Modified Embedded Atom Method Potential Research Articles

Atomistic study of intermetallics of Fe–Al–Zn system and their interfacial properties

Galvanizing is an important industrial process to improve the corrosion resistance of advanced high strength steels (AHSSs) that are vital for automotive industries. During galvanizing, nanoscale intermetallic phases with complex crystal structures are formed at the interface between the steel substrate and the zinc overlay. To better understand the nanoscale structures and the interfacial properties between the intermetallics, in this work, we develop a second nearest neighbor (2NN) Fe–Al–Zn ternary Modified Embedded Atom Method (MEAM) potential to describe the crystal structures of the intermetallics, i.e. Fe3Al8, Fe4Zn9 and FeZn13 and to calculate the interfacial structure and energy between them. The developed MEAM potential describes well the complex crystal structures and can be used to investigate the interfacial properties that are difficult to obtain from experiments. The Fe4Zn9, FeZn13 surface energies; the Fe–Fe4Zn9, Fe–FeZn13, Fe3Al8–FeZn13 interfacial energies; and the work of adhesion are calculated with the developed MEAM potential. The results show that FeZn13 crystal orientation has an insignificant effect on the FeZn13 surface energy and the Fe–FeZn13 interfacial energy. A negative interfacial energy is obtained for the Fe–Fe4Zn9 and the Fe–FeZn13 interface. The lowest interfacial energy is obtained in the {100}Fe case. The interfacial energy of Fe3Al8–FeZn13 depends on the surface termination of Fe3Al8 and FeZn13. A low interfacial energy is obtained when the surface termination of Fe3Al8 and FeZn13 are both Fe rich. In contrast, when the surface termination of Fe3Al8 is Al rich or the surface termination of FeZn13 is Zn rich, no low energy, stable interface can be formed between the two phases.

Microstructural Evolution of Al under Computational Analysis of Uniaxial [100] Compression

The strain rate exerts a profound influence on the mechanical characteristics of nanomaterials. To investigate this phenomenon, the molecular dynamics approach was employed to examine the impact of uniaxial compression along the [100] crystallographic direction in monocrystalline Al. The purpose of this research was to determine the differences in reactions observed during the elastic and plastic phases. It employed the Embedded Atom Method (EAM) as well as the Modified Embedded Atom Method (MEAM) potentials at 300 K. A comparative analysis of the outcomes from these potentials demonstrated considerable disparities. The results encompassed the percentage distribution of crystal structures (fcc, hcp, bcc, and others) as well as their atomic configurations. Several analytical factors were examined, including the strain-stress curve, the radial distribution function (RDF), the common neighbor analysis (CAN). The applied MEAM potential represents a subsequent occurrence of transitions following EAM, encompassing both increasing and decreasing phase transitions.

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.

Grain-boundary thermodynamics with artificial-neural-network potential: Its ability to predict the atomic structures, energetics, and lattice vibrational properties for Al

An artificial neural network (ANN) potential for Al, trained with density-functional-theory (DFT) data, is constructed to accurately predict lattice vibrational properties and thermodynamics of grain boundaries (GBs) in Al. The ANN potential is demonstrated to accurately predict not only atomic structures and energetics of the GBs at 0 K but also partial phonon densities of states and vibrational entropies, even for GBs absent in the training data sets. In addition, their total potential energies and atomic forces by DFT at elevated temperatures up to 800 K can also be well reproduced by molecular dynamics with the ANN potential. In contrast, a modified embedded atom method (MEAM) potential shows larger errors in phonon frequencies and atomic forces for atoms at GBs, as well as in the bulk, than the ANN potential. The MEAM potential is thus likely to be inadequate to quantitatively predict thermodynamic properties of GBs, particularly at high temperature. The present ANN potential is also applied to systematically examine thermodynamic stability of asymmetric tilt GBs. It is predicted that for the \ensuremath{\Sigma}9 system, the GB free-energy profile as a function of inclination angle exhibits a cusp at elevated temperatures, due to its larger vibrational entropies of asymmetric tilt GBs than those of \ensuremath{\Sigma}9 symmetric tilt GBs.

