Embedded Atom Method Potential Research Articles

Response surface for screw dislocation: Twin boundary interactions in FCC metals

In a previous manuscript, large scale 3D atomistic simulations were used to study the interaction between a curved dislocation with a dominant screw character and a Coherent Twin Boundary (CTB) for three FCC metals (Al, Cu and Ni) using 6 embedded-atom method (EAM) potentials [1]. Under both uniaxial and multiaxial stresses, both transmission mechanism and critical transmission stress differ from the results reported in 2D simulations [1]. Transmission mechanisms were found to be material dependent, and non-glide (Escaig) stresses have a profound effect on the transmission. In order to provide input for constitutive equations for mesoscopic approaches, the previous results are used to inform analytic models that incorporates mechanisms observed in the atomistic simulations [1]. For Al, the Fleischer mechanism of cross-slip at the twin boundary [2] is used whereas for Cu and Ni, Escaig mechanism of cross-slip [3] at the twin boundary is invoked. For Cu and Ni the transmission stress is determined by the critical stress required to grow the cross-slip nucleus in the adjacent grain, as opposed to growth of cross-slip nucleus in the twin boundary. As a result, the critical transmission stress in these materials is almost athermal. The analytic, mechanistic model reproduces the atomistic simulation results for the Escaig stress dependence of the transmission stress as well as its dependence on a shear component in the CTB fairly well, within 10% for the Escaig stress dependence.

Predicting the dynamic behavior of the mechanical properties of platinum with machine learning.

Over the last few decades, computational tools have been instrumental in understanding the behavior of materials at the nano-meter length scale. Until recently, these tools have been dominated by two levels of theory: quantum mechanics (QM) based methods and semi-empirical/classical methods. The former are time-intensive but accurate and versatile, while the latter methods are fast but are significantly limited in veracity, versatility, and transferability. Recently, machine learning (ML) methods have shown the potential to bridge the gap between these two chasms due to their (i) low cost, (ii) accuracy, (iii) transferability, and (iv) ability to be iteratively improved. In this work, we further extend the scope of ML for atomistic simulations by capturing the temperature dependence of the mechanical and structural properties of bulk platinum through molecular dynamics simulations. We compare our results directly with experiments, showcasing that ML methods can be used to accurately capture large-scale materials phenomena that are out of reach of QM calculations. We also compare our predictions with those of a reliable embedded atom method potential. We conclude this work by discussing how ML methods can be used to push the boundaries of nano-scale materials research by bridging the gap between QM and experimental methods.

Mixed-mode fracture toughness testing of a Cu/Ag bimetallic interface via atomistic simulations

This work presents the evaluation of mixed-mode fracture toughness for an interface crack using molecular dynamics simulations. A Cu/Ag bimetallic structure with an interface crack was configured, where the atomic interactions were characterized based on the embedded-atom method potential. A bimaterial K-field of linear elastic fracture mechanics was employed as a remote loading for the mixed-mode failure. The traction ratio of the shear to normal component in front of a crack tip was defined as the mode mixity. The critical value of the J-integral for the onset of crack growth along the interface was measured as the interfacial fracture toughness; the value was also compared to the critical energy release rate and the Griffith fracture toughness. The interfacial fracture toughness of a Cu/Ag bimaterial was found to exhibit significant dependence on mode mixity for an interface crack, which resulted from various types of atomic-scale deformation at the interface.

Two-dimensional discrete breathers in fcc metals

The interest in discrete breathers (DB), i.e. a time-periodic and spatially localized vibrational mode in a defect free nonlinear lattice, is related to their ability to localize vibrational energy of the order of several eV. In the present work, for the first time, a systematic study of eight nonlinear vibrational modes localized in one spatial dimension and delocalized in the two other dimensions is performed by means of molecular dynamics simulations in defect-free single crystals of fcc metals (Al, Cu and Ni). For this goal, the standard embedded atom method potentials are employed. Calculations are performed at a zero temperature in three-dimensional computational cells. Excitation of DBs takes place via displacement of the specified atoms from their equilibrium lattice sites according to the patterns corresponding to the delocalized nonlinear vibrational modes (DNVMs) found earlier for a two-dimensional triangular lattice. It is revealed that only four out of the eight studied DNVMs can support stable two-dimensional DBs with the lifetimes in the range of 24–47 ps and accumulate vibrational energy of the order of 2 eV per atom. All excited DBs are characterized by a hard type of nonlinearity, i.e. the frequency increases with the increasing oscillation amplitude. Obtained results indicate the presence of a wide variety of nonlinear, spatially localized vibrational modes in three-dimensional lattices of fcc metals.

