Modified Embedded Atom Method Research Articles

First-principles-based mesoscale modeling of the solute-induced stabilization of 〈1 0 0〉 tilt grain boundaries in an Al–Pb alloy

A first-principles disclination structural units (DSUM) model was used to calculate the energies of 12 〈0 0 1〉 symmetric tilt grain boundaries in Al for a pure system and a system in which Pb atoms substitute for Al at one-half of the lattices sites along the interfacial plane. The grain boundaries are modeled as disclination dipole walls with energies given as a weighted sum of individual disclination energies determined from special low-sigma structures, elastic terms and disclination core energies. Predictions of the DSUM using the bulk Al shear modulus and Poisson’s ratio in the elastic and core energy terms are found to be comparable to energies for fully atomistic simulations calculated using a modified embedded-atom method (MEAM) potential. No relation between grain boundary energies in pure Al and the degree of stabilization due to Pb doping was found. The DSUM parameterized to density functional theory calculations predicts a ∼50% reduction in the energy anisotropy with respect to angle due to doping compared to the pure system, while MEAM calculations yield no appreciable reduction in the energy anisotropy.

Atomistic simulation of a graphene-nanoribbon–metal interconnect * * Contribution of the National Institute of Standards and Technology, an agency of the US government. Not subject to copyright in the USA.

We report a molecular statics simulation of the physical processes responsible for binding and lattice distortions in a nanoscale electrical interconnect with realistic boundary conditions. The interconnect consists of a graphene ribbon interfaced with the (111) crystallographic surfaces (over 11 000 atoms overall) of two nickel electrodes. We quantify the graphene lattice distortions by mapping strains, as well as out-of-plane atomic displacements on a grid, throughout the simulated interconnect. The results suggest strongly localized graphene lattice distortions at the edges and strains that do not exceed 0.5% elsewhere. Such strains are not expected to affect the electrical properties of the graphene nanoribbon interconnect. A stand-alone graphene nanoribbon is simulated in order to identify the effect of electrodes partially supporting the graphene nanoribbon. Our results indicate that the electrodes reduce the in-plane strains induced by the nanoribbon edges, while causing rippling of the graphene lattice. The average graphene–nickel intersurface separation and the cohesive energy for the top-fcc configuration are calculated at ∼2.13 Å and 68.22 meV Å−2. In order to describe the interatomic interactions in the simulation, we utilize a set of accurate atomistic potentials for graphene on a nickel surface. The approach is based on the modified embedded atom method (MEAM) for the C–C and Ni–Ni interactions, and a Morse-type potential, which takes the surface configuration into account, for the Ni–C interactions. Our focus is on the Ni-(111) crystallographic surface interfaced with graphene in top-fcc, top-hcp, and hcp–fcc initial configurations. The interactions were validated by calculating the equilibrium binding energy and intersurface distance. The resulting binding energies and equilibrium intersurface separations obtained are in very good agreement with previous experimental and ab initio data obtained by use of density functional theory (DFT).

Atomistic modeling of the Al–H and Ni–H systems

Abstract

Structural and thermal properties of calcium using an MEAM potential

Structural and thermal properties of Ca are examined using a modified embedded-atom method (MEAM) interatomic potential. We developed an MEAM interatomic potential for calcium (Ca) using a first-principles method based on density functional theory (DFT). The material parameters, such as the cohesive energy, equilibrium atomic volume, and bulk modulus, are used to determine the MEAM potential parameters. The elastic constants and various point defect energies, such as monovacancy and interstitial defects, are also examined while developing the potential. Several structural properties of Ca, such as different surface formation energies, stacking fault energies, and thermal properties, such as coefficient of thermal expansion, specific heat and melting temperature, are investigated using the potential. We found that the present MEAM potential gives a good overall agreement with DFT calculations and experiments.