Comparative studies of interatomic potentials for modeling point defects in wurtzite GaN

In this paper, a new version of the Stillinger–Weber (SW) potential for wurtzite GaN is presented, by which we systematically explore the structural and thermodynamical properties of native point defects and their complexes. In parallel, the semi-empirical Modified Embedded-Atom Method (MEAM) potential is selected for comparison. The SW and MEAM potentials are assessed by the reproduction of the fundamental properties of wurtzite GaN and by the ability to describe the inversion domain boundaries and the wurtzite–rocksalt phase transition. Then the structural search of native point defects and their complexes in GaN is implemented using both SW and MEAM potentials with the benchmark of Density Functional Theory (DFT) calculations. Besides vacancies and antisites, four N and five Ga interstitials are confirmed by refining the DFT calculations, among which two N split interstitials N+−N⟨21̄1̄0⟩ and N+−Ga⟨011̄0⟩, and two Ga split interstitials, Ga+−Ga⟨011̄0⟩−g and Ga+−N⟨011̄0⟩, are observed for the first time. The SW potential correctly predicts the octahedral occupation GaOct to be the most stable Ga interstitial, while the MEAM potential predicts the ground state of the N+−N⟨011̄0⟩ split interstitial (N+−N⟨011̄0⟩−g) as the most stable N interstitial. However, neither of the two potentials could simultaneously generate the most stable configurations of N and Ga interstitials. The investigations of point defect complexes reveal that N octahedral Frenkel [FrenkelOct(N)] and paired antisite (NGaGaN) defects are unstable and get converted into VN⊕N+−N⟨011̄0⟩−g configurations with different separations between VN and N+−N⟨011̄0⟩−g point defects based on the DFT calculations. The formation energies calculated by the DFT and SW potential demonstrate that Schottky, Ga octahedral Frenkel [FrenkelOct(Ga)], and VN⊕N+−N⟨011̄0⟩−g point defect complexes are energetically feasible and that they should not dissociate into two isolated point defects. In contrast, the MEAM potential predicts the dissociation to be exothermic for Schottky and VN⊕N+−N⟨011̄0⟩−g. Overall, the structural features concerned with N–N or Ga–Ga bonds relaxed by the SW potential are more consistent with DFT calculations than the MEAM counterpart.

Computing the solid-liquid interfacial free energy and anisotropy of the Al-Mg system using a MEAM potential with atomistic simulations

The solid–liquid interfacial free energy, γ, and its associated anisotropy were computed for the Al-Mg binary alloy system using Molecular Dynamics (MD) simulations in conjunction with the capillary fluctuation method (CFM). Interactions between atoms were modeled based on a second nearest neighbor modified embedded atom method (MEAM) potential, a successor to the established embedded atom method (EAM) potential. The MEAM potential predicts a melting temperature of 938 K ± 17 K for pure Al and the solid–liquid phase equilibria as a function of temperature and composition was found using Monte Carlo technique implemented in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The average interfacial free energy, γ0, for pure Al was found to be 135.94 ± 3.62 mJ/m2 which agrees well with experimental values and an interfacial free energy relationship of γ100>γ110>γ111 was found across the majority of the temperatures which is consistent with FCC metals. The anisotropy values were found to fall within the 100 growth direction along the orientation selection map suggesting the addition of Mg stabilizes this growth direction. The results from the MEAM potential compares qualitatively well with other EAM potentials, however, experiences larger errors at lower temperatures.

Accurate path-integral molecular dynamics calculation of aluminum with improved empirical ionic potentials

We show that an accurate description of the interplay between the anharmonic ionic interaction and the zero-point fluctuation of ions in crystalline aluminum (Al) can be achieved using the path-integral molecular dynamics (PIMD) method in conjunction with improved empirical modified embedded-atom method (MEAM) potentials. Our results show that the zero-point fluctuation of ions is noticeable at a temperature between 200 K and 250 K, roughly half of the Al Debye temperature of 428 K, with a selective influence on mechanical properties. The effect provides appreciable corrections to the lattice constant $a$, bulk modulus $B$, and elastic constant ${C}_{11}$ at low temperature, but without much influence on elastic constants ${C}_{12}$ and ${C}_{44}$. With a revised MEAM potential which takes into consideration the influence of zero-point fluctuations, the PIMD method has a much improved accuracy in $a, B$, and the $C$'s up to 700 K, when compared with precision experimental measurements. The largest errors of $a$ and $B$ can even be reduced by about an order in percentage below 300 K.

MEAM potential-based MD simulations of melting transition on Ni surfaces.