Optimization and validation of a deep learning CuZr atomistic potential: Robust applications for crystalline and amorphous phases with near-DFT accuracy.

We show that a deep-learning neural network potential (DP) based on density functional theory (DFT) calculations can well describe Cu-Zr materials, an example of a binary alloy system, that can coexist in as ordered intermetallic and as an amorphous phase. The complex phase diagram for Cu-Zr makes it a challenging system for traditional atomistic force-fields that cannot accurately describe the different properties and phases. Instead, we show that a DP approach using a large database with ∼300k configurations can render results generally on par with DFT. The training set includes configurations of pristine and bulk elementary metals and intermetallic structures in the liquid and solid phases in addition to slab and amorphous configurations. The DP model was validated by comparing bulk properties such as lattice constants, elastic constants, bulk moduli, phonon spectra, and surface energies to DFT values for identical structures. Furthermore, we contrast the DP results with values obtained using well-established two embedded atom method potentials. Overall, our DP potential provides near DFT accuracy for the different Cu-Zr phases but with a fraction of its computational cost, thus enabling accurate computations of realistic atomistic models, especially for the amorphous phase.

Crack and its interaction with defects in Al coated with Cu50Zr50 metallic glass thin film: an MD simulation study.

Molecular dynamics (MD) simulation studies are carried out to investigate the crack propagation behavior and crack-void interactions in Al coated with Cu50Zr50 metallic glass (MG) thin film model. The model thin film is subjected to mode I and mode II loading conditions at a temperature of 300K and a strain rate of 1010s-1. The simulations are carried out in the framework of EAM (embedded atom method) potential based on the CZM (cohesive zone model). The model size is 435Å (x-axis) × 174Å (y-axis) × 17Å (z-axis). Nine models are investigated containing an edge crack (length, L = 43Å, and 118Å) located at the interface and voids (diameter, ϕ = 10-36Å) located in the Al region and at the interface. The results show that crack propagation occurs by dislocation emission and blunts the crack tip. The presence of void ahead of the crack tip restricts the crack propagation due to the stress field resulting in bowing out of the crack and is effective with an increase in the void size which grows normal and parallel to the loading direction. The estimated crack speeds in mode I and mode II are 366m/s and 370m/s during stable crack growth. Separation of the interface occurs by fracture of the ligaments between the voids. Shockley partial dislocations are found nucleating from the void surfaces; twinned regions are found between the voids. The work of separation is found to be 11.56J/m2 for mode I and 3.7J/m2 in mode II, indicating that failure occurs in mode II. Graphical abstract.

Hydrogen in zirconium: Atomistic simulations of diffusion and interaction with defects using a new embedded atom method potential

A new interatomic embedded atom method (EAM) potential, called BMD19, has been developed for simulations of hexagonal zirconium with dissolved hydrogen. The parameters are fitted to data from density functional calculations and calibrated using the experimental room-temperature density of zirconium. The new potential overcomes the unphysical negative thermal expansion coefficient between 0 and 200 K obtained with the frequently used Mendelev-Ackland potential (MA#3). It reproduces the geometry around self-interstitial atoms (SIA’s) obtained with DFT while the MA#3 and the COMB3 potentials yield structures with the SIA between basal planes. The energies of forming vacancies and self-interstitials as well as the elastic coefficients are of similar quality for all potentials investigated in the present work. Compared with DFT results, the new potential describes the interactions of H with Zr better overall than any previously published interatomic potentials. This includes the binding energy of interstitial H and its dependence on lattice strain for tetrahedral and octahedral sites, the trapping energy in vacancies, surface segregation energy, and the energy of diffusion barriers. The present work illustrates the usefulness of the BMD19 potential by showing the dependence of diffusion coefficients on lattice strain, the accumulation of H in vacancy c-loops and by correctly describing the Soret effect, i.e. the diffusion of H from hotter to colder regions of the material. Simulations of the effect of grain boundaries and internal surfaces (e.g. nano-voids) and diffusion on surfaces provide further demonstrations of the usefulness of this new potential.