ICONE19-43987 ATOMISTIC STUDY ON THE EUTECTICS FOR METALLIC FUEL AND COMPONENT MATERIALS IN CDAs OF SFRs : (3) SIMULATION OF THE ATOMIC DIFFUSION ACROSS THE INTERFACE BETWEEN PLUTONIUM AND IRON BY CLASSICAL MOLECULAR DYNAMICS

Eutectic melting between metallic fuel and steel cladding and/or steel structures is one of dominant phenomena for the progress of core disruptive accidents (CDAs) of SFRs. In this study the atomic diffusion at the interface between Pu and Fe was investigated by using classical molecular dynamics (CMD). The simulation was performed using Modified Embedded Atom Method (MEAM) (Baskes, 1992). For plutonium the potential model developed by Baskes (2000) was used and for iron that by Lee et al.(2001) was applied. The interactions between plutonium and iron atoms were calculated by using the potential model determined so as to reproduce the material properties of PuFe_2. The simulation was made with a system in which a semi-infinite, two-dimensional plate of iron with a thickness of 2.5 nm was in contact with solid or liquid plutonium with almost same thickness as the iron plate. The diffusion of atoms across the interface was observed for all the temperature conditions in the present study (900K〜1850K). The diffusion rate was increased exponentially with temperature. The diffusion rate depended on the plane direction of the surface of the iron plate as well as the temperature.

Optimizing the MEAM potential for silicon

By applying simulated annealing techniques we fit the modified embedded atom method (MEAM) potential to a database of ab initio energies for silicon and construct an improved parametrization of this potential. In addition, we introduce a new, reference-free version of the MEAM potential. This MEAM version is also fitted to the silicon data and shows an even better agreement, although the improvement is modest. Finally, we investigate whether increasing the number of different angular terms in the MEAM potential from 3 to 4 will lead to a better potential. The aim of this work is to determine a broad-ranged potential, one that is reliable in many different low- and high-energy atomic geometries in silicon crystals, molecules, near defects and under strain. To verify this, the performance of the new potentials is tested in different circumstances that were not explicitly included in the fit: relaxed defect energies, thermal expansion, melting temperature and liquid silicon. The new MEAM parametrizations found in this work, called MEAM-M and RF-MEAM, are shown to be overall more accurate than previous potentials—although a few defect energies are exceptions—and we recommend them for future work. The melting temperatures are closer to the experiment than those of other MEAM potentials, but they are still too high.

Solubility of carbon in α-iron under volumetric strain and close to the Σ5(3 1 0)[0 0 1] grain boundary: Comparison of DFT and empirical potential methods

The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the ∑5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al. [1], Ruda et al. [2] and Hepburn et al. [3], and the modified embedded-atom method (MEAM) potential of Lee [4]. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy.

Molecular Dynamics Simulations of Pre-Crack Effects on Deformation and Failure Mechanisms for Pure Aluminum

Micro-cracks which seriously affect the strength of metal materials always exist in metal or alloys during the manufacturing process. In order to investigate the pre-crack effects on deformation and failure mechanisms for pure aluminum at atomic scale, the plastic deformation processes of pure aluminum with face-centered cubic (fcc) crystal structure around the pre-crack tips at atomic scale were examined by means of molecular dynamics (MD) method. The Modified Embedded Atom Method (MEAM) potential was used to describe the interaction among atoms of pure aluminum. The crack propagation and failure processes for fcc structure were observed near the pre-crack tip zone. The calculation results reveal that the pre-crack blunting occurred at first, then the dislocation emitted at the pre-crack boundary and moved along with the specific direction obviously, eventually, cracks propagated along the crystallographic direction family of <110>. By means of VMD software, the graphic pictures of dislocation movement and crack propagation were obtained under different load conditions. The results and methodology given in this study are very significant for understanding more about plastic deformation and destruction at atomic scale for pure Aluminum with fcc structure.

Molecular Dynamics Study on Interaction between Voids for Pure Aluminum

The voids in pure Aluminum always exit in the manufacturing process. The Modified Embedded Atom Method (MEAM) potential is employed in the molecular dynamics (MD) simulation at atomic scale to investigate the interaction between voids under the impact loading for pure Aluminum. The distance between the voids distributed along the loading orientation affects the failure mechanism seriously. The results show that there are 3 kinds of mechanisms with the change of the distance between voids: 1) coalescence takes place within a critical distance between voids under extra loading, 2) when the distance between voids reaches a certain value, each void cracks at 4 locations along with the slide direction <110> of face-centered cubic (fcc), respectively, 3) a stress shield zone appears when the ligament between the voids is at the size between the cases mentioned above, which brings out the phenomena that each of the voids cracks only at 2 locations, and no crack appeared at the stress shield zone.