Based on the modified embedded atom method (MEAM) potential suggested by Jin et al. (Appl. Phys. A120: 189, 2015), the molecular dynamics (MD) simulations were adopted to investigate the melting transition of the FCC transition metal Ni, and in the MD simulations, the forces acting on atoms were calculated by using the newly derived formulas. We first studied the melting points of Ni samples with low-index surfaces including Ni(100), Ni(110), and Ni(111). Then, we investigated the structural properties on the surface layers with increasing temperature up to the melting points. The simulation results exhibit that with the temperature increasing, the (110) surface firstly disorders, followed by the (100) surface, while the stability of the (111) surface is maintained until near the melting point. The disorder of surface layer atoms diffuses from the surface to the inside of the crystal lattice. With the density of atoms decreasing on the surface, the premelting effect also increases, being most pronounced on Ni(110) which corresponds to the lowest surface density. This conclusion is linked with the behavior found for the BCC transition metal Fe in our previous simulation study.

Development of 2NN MEAM potential for Fe–Al and atomistic investigation of surface and interface properties of the inhibition layer in galvanized Fe

Hot-dip Zn coating or galvanizing is an important process for high strength steels that are extensively used in automotive industries. During galvanizing, Fe in the steel substrate quickly reacts with Al that is dissolved in the Zn bath and an inhibition layer is formed. To better understand the formation of the inhibition layer that occurs on a small scale (typically ∼100 nm), it is necessary to understand the physical properties of the interfacial phases on the atomic scale. In the present work, we develop a second nearest neighbor Fe–Al modified embedded atom method (MEAM) potential to calculate the surface and interface properties of the inhibition layer. The as-developed potential is able to well describe the complex crystal structure of the inhibition layer. Also, this potential satisfies three criteria for the experimentally observed phases: phase stability, convex hull, and elastic stability. The calculation results show a negative interfacial energy between Fe and the inhibition layer, a manifestation of the high affinity between Fe and Al. The formation of the inhibition layer on the Fe surface lowers the interfacial energy. Our results also show that the crystal orientation of Fe strongly affects the interfacial energy, and the (110) plane gives the lowest interfacial energy. The work of adhesion is also calculated with the developed MEAM potential, and the results agree well with the results obtained by other methods.

Development of neural network potential for MD simulation and its application to TiN

Titanium nitride (TiN) is used in various applications because of its excellent wear and corrosion resistance. TiN with a rock-salt-type crystal structure has been investigated extensively, but the existence of non-rock-salt-type phases (e.g., Ti2N) has only been reported recently from first-principles calculations. Molecular dynamics (MD) simulation is a powerful tool to predict mechanical properties, but it generally requires interatomic potentials. The conventional many-body interatomic potentials (e.g., modified embedded-atom method (MEAM) potential) for rock-salt TiN are not applicable to these other phases. Hence, in this study, a neural network (NN)-based method to create interatomic potentials is developed, which are referred to as neural network potentials (NNPs); hence, MD simulations can be conducted for TiN and other phases. First, ab initio molecular dynamics (AIMD) simulations are conducted to obtain the relationships between atomic configurations and the corresponding total potential energies and forces on each atom. Subsequently, these relationships are used for the NN to generate NNP. NNP can accurately reproduce the energies and forces calculated by AIMD simulations. The mechanical properties of TiN are computed using the NNP and MD simulation and verified with the MEAM potential and its experiment. Finally, MD simulation using the developed NNP is conducted for the other phase (Ti2N) to investigate its mechanical properties.

A modified embedded-atom method interatomic potential for bismuth

A semi-empirical interatomic potential for the post-transition metal, bismuth, is developed based on the second nearest-neighbor modified embedded-atom method (MEAM). The potential reproduces a range of physical properties, such as the lattice constant, cohesive energy, elastic constants, vacancy formation energy, surface energy, and the melting point of pure bismuth. The calculations are done for the rhombohedral ground state of Bi. The results show good agreement with density functional theory and experimental data. The developed MEAM potential for bismuth is useful for material and mechanical behavior studies of the pure material at different conditions and sets the stage for the development of interatomic potentials for bismuth alloys or other bismuth compounds.

Vacancy and phonon dispersion properties of Be, Co, Hf, Mg, and Re by modified embedded atom method potentials.