Research on microstructure deformation mechanism of crack tip in titanium under tension along different orientations

ABSTRACTThe deformation process of titanium with an initial crack was simulated under uniaxial tension by the molecular dynamics method. The effect of [0001], and orientations on the microstructure deformation mechanisms at the crack tip was investigated using embedded atom method potentials. In the simulation, various deformation evidence were clearly observed, such as dislocation nucleation and movement, stacking faults formation, deformation twinning and phase transformation. The stress–strain curves showed that orientations had a greater influence on the plastic stage and less on the elastic stage. By applying uniaxial tension with a constant strain rate along different orientations, microstructure deformation at the crack tip was analysed. When loading along [0001] orientation, twinning was the main deformation mechanism and stacking fault occurred and expanded along slip system with the increase in strain. Applying uniaxial tension along orientation, an abnormal ‘secondary increase’ phenomenon was observed in the stress–strain curve. At the same time, dislocation loops appeared at the crack tip and they expanded, merged with the increase in strain. The massive phase transformation from HCP to BCC was observed in the model when loading along orientation, which was caused by multiple Shockley incomplete dislocations under the size limitation.

Molecular Dynamics Study of Tension Process of Ni-Based Superalloy

To understand the atomistic mechanisms of tension failure of Ni-based superalloy, in this study, the classical molecular dynamics (MD) simulations were used to study the uniaxial tension processes of both the Ni/Ni3Al interface systems and the pure Ni and Ni3Al systems. To examine the effects of interatomic potentials, we adopted embedded atom method (EAM) and reactive force field (ReaxFF) in the MD simulations. The results of EAM simulations showed that the amorphous structures and voids formed near the interface, facilitating further crack propagation within Ni matrix. The EAM potentials also predicted that dislocations were generated and annihilated alternatively, leading to the oscillation of yielding stress during the tension process. The ReaxFF simulations predicted more amorphous formation and larger tensile strength. The atomistic understanding of the defect initiation and propagation during tension process may help to develop the strengthening strategy for controlling the defect evolution under loading.

Temperature and Loading Rate Effect on the Load-Displacement Response of Metal-Metallic Glass (Al-Cu<sub>50</sub>Zr<sub>50</sub>) Layered Structure during Nano-Indentation

Molecular dynamics (MD) simulations of metal-metallic glass (Al-Cu50Zr50) multilayer during nanoindentation is carried out to investigate the load-displacement response, mechanical properties and deformation mechanisms. The indentation study is carried out at temperatures in the range of cryogenic to room temperature (10 K-300 K). The indenter speeds are varied between 0.5-5 Å/ps to study the effect of loading rate. The interaction between Al-Cu-Zr atoms are defined by EAM (Embedded Atom Method) potential. A sample size of 200 Å × 200 Å × 200 Å (in x y z-direction) comprising of 538538 atoms is used for nanoindentation. P P S boundary condition (BC) in x y z direction and NVT ensemble are used. We observed a peak load of 117 nN, at a temperature of 10 K with a loading rate of 5 Å/ps. We found that as the loading rate increase, the peak load also increases. As anticipated, the increase in temperature decreases the strength of the multilayer. The atomic displacement vector plots reveal that MG act as hurdles to the movement of dislocations nucleated at the interface.

Temperature-Dependent Mechanical Properties of Graphene/Cu Nanocomposites with In-Plane Negative Poisson's Ratios.

Negative Poisson's ratio (NPR), also known as “auxetic”, is a highly desired property in a wide range of future industry applications. By employing molecular dynamics (MD) simulation, metal matrix nanocomposites reinforced by graphene sheets are studied in this paper. In the simulation, single crystal copper with crystal orientation [1 1 0] is selected as the matrix and an embedded-atom method (EAM) potential is used to describe the interaction of copper atoms. An aligned graphene sheet is selected as reinforcement, and a hybrid potential, namely, the Erhart-Albe potential, is used for the interaction between a pair of carbon atoms. The interaction between the carbon atom and copper atom is approximated by the Lennard-Jones (L-J) potential. The simulation results showed that both graphene and copper matrix possess in-plane NPRs. The temperature-dependent mechanical properties of graphene/copper nanocomposites with in-plane NPRs are obtained for the first time.

