, these findings reveal that the presence of scattered vacancies in the crystal structure causes a more significant decrease in the substance's properties than a void in the center of the crystal (with the same percentage). The presence of any vacancy weakens the interatomic bonds of the atoms around the vacancy, while the existence of a void in the center has less effect on the interatomic bonds of atoms further away from the center of the crystal.

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.

Prediction of the binding energy of self interstitial atoms in alpha iron by a graph neural network

The estimation of neutron irradiation embrittlement is crucial for the long-term operation of nuclear power plants. The jump of self-interstitial atoms is an essential process for understanding embrittlement, and their binding energy is critical to estimating the activation energy for jumping. This study presents a fast estimation method for the binding energy of self-interstitial atoms in iron using a graph neural network. The network assigns a self-interstitial atom to a node and the relationship between self-interstitial atoms to an edge. The graph neural network was trained using a large dataset of binding energies between self-interstitial atoms (∼0.5 % density) calculated using an embedded atom method interatomic potential. The network was also trained using smaller datasets of binding energies between self-interstitial atoms (∼2.0 % density) calculated using first principles calculations. The graph neural network accurately predicts binding energy with a mean absolute error of 0.05–0.06 eV and coefficient of determination (R2) of 0.9 without overfitting, using the large interatomic potential dataset. When trained on smaller first principles datasets, the network predicted binding energies with a mean absolute error of 0.15–0.16 eV and coefficient of determination (R2) of 0.6 with some degree of overfitting. The developed graph neural network provides a fast and accurate estimation method for the binding energy of self-interstitial atoms in iron.

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.

Modified embedded atom method interatomic potentials for the Fe-Al, Fe-Cu, Fe-Nb, Fe-W, and Co-Nb binary alloys

In this study, we developed interatomic potentials for the Fe-Al, Fe-Cu, Fe-Nb, Fe-W, and Co-Nb binary systems using the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The interatomic potentials were parameterized through fitting to available data on essential physical properties such as enthalpies of formation, structural parameters, and elastic constants. The fitted interatomic potentials are capable of accurately reproducing these properties, demonstrating a satisfactory level of concordance with data collected through experimentation, CALPHAD evaluations, and first-principles calculations. These potentials can be merged with existing MEAM potentials to study the physical metallurgy of multicomponent alloys such as FeCo-X (X = Al, Cu, Nb and W) and high entropy alloys (HEA), enabling deeper understanding of their unique properties at the atomic scale.

Modified embedded atom method interatomic potential for FCC γ-cerium

As interest in Cerium containing alloys and Al-Ce alloys in particular grows, the need to generate predictions of mechanical, thermodynamic and transport properties across a compositional space becomes more pronounced. The absence of a reliable interaction potential to be used in classical molecular dynamics (MD) simulation of γ-Ce is a fundamental bottleneck to subsequent alloy simulation. In this work, a Modified Embedded Atom Method (MEAM) potential to be used in MD simulation for γ-Ce has been generated. The parameterization process involved two steps. First, the iterative Latin hypercube sampling (LHS) method was used to generate MEAM parameter sets based on an automated optimization of energies and forces relative to a training set of small configurations evaluated through Density Functional Theory (DFT). Second, a human-guided optimization in that local parameter space was performed to refine the parameters to satisfy an array of mechanical, thermodynamic and transport properties available from the experimental literature. When used in an MD simulation, the resulting potential provides excellent estimates of all tested material properties across a broad temperature range. This γ-Ce potential, when combined with existing MEAM potential for Al, will form the necessary foundation for the subsequent development of a mixture potential, enabling the simulation of Al-Ce and Al-Ce-X alloys.

