Embedded Atom Model Research Articles

A grand canonical genetic algorithm for the prediction of multi-component phase diagrams and testing of empirical potentials

We present an evolutionary algorithm which predicts stable atomic structures and phase diagrams by searching the energy landscape of empirical and ab initio Hamiltonians. Composition and geometrical degrees of freedom may be varied simultaneously. We show that this method utilizes information from favorable local structure at one composition to predict that at others, achieving far greater efficiency of phase diagram prediction than a method which relies on sampling compositions individually. We detail this and a number of other efficiency-improving techniques implemented in the genetic algorithm for structure prediction code that is now publicly available. We test the efficiency of the software by searching the ternary Zr–Cu–Al system using an empirical embedded-atom model potential. In addition to testing the algorithm, we also evaluate the accuracy of the potential itself. We find that the potential stabilizes several correct ternary phases, while a few of the predicted ground states are unphysical. Our results suggest that genetic algorithm searches can be used to improve the methodology of empirical potential design.

Molecular dynamics simulations of shock-induced plasticity in tantalum

We present Non-Equilibrium Molecular Dynamics (NEMD) simulations of shock wave compression along the [001] direction in monocrystalline Tantalum, including pre-existing defects which act as dislocation sources. We use a new Embedded Atom Model (EAM) potential and study the nucleation and evolution of dislocations as a function of shock pressure and loading rise time. We find that the flow stress and dislocation density behind the shock front depend on strain rate. We find excellent agreement with recent experimental results on strength and recovered microstructure, which goes from dislocations to a mixture of dislocations and twins, to twinning dominated response, as the shock pressure increases.

Effects of atomic size difference and heat of mixing parameters on the local structure of a model metallic glass system

Atomic size differences between constituting elements and the heat of mixing are key factors in designing a metallic glass system. In this study, the effects of atomic size differences and the heat of mixing on the glass-forming ability and the local structure of metallic glasses were studied via molecular dynamic simulations of an ideal system known as the Lennard-Jones embedded-atom method model. The atomic size difference and the heat of mixing of the system were varied by means of the Lennard-Jones parameters. The glass transition behavior was characterized based on the chemical short-range order and by a Voronoi analysis. Our simulations lead to optimized windows of atomic size differences and heat of mixing parameters for metallic glass-forming of the model system. Both a greater negative heat of mixing and a larger atomic size difference are necessary for the enhancement of the glass-forming ability.

Impact compression of alkali metals: Computer-aided simulation

This article describes a method for calculation of the potential of the embedded atom model (EAM), suitable for calculation of the properties of alkali metals in highly compressed states. For the first time, sequential consideration of the thermal energy and thermal pressure of collective electrons has been introduced into the EAM flowchart. The parameters of the EAM potential have been calculated, which make it possible to obtain good agreement in terms of pressure and energy for five alkali metals under impact compression. The properties of the molecular dynamic models of alkali metals at 300 and 0 K are compared with the data of static compression. The agreement between them is sufficient up to pressures of 15–20 GPa, and at higher compression rates divergences become significant. A lack of experimental data makes it impossible to understand whether the reason for these divergences is incomplete adequacy of the EAM potential or systematic errors contained in the experimental data in the range of high pressures. The proposed potentials make it possible to calculate the thermodynamic, structural, and diffusion properties of alkali metals in highly compressed states at temperatures up to 20000–30000 K.

MD simulations of phase stability of PuGa alloys: Effects of primary radiation defects and helium bubbles

We present classical molecular dynamics (MD) with Modified Embedded Atom Model (MEAM) simulations to investigate the role of primary radiation defects and radiogenic helium as factors affecting the phase stability of PuGa alloys in cooling–heating cycles at ambient pressure. The models of PuGa alloys equilibrated at ambient conditions were subjected to cooling–heating cycles in which they were initially cooled down to 100 K and then heated up to 500 K at ambient pressure. The rate of temperature change in the cycles was 10 K/ns. The simulations showed that the initial FCC phase of PuGa alloys undergo polymorphous transition in cooling to a lower symmetry α'-phase. All the alloys undergo direct and reverse polymorphous transitions in the cooling–heating cycles. The alloys containing vacancies shift in both transitions to lower temperatures relative to the defect-free alloys. The radiogenic helium has much less effect on the phase stability compared to that of primary radiation defects (in spite of the fact that helium concentration is twice of that for the primary radiation defects). Lastly, this computational result agrees with experimental data on unconventional stabilization mechanism of PuGa alloys.