Molecular dynamics simulation of shock-induced isostructural phase transition in single crystal Ce

Cerium (Ce), a rare earth metal, undergoes a significant (14%−17%) and discontinuous volume shrinkage when subjected to ~0.7 GPa compression at ambient temperature: there happens a first-order isostructural phase transition from <i>γ</i>-Ce phase to <i>α</i>-Ce phase (these two phases are both face-centered-cubic (fcc) phase). Because of the <i>α</i>→ <i>γ</i> transition in Ce under shock compression, the shock front in cerium exhibits a 3-wave configuration: elastic precursor, plastic shock wave in <i>γ</i>-Ce, and phase transition wave corresponding to the <i>γ </i>→ <i>α</i> transition according to the experimental observation. In this paper, a recently developed embedded-atom-method (EAM) potential for fcc Ce is employed in the large-scale molecular dynamics simulations of shock loading onto single crystal Ce to study its dynamic behavior, especially the shock-induced <i>α</i>→ <i>γ</i> phase transition, and the orientation dependence with [001], [011] and [111] shock loading. The simulation results show single-wave or multi-wave configuration for shock wave profiles. Under the shock loading along the [001] or [011] crystallographic orientation, the shock wave possesses a 2-wave structure: an elastic precursor and a phase transition wave, while under shock loading along the [111] crystallographic orientation, the obtained shock wave shows a 3-wave profile as observed experimentally. Thus the shock wave structure is obviously dependent on loading orientation. The Hugoniot data obtained in MD simulation show good agreement with the experimental results. The shock loading MD simulation shows lower phase transition pressure than hydrostatic loading, indicating an accelerant role of the deviatoric stress played in the shock induced <i>γ </i>→ <i>α</i> phase transition in Ce. The local lattice structure before and after shocked are recognized with polyhedral template matching and confirmed with radial distribution functions. Under the [011] and [111] loading, the lattice structure maintains the fcc before and after the shocks, and experiences a collapse during the last shock (the second shock for the [011] loading and the third shock for the [111] loading). The lattice structure also maintains fcc before and after the first shock for the [001] loading, while after the second shock the structure type is considered to be body-centered-tetragonal (bct) which is a meta-stable structure resulting from the used EAM potential for Ce. The fcc lattice rotation after shock is observed in the [011] and [111] loading after the phase transition, while no re-orientation occurs in the [001] loading.

Stability of small vacancy clusters in tungsten by molecular dynamics

The vacancies produced in collision cascades of irradiated metals form voids and vacancy clusters. The stability of vacancy clusters and voids is usually studied by kinetic Monte-Carlo methods. We investigated the stability of these vacancy defects at high temperatures using molecular dynamics and recent embedded-atom method potential. We confirm that the vacancy cluster dissociation is thermally activated. We have obtained dissociation energies and characteristic temperatures, both increasing with the number of vacancies and tending to saturate at 3.5 eV and 1200 K, respectively, for large vacancy clusters. Our results qualitatively agree with Monte-Carlo results, but predict somewhat smaller values for both the dissociation energy and characteristic temperature.

Amorphous structure in single-crystal magnesium under compression along the c axis with ultrahigh strain rate

It is well known that twinning deformation plays an important role in the plastic deformation of hexagonal close-packed (HCP) metals because of the insufficient independent slip systems in HCP metals. However, recent works show twinning deformation does not happen in compression in the $c$ axis of the magnesium (Mg) single crystal, and it is not clear that how it deforms with limited dislocation glide in absence of twinning deformation. In the present work, molecular dynamics simulations with well validated modified embedded-atom method potential for Mg are performed to reveal the microscopic deformation behaviors of Mg single crystal compressed in the $c$ axis. We focus on the microstructures and the evolution during both the deformation and the relaxation of the Mg single crystal. Twinning deformation is not observed in the simulations as expected, and dislocations and the amorphous regions are found to be dominant under different loading conditions. The amorphous regions are dominant in the deformation under ultrahigh strain rate, and it results in more homogenous deformation and lower flow stress than dislocation glide. The dislocation glide is dominant under lower strain rate, and the insufficient dislocations may lead to quite inhomogeneous plastic deformation. Furthermore, it is revealed that the amorphous regions consist of irregularly distributed atoms with higher per-atom potential than those in the crystalline state. The amorphous regions thus annihilate rapidly once the high-rate deformation is stopped. The annihilated amorphous regions turn into crystalline ones with dense dislocation networks. The annihilation rate of the amorphous regions decreases with increasing pressure, while it hardly depends on temperature.