Simple Parameterization of Embedded Atom Method Potentials for FCC Alloys

We extend our simple parametric form for Embedded Atom Method interatomic potentials for FCC metals [Daw & Chandross, “Simple Parameterization of Embedded Atom Method Potentials FCC Metals”] to treat alloys. Using this model, which we refer to as “EAM-X”, we study the generic dependence of alloy properties on the model parameters. We introduce the idea of spread alloys, where the constituent elements are defined as parametric perturbations from a central, “average” FCC metal, and where different alloys are quantified by a measure of the magnitude of the perturbation. As an example, we consider a spread binary where the only differences between the constituent elements are lattice mismatch and the cross-interaction parameters and show that the model robustly describes the clustering and ordering tendencies of metal alloys. We use the model to prove a general theorem of “parametric simplicity” in random equimolar alloys: alloy properties differ from a simple rule of mixtures in a way that depends only on the standard deviation among the constituent parameters but are otherwise not dependent on the number of constituents, consistent with previous theoretical results.

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.

Second nearest-neighbor modified embedded atom method interatomic potentials for Na-M−Sn (M = Cu, Mn, Ni) ternary systems

Interatomic potentials for Mn-Sn, Ni-Sn, Na-Cu, Na-Mn, and Na-Ni binary systems and Na-Cu-Sn, Na-Mn-Sn, and Na-Ni-Sn ternary systems have been developed on the basis of the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials can describe various fundamental materials properties such as structural, elastic, thermodynamic, and thermal properties in reasonable agreement with experiments and DFT calculations. It is demonstrated that the potentials can be used for atomistic simulations to understand material phenomena and to search for optimal tin-based alloy anode materials for sodium ion batteries.

The impact of misorientation on the grain boundary energy in bi-crystal copper: an atomistic simulation study.

Atomistic simulations were performed to investigate the relationships among the misorientation, dislocation density, and grain boundary energy of twist and tilt bi-crystal grain boundaries. In this work, the grain boundary energies were calculated based on the embedded-atom method interatomic potential for Cu. The results show that the dislocation density of the grain boundary changes with the rotation angle, thereby affecting the grain boundary energy. Furthermore, the grain boundary energy of a grain boundary with no dislocations is greater than that of a grain boundary with dislocations, which results from the distribution of the atomic potential energy on the grain boundaries. Additionally, the grain boundary energy increases with the dislocation density of the grain boundary in the case of dislocations on the grain boundary. On this basis, a new relationship is proposed for the misorientation angle and grain boundary energy. We assume that when the driving force of dislocation nucleation breaks through the grain boundary energy barrier, the grain boundary energy declines.

Computational modelling studies for high temperature monazite systems

Monazite is widely considered as a potential source of fissile feedstock for nuclear power generation, as it generally contains significant quantity of thorium (Th), uranium (U) and rare earth elements (REEs) within the mineral ore structure. Currently, a new process of high-temperature cracking of monazite is under development to improve the liberation of these cations from the robust monazite lattice. The current process for extraction of the REEs from the mineral involves complicated processes which makes use of harsh chemicals. These process therefore has significant scope for optimisation. With this in mind, the stability of monazite systems, t-CeSiO4 and m-LaSiO4 was investigated using first-principle calculation employing density functional theory (DFT) to gain a better understanding of the inherent molecular structures and the influence of temperature on conformation. The calculated lattice parameters for the model of t-CeSiO4 were found to be in good agreement with the experimental values (within 3%) and deemed a sufficient m-LaSiO4 of the system to be exposed to simulated reaction conditions. The elastic properties suggested that t-CeSiO4 is the more stable structure compared to m-LaSiO4 structure at 0 K. Semi-empirical embedded atom method interatomic potentials incorporated in the LAMMPS code were also employed to investigate the lattice expansion of t-CeSiO4 at high temperatures. It was found that calculated a and b lattice parameters expand with a linear ratio to a temperature of 2200 K whereas the c parameter was found to contract in the same temperature range. The findings provided an in depth understanding of the monazite molecular structure change at higher temperatures that may be helpful in plasma cracking optimisation experimental methodologies.