Molecular dynamics simulation on plasticity deformation mechanism and failure near void for magnesium alloy

The plastic deformation processes of magnesium alloys near a void at atomic scale level were examined through molecular dynamics (MD) simulation. The modified embedded atom method (MEAM) potentials were employed to characterize the interaction between atoms of the magnesium alloy specimen with only a void. The void growth and crystal failure processes for hexagonal close-packed (hcp) structure were observed. The calculating results reveal that the deformation mechanism near a void in magnesium alloy is a complex process. The passivation around the void, dislocation emission, and coalescence of the void and micro-cavities lead to rapid void growth.

Modified embedded-atom method interatomic potentials for the Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems

Modified embedded-atom method (MEAM) interatomic potentials for Nb-C, Nb-N, Fe-Nb-C, and Fe-Nb-N systems have been developed based on the previously developed MEAM potentials for lower order systems. The potentials reproduce various fundamental physical properties (structural properties, elastic properties, thermal properties, and surface properties) of NbC and NbN, and interfacial energy between bcc Fe and NbC or NbN, in generally good agreement with higher-level calculations or experimental information. The applicability of the present potentials to atomic-level investigations to the precipitation behavior of complex-carbonitrides (Nb,Ti)(C,N) as well as NbC and NbN, and their effects on the mechanical properties of steels are also discussed.

Density and related thermophysical properties of metastable liquid Ni–Cu–Fe ternary alloys

The densities of liquid Ni–Cu–Fe ternary alloy system were investigated by molecular dynamics method in combination with a MEAM ( Modified Embedded Atom Method) potential model. The temperature range is from 1000 to 2200 K, including both a broad superheating range and a large undercooled regime. The densities of six Ni 100 − 2 x Cu x Fe x alloys ( x = 0 , 10 , 20 , 30 , 40 , 50 ) decrease linearly with the rise of temperature at the superheated and undercooled states, and increase with the enhancement of Ni content. Among the simulated alloys, the densities of only liquid pure Ni and Ni 60Cu 20Fe 20 alloy are available in literatures, which are in good agreement with the calculated values. According to the relationship between the excessive volume and the alloy composition, it can be deduced that Ni 100 − 2 x Cu x Fe x alloys deviate from ideal solution. Moreover, a comparison was also performed between the calculated results and the approximated values by Neumann–Kopp's rule. Based on the obtained density data, the thermal expansion coefficients are also derived. It firstly decreases to a minimum value, and then displays a rise with the increase of Ni content.

Atomistic analysis of phase segregation patterning in binary thin films using applied mechanical fields

The patterned compositional evolution in thin films of a binary alloy controlled by modulated stress fields is studied by employing Monte Carlo simulations. General features of stress-patterned phase segregation are probed using a binary Lennard-Jones potential in which the lattice misfit between the two components of the alloy is varied systematically. In general, patterning of the microstructure is found to be more robust in the low-mismatch binary systems because large lattice mismatch promotes plastic, and therefore, irreversible relaxation, during annealing. It is shown that some control over the relaxation process can be achieved by careful design of the applied thermal annealing history. Additional calculations have been performed using two other potentials for binary metallic systems, an embedded-atom method (EAM) potential for Cu–Ag and a modified embedded-atom method (MEAM) potential for Cu–Ni that represent examples of high and low-mismatched systems, respectively. The results obtained with generic Lennard-Jones potentials are in excellent agreement with those from the EAM and MEAM potentials suggesting that it is possible to derive general guidelines for accomplishing stress-patterned segregation in a variety of thin films of binary alloys.

Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations

We present molecular dynamics simulations of [1 1 0]-oriented Si nanowires (NWs) under a constant strain rate in tension until failure, using the modified embedded-atom-method (MEAM) potential. The fracture behavior of the NWs depends on both temperature and NW diameter. For NWs of diameter larger than 4 nm, cleavage fracture on the transverse (1 1 0) plane are predominantly observed at temperatures below 1000 K. At higher temperatures, the same NWs shear extensively on inclined {1 1 1} planes prior to fracture, analogous to the brittle-to-ductile transition (BDT) in bulk Si. Surprisingly, NWs with diameter less than 4 nm fail by shear regardless of temperature. Detailed analysis reveals that cleavage fracture is initiated by the nucleation of a crack, while shear failure is initiated by the nucleation of a dislocation, both from the surface. While dislocation mobility is believed to be the controlling factor of BDT in bulk Si, our analysis showed that the change of failure mechanism in Si NWs with decreasing diameters is nucleation controlled. Our results are compared with a recent in situ tensile experiment of Si NWs showing ductile failure at room temperature.

Density functional theory (DFT)-based modified embedded atom method potentials: Bridging the gap between nanoscale theoretical simulations and DFT calculations

A density functional theory (DFT)-calculation scheme for constructing the modified embedded atom method (MEAM) potentials for face-centered cubic (fcc) metals is presented. The input quantities are carefully selected and a more reliable DFT approach for surface energy determination is introduced in the parameterization scheme, enabling MEAM to precisely predict the surface and nanoscale properties of metallic materials. Molecular dynamics simulations on Pt and Au crystals show that the parameterization employed leads to significantly improved accuracy of MEAM in calculating the surface and nanoscale properties, with the results agreeing well with both DFT calculations and experimental observations. The present study implies that rational DFT parameterization of MEAM may lead to a theoretical tool to bridge the gap between nanoscale theoretical simulations and DFT calculations.

Nanostructurally small cracks (NSC): A review on atomistic modeling of fatigue

Fatigue is one of the most damaging mechanisms in structural components. With the development of structural nanomaterials, it is imperative to investigate the fatigue damage phenomena at the atomic scale. To study fatigue behavior at the nanoscale, one must apply non-continuum modeling frameworks, such as molecular statics (MS), molecular dynamics (MD), and Monte Carlo (MC) methods. To date, only MD and MS simulations using embedded atom method (EAM) and modified embedded atom method (MEAM) potentials have been conducted, and this paper reviews these simulations of the nanoscale fatigue-crack growth in nickel and copper including single crystals, bicrystals, and polycrystals. A nanoscale size middle tension (MT) specimen with the lateral side applied periodic boundary conditions was used to investigate the fatigue behavior in nickel and copper single crystals. Simulation results revealed that the cyclic plastic deformation at the crack tip was the main influencing factor for fatigue-crack growth. Two main nanoscale mechanisms of crack propagation were observed: (1) the main cracks linked with the voids nucleated in front of crack tip due to high dislocation density generated by the cyclic loading; and (2) the main cracks broke the atomic bonds in the crack plane without much plasticity. For the bicrystals and polycrystals, the grain boundaries exerted resistance to the crack propagation. To study the interactions between cracks and grain boundaries, four cases of grain boundary interfaces for copper and two cases of grain boundaries for nickel were simulated. In copper bicrystals, the crack path deviated and moved from one grain to another for high misorientations, while there were voids nucleating at grain boundaries in front of the crack tip that linked back with the main crack. Similar to macroscale fatigue, dislocation substructures were observed to develop in the atomic lattice during cyclic loading. In nickel bicrystals, for large misorientations, the cracks were stopped by grain boundaries. For small misorientations, the crack propagated through the grain boundary, but the growth rate was reduced due to the resistance of the grain boundary. Fatigue-crack growth rates for nanocracks were computed and compared with growth rates published in the literature for microstructurally small cracks (micron range) and long cracks (millimeter range). A nanostructurally small crack (NSC) was introduced in terms of the CTOD. The quantified NSC growth rates in copper single crystals were very similar with those experimentally measured for small cracks (micron range) and with those at stress-intensity-factor ranges lower than the threshold for long cracks (millimeter range). The atomistic simulations indicated that reversible plastic slip along the active crystallographic directions at the crack tip was responsible for advancing the crack during applied cycling. In the case of single or double plastic slip localization at the crack tip, a typical Mode I fatigue crack arose along a slip band and then grew into a mixed Mode I + II crack growth mechanism. For crystal orientations characterized by multiple slip systems concomitantly active at the crack tip, the crack advance mechanism was characterized by nanovoid nucleation in the high density nucleation region ahead of the crack tip and by linkage with the main crack leading to crack extension. To facilitate observations of fatigue-crack growth, the simulation of a copper polycrystal was performed at low temperature 20 K as well. The crack propagated along persistent slip bands within the grain. The crack propagated along grain boundaries when the angle between the direction of crack propagation and the grain boundary was small, while it was impeded by the grain boundary when the angle was large. The results obtained for the crack advance as a function of stress intensity amplitude are consistent with experimental studies and a Paris law exponent of approximately two.