Cooling rate dependence of the icosahedral order of amorphous CuNi alloy: A molecular dynamics simulation

In this study, a molecular dynamics (MD) simulation is carried out to obtain glass formation and icosahedral order for Cu–%50Ni model alloy system with 10,976 atoms based on embedded atom model (EAM) during the cooling processes. The structural development and icosahedral order of alloy system are analysed with the radial distribution function (RDF), the bond orientational order parameters and Honeycutt–Andersen (HA) bond-type index method. By looking into the amorphous-type bonded pairs within the atomic clusters and by analysing bond orientational order parameters (icos Q6 and icos Wˆ6), the icosahedral order is investigated under different cooling processes for the model alloy system.

A dynamical atomic simulation for the Ni[sbnd]Al Wulff nanoparticle

NiAl bimetallic nanoparticle structures are studied from a kinetic point of view. The diffusion and growth of Ni (or Al) atoms on Al (or Ni) cores with the Wulff structure are simulated by molecular dynamics and nudged elastic band methods. An analytic embedded atom model is applied to the two metals. The energy barriers of several typical diffusion processes of the adatoms on the nanoparticle surface are calculated. Results show that the incorporation of the Ni atoms into the Al core easily occurs, and the reverse process does not readily proceed. The growth simulations reveal that a better core-shell nanoparticle is obtained when the Al atoms are deposited on the Ni core at lower temperatures, and the deposition of the Ni atoms on the Al core leads to an amorphous surface.

A ternary EAM interatomic potential for U–Mo alloys with xenon

A new interatomic potential for a uranium–molybdenum system with xenon is developed in the framework of an embedded atom model using a force-matching technique and a dataset of ab initio atomic forces. The verification of the potential proves that it is suitable for the investigation of various compounds existing in the system as well as for simulation of pure elements: U, Mo and Xe. Computed lattice constants, thermal expansion coefficients, elastic properties and melting temperatures of U, Mo and Xe are consistent with the experimentally measured values. The energies of the point defect formation in pure U and Mo are proved to be comparable to the density-functional theory calculations. We compare this new U–Mo–Xe potential with the previously developed U and Mo–Xe potentials. A comparative study between the different potential functions is provided. The key purpose of the new model is to study the atomistic processes of defect evolution taking place in the U–Mo nuclear fuel. Here we use the potential to simulate bcc alloys containing 10 wt% of intermetallic Mo and U2Mo.

Account for electron contributions in embedded atom model for iron and nickel in molecular dynamics simulation

Potentials of embedded atom model (EAM) are calculated in analytical form for liquid iron and nickel. A series of models of these metals is created up to the temperature of 4000–4200 K. It is shown that these potentials enable us to obtain good agreement between the density of models and real metals; upon heating, however, the energy of the models is reduced relative to the real energies. It is established that the divergence of energies at ∼4000 K is 32 kJ/mol for iron and 33 kJ/mol for nickel. It is shown that most of this divergence is determined by the contribution from the heat energy of electrons; after subtracting this contribution, a divergence of energies of 8.1 kJ/mol for iron and 14.3 kJ/mol for nickel remains. It is concluded that this divergence could be due partly to the insufficient adequacy of EAM potential in describing broad temperature ranges.