Development and application of EAM potentials for Ti, Al and Nb with enhanced planar fault energy of Ti

Interatomic potentials of Ti, Al and Nb have been constructed under the embedded-atom method (EAM) framework with focus on defect properties. The parameters of the potential functions are determined by reproducing selected physical properties by the minimum mean square deviation method. The structural stability of Ti, Al and Nb, as well as point and planar defect properties, e.g., vacancy formation energies, surface energies and stacking fault energies, under the present interatomic potentials was examined. The calculated stacking fault energies are 107.54 mJ/m2 and 207.44 mJ/m2 for the basal and prism planes of Ti, respectively, and 105 mJ/m2 for Al. In general, the present potentials reproduce better defect properties compared with previous potentials under the EAM framework and first principles calculations, and thus benefit molecular dynamics simulations on defect properties. In the calculation of dislocation properties, the interatomic potentials in this work are better than that in previous work, which is very rare in EAM potential.

The effect of many-body potential type and parameterisation on the accuracy of predicting mechanical properties of aluminium using molecular dynamics

ABSTRACTAs opposed to traditional laboratory testing, Molecular Dynamics (MD) offers an atomistic scale method to estimate the mechanical properties of metals. However, there is limited literature that shows the effect of interatomic potentials when determining mechanical properties. Hence, the present research was conducted to investigate the accuracy of various interatomic potentials in estimating mechanical properties of aluminium. Several types of potentials, including Embedded Atom Method (EAM), Modified EAM (MEAM) and Reactive Force Field (ReaxFF) were compared with available experimental data for pure aluminium to determine the most accurate interatomic potential. A uniaxial tensile test was performed at room temperature using MD simulations for nanoscale aluminium. Results demonstrated that those potentials parameterised with elastic constants at physically realisable temperatures were consistently more accurate. Overall, the Mishin et al. EAM potential was the most accurate when compared to single-crystal experimental values. Regardless of the potential type, the error was significantly higher for those potentials that did not consider elastic constants during development. In brief, the application of the interatomic potentials to estimate mechanical properties of a nanoscale aluminium was investigated.

Modified embedded-atom method potential for high-temperature crystal-melt properties of Ti–Ni alloys and its application to phase field simulation of solidification

We developed new interatomic potentials, based on the second nearest-neighbor modified embedded-atom method (2NN-MEAM) formalism, for Ti, Ni, and the binary Ti–Ni system. These potentials were fit to melting points, latent heats, the binary phase diagrams for the Ti rich and Ni rich regions, and the liquid phase enthalpy of mixing for binary alloys, therefore they are particularly suited for calculations of crystal-melt (CM) interface thermodynamic and transport properties. The accuracy of the potentials for pure Ti and pure Ni were tested against both 0 K and high temperature properties by comparing various properties obtained from experiments or density functional theory calculations including structural properties, elastic constants, point-defect properties, surface energies, temperatures and enthalpies of phase transformations, and diffusivity and viscosity in the liquid phase. The fitted binary potential for Ti–Ni was also tested against various non-fitted properties at 0 K and high temperatures including lattice parameters, formation energies of different intermetallic compounds, and the temperature dependence of liquid density at various concentrations. The CM interfacial free energies obtained from simulations, based on the newly developed Ti–Ni potential, show that the bcc alloys tend to have smaller anisotropy compared with fcc alloys which is consistent with the finding from the previous studies comparing single component bcc and fcc materials. Moreover, the interfacial free energy and its anisotropy for Ti-2 atom% Ni were also used to parameterize a 2D phase field (PF) model utilized in solidification simulations. The PF simulation predictions of microstructure development during solidification are in good agreement with a geometric model for dendrite primary arm spacing.