Computational study of the impurity induced reduction of grain boundary energies in nano- and bi-crystalline Al–Pb alloys

Segregation of impurities with limited solubilities to grain boundaries can slow or even eliminate grain growth in nanocrystalline materials. Due to a very limited miscibility Pb is a potential candidate for thermodynamically stabilizing nanocrystalline Al. To investigate this we have used atomic modeling to characterize the structure and energy of substitutional Pb defects in bulk Al, in Al bi-crystals and in an Al nanocrystal. Monte Carlo simulations using a modified embedded-atom method (MEAM) potential fit to the results of density functional theory (DFT) calculations predict the formation of Pb clusters, in agreement with prior experiments. In addition, the simulations show strong segregation of Pb atoms to grain boundaries, a result that supports prior suggestions that Pb is distributed along grain boundaries in nanocrystals created by ball milling. Analysis of the enthalpies for Pb defects using MEAM and DFT calculations suggests that Pb impurities can help stabilize nanocrystalline Al against grain growth.

Molecular Dynamics Simulation on Crack Propagation for Magnesium

The crack propagation for pure Magnesium at an atomic scale level under external loading was carried out by using a molecular dynamics method. In this study, the Modified Embedded Atom Method (MEAM) was used to characterize the interactions of atoms and the Newtonian equations were solved by Velocity-Verlet algorithm. The crack propagation and failure processes were observed around the crack tip. The calculation results reveal that vacancies were formed near the crack tip during the failure processes for pure Magnesium, and the coalescence between crack tip and vacancies induced the crack growth with the increase in loading.

Semi-Empirical Potential Methods for Atomistic Simulations of Metals and Their Construction Procedures

General theory of semi-empirical potential methods including embedded-atom method and modified-embedded-atom method (MEAM) is reviewed. The procedures to construct these potentials are also reviewed. A multi-objective optimization (MOO) procedure has been developed to construct MEAM potentials with minimal manual fitting. This procedure has been applied successfully to develop a new MEAM potential for magnesium. The MOO procedure is designed to optimally reproduce multiple target values that consist of important material properties obtained from experiments and first-principle calculations based on density-functional theory. The optimized target quantities include elastic constants, cohesive energies, surface energies, vacancy-formation energies, and the forces on atoms in a variety of structures. The accuracy of the present potential is assessed by computing several material properties of Mg including their thermal properties. We found that the new MEAM potential shows a significant improvement over previously published potentials, especially for the atomic forces and melting temperature calculations.

Atomistic Modeling of pure Mg and Mg–Al systems

Interatomic potentials for pure Mg and the Mg–Al binary system have been developed based on the modified embedded-atom method (MEAM) potential formalism. The potentials can describe various fundamental physical properties of pure Mg (bulk, point defect, planar defect and thermal properties) and alloy behaviors (thermodynamic, structural and elastic properties) in reasonable agreement with experimental data or higher-level calculations. The applicability of the potential to atomistic investigations on the deformation behavior of pure Mg and the effect of alloying element Al on it is discussed.