Molecular dynamics study of Ag, Ar, Cu, Ni, Al, Fe, Ta, K, and Cs nanoclusters within the embedded atom model

The effect of the form of particle-particle potentials on the nanocluster structure has been investigated by the molecular-dynamics method. The nanocluster structure is characterized by multidimensional vectors of tetrahedral and octahedral indices for Delaunay simplexes. The similarity or distinction of the structures of a pair of clusters identical in size has been estimated from the distance between these vectors. Two groups of potentials have been applied: (1) multiparticle potentials of the embedded atom model (EAM), developed to describe fcc metals (Ag, Cu, Ni, and Al), and the Lennard-Jones pairwise potential for argon (fcc lattice) and (2) EAM potentials for bcc metals (Fe, Ta, K, and Cs). Nanoclusters with a number of atoms from 11 to 64 and of magic sizes (55, 147, 309, 561, and 923 atoms) have been investigated. In the case of nanoclusters with less than 27 atoms, the structure is independent of the affiliation of the potential to a certain group. If all potentials belong to the first group, clusters with magic sizes have the same (regular icosahedral) structure. In the case of second-group potentials, identical structures are found for only nanoclusters with no more than 29 atoms.

Maximum entropy reconstruction of the configurational density of states from microcanonical simulations

In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.

Application of the embedded atom model to liquid mercury

The pair contribution to the potential of the embedded atom model (EAM) for liquid mercury has been corrected and arranged in a more convenient analytical form. A series of 2000 atom models of liquid mercury has been developed using molecular dynamics at temperatures up to 1673 K, and a good agreement with the data on density has been obtained. The pair correlation functions (PCFs), energy, bulk compression modulus, and self-diffusion coefficients have been calculated. Standard deviations of the PCF of the models from the diffraction PCF of mercury at all temperatures except for 293 K are rather high (0.08–0.10). As in the case of alkaline metals, the energy of the models at high temperatures is lower compared with actual mercury, which is due to insufficient adequacy of the EAM potential and neglect of thermal energy of electrons in the embedded atom model. Using the data on shock compression of mercury, an equation for the embedding potential of the EAM is proposed, which is suitable for description of strong compression states, and an agreement has been obtained with the experimental data on the energy and pressure of mercury along the Hugoniot curve at pressures up to 46 GPa.

Molecular dynamics simulation of isothermal crystallization dynamics in Cu nanocluster

We investigate the isothermal crystallizations of nanoparticles composed, respectively, of 4000 Cu atoms (Cu4000) and 13500 Cu atoms (Cu13500), and bulk Cu according to on embedded atom model, using molecular dynamics simulations. We note that different sizes of Cu nanoparticles display multistep crystallization at low temperature, and their crystallization time distribution is wider than at high temperature, shown by analyzing the structural and dynamic properties of isothermal crystallization. Moreover, the size of particle plays an important role in the crystallization process. The larger the size, the longer the crystallization time is. However, we find that there is a critical size rc. The crystallization time increases with particle size increasing when the size is less than rc. On the contrary, when the size is more than rc, the crystallization time decreases with particle size increasing.

The generalized embedded atom model of interatomic interaction and its application to α-Pu

The generalized embedded-atom model (GEAM) for interatomic interaction in metals with complex electronic and crystal structure has been developed as a modification of the angular dependence term of well-known MEAM potential. Here we present an analytical form of the new interatomic potential, including partial forces ready to be implemented into MD computer code. The new model has been applied to low-temperature monoclinic α-phase of plutonium. In rather long MD simulations with flexible unit cell geometry it has been shown that monoclinic lattice proved to be mechanically stable in temperature range 0–300K and at zero stress tensor. Results of MD simulations obtained with the new model at finite temperatures were compared with experimental and ab initio data on the properties of the material.

Temperature dependence of the structure and shear response of a Σ11 asymmetric tilt grain boundary in copper from molecular-dynamics

We investigate the effect of temperature on the structure and shear response of a Σ11 asymmetric tilt grain boundary in a classical embedded-atom model of elemental copper using molecular dynamics simulations. As the temperature is increased the structure of the boundary disorders considerably, but with a boundary width that remains finite at the melting point. The disordering of the boundary structure becomes significant for homologous temperatures above 0.83 (1100 K). As temperature increases above this point the boundary width and roughness increases monotonically. Near the temperature where the boundary starts to disorder we observe a change in the temperature dependence of the ideal shear strength of the boundary, as well as the value of the coupling parameter β, defined as the ratio of the velocity of relative translation of the grains parallel to the boundary plane to that corresponding to the motion of the boundary normal to its plane.