The modified embedded atom method (MEAM) potentials improved by Jin et al. (Appl. Phys. A120 (2015), p. 189) were applied to calculate the mono- and bi-vacancy properties as well as the phonon dispersions for hexagonal close-packed (HCP) metals Be, Co, Hf, Mg, and Re. We expressed the formulas for calculating the mono- and bi-vacancy properties by the molecular static (MS) method based on the MEAM potentials for HCP metals. The lattice dynamics (LD) method and the MEAM potentials were adopted to calculate the phonon dispersion properties. The calculation results show better agreement with the experimental data than the previous calculations by using the unimproved embedded atom model.

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.

Thermodynamic properties of fcc metals using reparameterized MEAM potentials

The modified embedded atom method (MEAM) potentials of Jin et al. (Appl Phys A 120:189, 2015) are reparameterized through fitting the available experimental data and ab initio results of several physical properties better for seven face-centered cubic metals, Ag, Al, Au, Cu, Ni, Pd, and Pt. Results for the structure stabilities, point defects, and phonon dispersion properties are in better agreement with the measured values than those from the original MEAM potentials, showing the reliability of the reparameterized potentials. Also, the thermodynamic properties for these metals are studied within the quasi-harmonic approximation. Calculation results for the temperature dependence of lattice constants, thermal expansion coefficients, molar heat capacities at constant volume and/or constant pressure, isothermal and adiabatic bulk moduli, Gruneisen parameters, and Debye temperatures are compared to those from the earlier embedded atom methods and ab initio method calculations as well as the experimental data.

Lattice Dynamics of CrW Dilute Alloy Using Modified Embedded Atom Method Potential

A modified embedded atom method (MEAM) has been used to study the lattice dynamics and vibrational properties of CrW alloy. Using the MEAM potential the force-constants up to second neighbours for pure Cr and its dilute alloy with small concentration of W as substitutional impurity are calculated. The Phonon dispersions for dilute CrW alloy at 0.3%, 0.8% and 1.6 % concentration of W substitutional impurity have been computed and the obtained results are compared with the available experimental data. We have obtained a very good agreement with the experimentally measured results of phonon dispersions. With the application of obtained force-constants from MEAM potential, the local vibrational density of states in ideal crystal and its alloys using Green’s function method has been calculated. On the basis of the results of local vibrational density of states, the condition of resonance modes has been investigated. Using the calculated vibrational local density of states, the mean square thermal displacements of impurity atoms in CrW alloys are also calculated.

Calculation of formation enthalpies and dilute heats of bcc–bcc binary alloys by modified ones of EAM potentials

The formation enthalpies and the dilute heats of body-centered cubic–body-centered cubic (bcc–bcc) binary alloys are evaluated by employing the modified ones of the embedded atom method potentials for bcc metals. The modified embedded atom method (MEAM) potentials for bcc transition metals proposed by Jin et al. (Appl Phys A 120:189, 2015), Johnson’s alloy potential form, and Vegard’s law are applied to calculate the formation enthalpies in the whole composition range for 21 kinds of bcc–bcc binary alloys bearing bcc transition metals Cr, Fe, Mo, Nb, Ta, V, and W. Several formulas are suggested to calculate the dilute heats of the binary alloy solid solutions using the MEAM potentials for bcc transition metals and used in the evaluation of the dilute heats of 42 kinds of bcc–bcc binary alloy solid solutions. The present results of the formation enthalpies and the dilute heats for most bcc–bcc binary alloys are in mainly agreement with the experimental data and the calculations by the Miedema theory, as well as agree with the experimental data and the Miedema theory results better than the precedent MEAM results.

The solid–liquid interface free energy of Al: A comparison between molecular dynamics calculations and experimental measurements

In this study, molecular dynamics (MD) simulations were performed to calculate the solid–liquid interface (SLI) free energy and its anisotropy of Al using the capillary fluctuation method (CFM) and a third generation of charge-optimized many body (COMB3) potential. The two thresholds (ϕmin, ϕmax) used to define interfacial atoms and the thickness of the bin (Δ) used to define the SLI profile significantly affect the obtained stiffness. The influence of the three parameters is discussed and optimal values for these parameters are also given. The magnitude of the SLI free energy of pure Al at the melting point is found to be 172.67 ± 22.90 mJ/m2 through a detailed discussion of available experimental results. This result is compared with the SLI free energies of Al calculated from the COMB3 potential, two embedded-atom method (EAM) potentials and a modified embedded-atom method (MEAM) potential. It is found that both the COMB3 potential and the MEAM potential give predictions of the SLI free energy very close to the true value, while the EAM potentials underestimate this value quite a lot.