Atomistic simulations of Ag\u2013Cu\u2013Sn alloys based on a new modified embedded-atom method interatomic potential

An interatomic potential for the ternary Ag–Cu–Sn system, an important material system related to the applications of lead-free solders, is developed on the basis of the second nearest-neighbor modified embedded-atom-method formalism. Potential parameters for the ternary and related binary systems are determined based on the recently improved unary description of pure Sn and the present improvements to the unary descriptions of pure Ag and Cu. To ensure the sufficient performance of atomistic simulations in various applications, the optimization of potential parameters is conducted based on the force-matching method that utilizes density functional theory predictions of energies and forces on various atomic configurations. We validate that the developed interatomic potential exhibits sufficient accuracy and transferability to various physical properties of pure metals, intermetallic compounds, solid solutions, and liquid solutions. The proposed interatomic potential can be straightforwardly used in future studies to investigate atomic-scale phenomena in soldering applications.Graphical abstract

Modified embedded-atom method interatomic potentials for Al-Cu, Al-Fe and Al-Ni binary alloys: From room temperature to melting point

Second nearest neighbor modified embedded-atom method (2NN-MEAM) interatomic potentials are developed for binary aluminum (Al) alloys applicable from room temperature to the melting point. The binary alloys studied in this work are Al-Cu, Al-Fe and Al-Ni. Sensitivity and uncertainty analyses are performed on potential parameters based on the perturbation approach. The outcome of the sensitivity analysis shows that some of the MEAM parameters interdependently influence all MEAM model outputs, allowing for the definition of an ordered calibration procedure to target specific MEAM outputs. Using these 2NN-MEAM interatomic potentials, molecular dynamics (MD) simulations are performed to calculate low and high-temperature properties, such as the formation energies of stable phases and unstable intermetallics, lattice parameters, elastic constants, thermal expansion coefficients, enthalpy of formation of solids, liquid mixing enthalpy, and liquidus temperatures at a wide range of compositions. The computed data are compared with the available first principle calculations and experimental data, showing high accuracy of the 2NN-MEAM interatomic potentials. In addition, the liquidus temperature of the Al binary alloys is compared to the phase diagrams determined by the CALPHAD method.

Interatomic potential for metal diborides

ABSTRACT Parameters of the embedded atom method inter-atomic potential for metal diborides MB2 (M = Al, Mg, Mo, Hf, Nb, Sc, Ti, Y, Zr, V) are presented in this paper. The potential parameters were determined empirically by fitting to a first-principles and experimental data of the equilibrium lattice constant, cohesion energy and bulk modulus of metal diborides. The potential provides a good representation of the desired properties of considered metal diborides. To test the applicability of the proposed potential to molecular dynamics simulation of metal diborides, the specific heat capacities of TiB2 and ZrB2 were determined. The proposed potential is intended for use in molecular dynamics simulations of metal diboride nanostructures.

Second nearest-neighbor modified embedded-atom method interatomic potentials for the Mo-M (M = Al, Co, Cr, Fe, Ni, Ti) binary alloy systems

Interatomic potentials for the Mo-M (M = Al, Co, Cr, Fe, Ni, Ti) binary alloy systems have been newly developed based on the second nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The new interatomic potentials reproduce structural and thermodynamic properties of binary alloys reasonably well. They can be utilized to generate interatomic potentials for Pt-Mo-M multicomponent alloy systems. The present work extends the coverage of the atomistic simulations using 2NN MEAM interatomic potentials into Pt-based multicomponent systems, and the design of efficient noble metal catalysts using atomistic simulations is now enabled with a greater variety of alloying elements.

An atomistic study of defect energetics and diffusion with respect to composition and temperature in γU and γU-Mo alloys