Local order and dynamic properties of liquid AuxSi1−x alloys by molecular dynamics simulations

Molecular dynamics simulations are performed to examine structural and dynamic properties of liquid Au-Si alloys around the eutectic composition, with interactions described via a modified embedded-atom model suitable for the liquid properties. The local structure as defined by the partial pair-correlation functions, coordination numbers, and partial structure factors is found to display a strong evolution with composition. In addition, a structural study using a three-dimensional pair-analysis technique evidences a strong evolution of the icosahedral short-range order over the range of concentrations, 0 < x(Si) < 0.5. In examining the dynamic properties of these alloys, we show a strong interplay between the structural changes and the evolution of the self-diffusion coefficients as a function of composition.

Perturbation theory of solid-liquid interfacial free energies of bcc metals

A perturbation theory is used to calculate bcc solid-liquid interfacial free energies of metallic systems with embedded-atom model potentials. As a reference system for bcc crystals we used a single-occupancy cell, hard-sphere bcc system. Good agreements between the perturbation theory results and the corresponding results from simulations are found. The strategy to extract hard-sphere bcc solid-liquid interfacial free energies may have broader applications for other crystal lattices.

Effect of nanopatterns on Kapitza resistance at a water-gold interface during boiling: A molecular dynamics study

The effect of nanopatterns on Kapitza resistance of water boiling on a gold surface is examined via molecular dynamics simulations. The TIP4P-Ew potential for water, embedded-atom model for gold, and the calibrated Lennard-Jones parameters for water-gold interactions are used to accurately predict the boiling point of water and the wetting angle of water on gold. The results show that boiling of water does not affect the Kapitza resistance of the water-gold interface. The increase of the height of nanopatterns leads to a reduction of the Kapitza resistance by increasing the interaction energy per unit area at the water-gold interface. With the increase of the width-to-spacing ratio of nanopatterns, the Kapitza resistance reduces due to the decrease of the mismatch between the vibrational density of states of water and gold.

Molecular dynamics investigation of the structural stability of body-centered cubic zirconium nanofilms

The influence of the film thickness and temperature on the phase stability of body-centered cubic (BCC) zirconium in infinite films with different crystallographic orientations has been investigated using the molecular dynamics method with a many-body interatomic interaction potential obtained within the embedded atom model. The calculations have been performed for BCC zirconium films with thicknesses ranging from 2 to 13 nm and with low Miller indices (001), (110), and (111). It has been shown that the BCC(001) zirconium nanofilms with thicknesses up to 6.1 nm, which are formed in the temperature range from 500 to 1300 K, undergo a reorientational phase transition through an intermediate metastable face-centered cubic (FCC) phase with the subsequent transformation into the hexagonal close-packed (HCP) structure (BCC(001)-FCC-BCC’(110)-HCP). When the temperature of initialization of the films is 500 K and below, the BCC-FCC transformation is observed and the FCC phase remains stable. The (110) films are characterized by a strong dependence of the temperature of the BCC-HCP phase transition on the film thickness up to values of 5.8 nm. In the (111) films, the amorphization of the initial BCC phase with the subsequent formation of the BCC phase with a twin structure is observed.

Molecular Dynamics Simulation of Liquid-Vapor Coexistence Curves of Metals

A Molecular dynamics implementation of Gibbs ensemble method is applied to determine liquid-vapor coexistence curves of metals using embedded atom model potentials. As an application of the code we developed, the liquid-vapor coexistence curves of Aluminum and Copper are simulated using Cai and Ye potential. The critical constants obtained were found to be slightly lower than the range of experimental results. The results show that the potentials parameters obtained by fitting to low temperature solid properties are not adequate to accurately determine the liquid-vapor phase diagram.