Fast, accurate, and transferable many-body interatomic potentials by symbolic regression

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine-learning algorithms to develop fast and accurate interatomic potential models, but it remains a challenge to develop models that generalize well and are fast enough to be used at extreme time and length scales. To address this challenge, we have developed a machine-learning algorithm based on symbolic regression in the form of genetic programming that is capable of discovering accurate, computationally efficient many-body potential models. The key to our approach is to explore a hypothesis space of models based on fundamental physical principles and select models within this hypothesis space based on their accuracy, speed, and simplicity. The focus on simplicity reduces the risk of overfitting the training data and increases the chances of discovering a model that generalizes well. Our algorithm was validated by rediscovering an exact Lennard-Jones potential and a Sutton-Chen embedded-atom method potential from training data generated using these models. By using training data generated from density functional theory calculations, we found potential models for elemental copper that are simple, as fast as embedded-atom models, and capable of accurately predicting properties outside of their training set. Our approach requires relatively small sets of training data, making it possible to generate training data using highly accurate methods at a reasonable computational cost. We present our approach, the forms of the discovered models, and assessments of their transferability, accuracy and speed.

Graphene Adhesion Mechanics on Iron Substrates: Insight from Molecular Dynamic Simulations

The adhesion feature of graphene on metal substrates is important in graphene synthesis, transfer and applications, as well as for graphene-reinforced metal matrix composites. We investigate the adhesion energy of graphene nanosheets (GNs) on iron substrate using molecular dynamic (MD) simulations. Two Fe–C potentials are examined as Lennard–Jones (LJ) pair potential and embedded-atom method (EAM) potential. For LJ potential, the adhesion energies of monolayer GN are 0.47, 0.62, 0.70 and 0.74 J/m2 on the iron {110}, {111}, {112} and {100} surfaces, respectively, compared to the values of 26.83, 24.87, 25.13 and 25.01 J/m2 from EAM potential. When the number of GN layers increases from one to three, the adhesion energy from EAM potential increases. Such a trend is not captured by LJ potential. The iron {110} surface is the most adhesive surface for monolayer, bilayer and trilayer GNs from EAM potential. The results suggest that the LJ potential describes a weak bond of Fe–C, opposed to a hybrid chemical and strong bond from EAM potential. The average vertical distances between monolayer GN and four iron surfaces are 2.0–2.2 Å from LJ potential and 1.3–1.4 Å from EAM potential. These separations are nearly unchanged with an increasing number of layers. The ABA-stacked GN is likely to form on lower-index {110} and {100} surfaces, while the ABC-stacked GN is preferred on higher-index {111} surface. Our insights of the graphene adhesion mechanics might be beneficial in graphene growing, surface engineering and enhancement of iron using graphene sheets.

Development of a deep machine learning interatomic potential for metalloid-containing Pd-Si compounds

Interatomic potentials based on neural-network machine learning (ML) approach to address the long-standing challenge of accuracy versus efficiency in molecular-dynamics simulations have recently attracted a great deal of interest. Here, utilizing Pd-Si system as a prototype, we extend the development of neural-network ML potentials to compounds exhibiting various types of bonding characteristics. The ML potential is trained by fitting to the energies and forces of both liquid and crystal structures first-principles calculations based on density-functional theory (DFT). We show that the generated ML potential captures the structural features and motifs in $\mathrm{P}{\mathrm{d}}_{82}\mathrm{S}{\mathrm{i}}_{18}$ and $\mathrm{P}{\mathrm{d}}_{75}\mathrm{S}{\mathrm{i}}_{25}$ liquids more accurately than the existing interatomic potential based on embedded-atom method (EAM). The ML potential also describes the solid-liquid interface of these systems very well. Moreover, while the existing EAM potential fails to describe the relative energies of various crystalline structures and predict wrong ground-state structures at $\mathrm{P}{\mathrm{d}}_{3}\mathrm{Si}$ and $\mathrm{P}{\mathrm{d}}_{9}\mathrm{S}{\mathrm{i}}_{2}$ composition, the developed ML potential predicts correctly the ground-state structures from genetic algorithm search. The efficient ML potential with DFT accuracy from our study will provide a promising scheme for accurate atomistic simulations of structures and dynamics of complex Pd-Si system.