Thermodynamic and kinetic behavior of low-alloy steels: An atomic level study using an Fe-Mn-Si-C modified embedded atom method (MEAM) potential

A quaternary element Modified Embedded Atom Method (MEAM) potential comprising Fe, Mn, Si, and C is developed by employing a hierarchical multiscale modeling paradigm to simulate low-alloy steels. Experimental information alongside first-principles calculations based on Density Functional Theory served as calibration data to upscale and develop the MEAM potential. For calibrating the single element potentials, the cohesive energy, lattice parameters, elastic constants, and vacancy and interstitial formation energies are used as target data. The heat of formation and elastic constants of binary compounds along with substitutional and interstitial formation energies serve as binary potential calibration data, while substitutional and interstitial pair binding energies aid in developing the ternary potential. Molecular dynamics simulations employing the developed potentials predict the thermal expansion coefficient, heat capacity, self-diffusion coefficients, and stacking fault energy for steel alloys comparable to those reported in the literature.

Molecular dynamics simulation of the uniaxial tensile test of silicon nanowires using the MEAM potential

The silicon nanowire is a novel nanometer-scale structure which can be used in various electronic and optoelectronic devices. While the plastic deformation and failure mechanisms, including the brittle-to-ductile transition at room temperature, of nanowires have been studied both experimentally and theoretically, the fundamental atomic-scale mechanisms of these behaviors still remain incompletely understood. In this article we study the mechanical and failure behaviors of the [110]-oriented single-crystalline silicon nanowires by performing uniaxial tensile tests using molecular dynamics simulations with three modified embedded-atom-method (MEAM) potentials, referred to as Baskes, Lee, and Lee-modified. The effects of several key parameters such as size, temperature, and strain rate are investigated. A preliminary examination of the three MEAM potentials reveals that Lee and Lee-modified models outperform Baskes model in predicting the thermal expansion coefficient and surface energies. The uniaxial tensile simulations show that some mechanical properties such as Young’s modulus and tensile strength exhibit size-dependence while there is little size-effect on the failure strain. A novel parameter named the ductile failure probability is introduced to quantify the failure behavior of the nanowire during the tensile test, which scales from 0 for the pure brittle to 1 for the pure ductile mode failure. Overall, the ductile failure probability increases with decreasing size and increasing temperature in all of the three models. The Baskes nanowires exhibit the most ductile failures among the three models whereas most Lee-modified nanowires fail through fractures on the (111) plane. The Lee model shows some intermediate levels of ductile failure behavior. The difference due to the strain rate is very small, but overall nanowires become slightly more brittle as the strain rate decreases.

The effectiveness of reference-free modified embedded atom method potentials demonstrated for NiTi and NbMoTaW

One of the effective potentials that has proven to be very versatile and useful for describing metals is the modified embedded atom method (MEAM) potential. The reference-free version of the MEAM (RF-MEAM) potential provides more flexibility for fitting than the 2NN-MEAM because it also describes the pair potential as an explicit function. In this work, we present a methodology to fit RF-MEAM potentials to DFT data. We then evaluate the performance of the fitted potential by comparing MD simulations with experimental and DFT data. As an example, the methodology is applied to a binary and a quaternary alloy, namely NiTi and NbMoTaW. In the case of the equi-atomic NiTi shape memory alloy, our attention focuses on designing a potential that properly captures its mechanical behavior, given that the existing potentials fail to predict elastic constants in agreement with experiments. To reach our aim, we included the stress tensors of different high temperature NiTi configurations in the fitting database. The obtained RF-MEAM potential outperforms existing EAM and MEAM potentials in predicting the lattice and elastic constants of austenitic and martensitic phases as well as the corresponding transformation temperatures. To demonstrate the suitability of this methodology also for more complex systems, a RF-MEAM potential is fitted to model the multi-component NbMoTaW high-entropy alloy. Validation is achieved through comparison between observables obtained through the MD output and ab initio data. The article also reports key improvements to the optimization code MEAMfit v2 and the freely-available LAMMPS implementation of the RF-MEAM formalism. Most notably, resorting to analytic derivatives of the objective function with respect to the potential parameters rather than derivatives through finite differences, the time necessary for fitting has decreased by an order of magnitude.