• Vacancy and self-interstitial formation energies were calculated in γ U and γ U-Mo. • Self-diffusion and interdiffusion coefficients in γ U- x Mo ( x = 7 , 10, 12 wt.%) were calculated. • Results can be used as input parameters in mesoscale and engineering scale fuel modeling. Uranium-molybdenum (U-Mo) alloys are promising candidates for high-performance research and test reactors, as well as fast reactors. The metastable γ phase, which shows acceptable irradiation performance, is retained by alloying U with Mo with specific quenching conditions. Point defects contribute to the atomic diffusion process, defect clustering, creep, irradiation hardening, and swelling of nuclear fuels, all of which play a role in fuel performance. In this work, properties of point defects in γ U and γ U- x Mo ( x = 7, 10, 12 wt. % ) were investigated. Vacancy and self-interstitial formation energies in γ U and γ U- x Mo were calculated with molecular dynamics (MD) simulations using an embedded atom method interatomic potential for the U-Mo system. Formation energies of point defects were calculated in the temperature range between 400 K and 1200 K. The vacancy formation energy was higher than the self-interstitial formation energy in both γ U and γ U- x Mo in the evaluated temperature range, which supports the previous results obtained via first-principles calculations and MD simulations. In γ U- x Mo, the vacancy formation energy decreased with increasing Mo content, whereas the self-interstitial formation energy increased with increasing Mo content in the temperature range of 400 K to 1200 K. The self-diffusion and interdiffusion coefficients were also determined in γ U- x Mo as a function of temperature. Diffusion of U and Mo atoms in γ U- x Mo were negligible below 800 K. The self-diffusion and interdiffusion coefficients decreased with increasing Mo concentration, which qualitatively agreed with the previous experimental observations. Point defect formation energies, self-diffusion coefficients, and interdiffusion coefficients in γ U- x Mo calculated in the present work can be used as input parameters in mesoscale and engineering scale fuel performance modeling.

Modified embedded-atom method potentials for the plasticity and fracture behaviors of unary fcc metals

The predictability of molecular dynamics simulations on the plasticity and fracture behaviors of metals is critically dependent on the accuracy of the employed interatomic potential. Here we present an approach to fitting modified embedded-atom method (MEAM) interatomic potentials to several key properties obtained from first-principles calculations and literature data that govern the continuous mechanistic processes in pure unary fcc Ni, Al, and Cu metals. Along with the commonly used lattice and elastic properties, our MEAM potentials are fitted to the cohesive energy curve, the decohesive energy curve, and the generalized stacking fault energy curve, which are the key properties governing the lattice response to volumetric, fracture, and shear deformations. We further demonstrate that these potentials are able to accurately predict the experimental values for a range of other mechanically relevant properties. Importantly, the potentials presented here outperform all existing EAM/MEAM interatomic potentials readily available from the literature and thus enable more accurate simulations of plasticity and fracture behavior of unary fcc metals.

Atomistic simulation of chemical short-range order in HfNbTaZr high entropy alloy based on a newly-developed interatomic potential

Chemical short-range order (CSRO) in high entropy alloys (HEAs) has attracted interests recently and is believed to be capable for tuning their mechanical properties. However, the characterization of CSRO in HEAs through experimental methods remains challenging. In this work, a modified embedded-atom method interatomic potential with good accuracy for studying CSRO in HfNbTaTiZr alloy system was developed. By employing the potential, molecular dynamic/Monte Carlo simulation was performed to investigate the CSRO in HfNbTaZr HEA. The results indicated that Hf-Zr and Nb-Ta atom pairs were preferred in the BCC solid solution of HfNbTaZr, and a new type of CSRO with topological B2 order was predicted, which can help to understand the mechanical properties of HfNbTaZr HEA. It was also found that forming of CSRO was an incubation process for the precipitation in HfNbTaZr, implying the significance of CSRO on the phase stability or precipitation behavior of HEAs. The findings in the present work can help in understanding CSRO and establishing its relationship with precipitates in HEAs, and more topics related to CSRO and phase stability in HfNbTaTiZr alloy system can be further investigated by atomistic simulation.

Second-nearest-neighbor modified embedded-atom method interatomic potential for V-M (M = Cu, Mo, Ti) binary systems

Interatomic potentials for V-M (M = Cu, Mo, Ti) binary systems have been developed within the framework of the second-nearest-neighbor modified embedded-atom method (2NN MEAM) formalism. The potentials reproduce a wide range of fundamental material properties such as thermodynamic and structural properties of compound and solution phases in reasonable agreement with experimental data or CALPHAD and first-principles calculations. The reasonable reproduction of material properties implies that the potentials can be combined with those of V-H and M-H systems for a permeability study of hydrogen in vanadium alloys or can be extended for further development of V-containing ternary system potentials.