Embedded Atom Model Potential Research Articles

Viscosity of liquid iron under high pressure and high temperature: Equilibrium and nonequilibrium molecular dynamics simulation studies

Using classical molecular dynamics simulations together with a many-body embedded atom model (EAM) potential, we calculate the viscosity of liquid iron under high temperature and high pressure. We show that this EAM potential, in addition to reproducing experimental data on the structure of liquid iron at high pressure, accurately predicts the shear viscosity of liquid iron. We carefully assess the validity of our results, obtained from equilibrium molecular dynamics simulations as well as from nonequilibrium molecular dynamics simulations. Our estimates for the viscosity are shown to be in good agreement with those obtained from ab initio molecular dynamics simulations. This demonstrates that the EAM potential accurately describes both the thermodynamic and transport properties of liquid iron under extreme conditions and provides a satisfactory alternative to ab initio molecular dynamics simulations for large-scale simulations.

Equilibrium properties of binary and ternary metallic immiscible nanoclusters

Metropolis Monte Carlo free energy minimization in the $(\mathit{NPT})$ canonical ensemble is used to predict at the atomic scale the configurations of isolated metallic clusters made of two and three metals that are immiscible in the bulk. Clusters studied are formed by 200--1300 atoms by combining cobalt, silver, and copper. An embedded atom model potential is used to describe their cohesion. It is found that not only binding and interfacial configuration energies govern the composition of atomic configurations, but also thermal vibrational entropy plays a substantial role in the balance of energy contributions to thermodynamic equilibrium. Core-shell Ag-Co, Ag-Cu, and ``onionlike'' Cu-Co equilibrium configurations are found, which can be tuned by monitoring the interplay between composition and temperature. In ternary clusters, Ag always forms the surface layer and it is found that the Co and Cu distributions in the core depend on the Ag layer thickness.

Uncommon features in the dynamic structure factor of a molten transition metal

The collective SC(Q,ω), single-particle SS(Q,ω) dynamic structure factors as well as the spectra for transverse-current correlations CT(Q,ω) for molten nickel close to melting have been calculated from a massive molecular dynamics simulation using an Embedded Atom Model potential. A number of features are found in the structure factors that are absent in the spectra of simpler liquids such as molten alkali metals. Estimates for the shear component of the generalized, wavevector-dependent viscosity are obtained from analysis of CT(Q,ω). Such data together with those concerning the strength of the thermal conduction channels for the excitation decay enable us to subtract such contributions to form the linewidths of Brillouin peaks and thus to evaluate the Q-dependent bulk viscosity coefficient. The result shows that contrary to inferences based upon geophysical data, both bulk and shear-viscosity coefficients are of the same order of magnitude.

Metropolis Monte Carlo predictions of free Co–Pt nanoclusters

The Metropolis Monte Carlo (MC) sampling method with a semi-empirical Embedded Atom Model (EAM) and a Modified EAM (MEAM) potentials is used to investigate structural properties of free Co–Pt nanoclusters. Sampling is achieved in the number–pressure–temperature (NPT) and the (Δ μ-NPT) ensembles, where Δ μ denotes the chemical potential difference between the Co and Pt subsystems. The model potentials are parameterised on the basis of the structure, the lattice distance, the vacancy formation energy, the bulk modulus and the cohesive energy of pure cobalt and platinum. The mixed repulsive contribution to the EAM configuration energy is here tuned in such a way to correctly predict the tetragonal ordered structure of CoPt at room temperature. MC predicts the ordered structure of Co 3Pt, CoPt and CoPt 3 phases as well as the order–disorder phase transition in CoPt. The results obtained with both potentials are compared. The study is then extended to isolated CoPt and Co 3Pt clusters containing a few hundred atoms and the consequences of temperature on predicted structural and segregation properties are investigated.

Embedded atom model for liquid metals: Liquid iron

A method for calculating the embedded atom model potential suggested earlier for liquid Ga and Bi uses data on the structure and thermodynamic properties of metals close to their melting points. This method was applied to liquid iron at temperatures and pressures up to 5000 K and 360 GPa. Several iron models with the potential of the embedded atom model were constructed by the method of molecular dynamics at temperatures from 1820 to 5000 K and densities from 8.00 to 12.50 g/cm3. The thermodynamic, structural, diffusion, and viscosity properties of iron were calculated. The self-diffusion coefficients decreased almost linearly as the volume of the system became smaller. The conclusion is drawn that iron in the external region of the Earth’s core behaves as a liquid with self-diffusion coefficients of about ∼10-5 cm2/s and viscosity ∼10-3−10-2 Pa s. At the boundary between the external and inner core regions, at densities of 11–12 g/cm3, iron has the properties of an amorphous phase and its self-diffusion coefficient becomes too low to be estimated by the method of molecular dynamics. Under the Earth’s inner core conditions, the embedded atom model of iron spontaneously crystallizes.

Diffusion rates of Cu adatoms on Cu(111) in the presence of an adisland nucleated at fcc or hcp sites

The surface diffusion of Cu adatoms in the presence of an adisland at fcc or hcp sites on Cu(111) is studied using the embedded atom model potential derived by Mishin et al. [Phys. Rev. B 63, 224106 (2001)]. The diffusion rates along straight (with close-packed edges) steps with (100) and (111)-type microfacets (respectively, step $A$ and step $B$) are first investigated using the transition state theory in the harmonic approximation. It is found that the classical limit beyond which the diffusion rates follow an Arrhenius law is reached above the Debye temperature. The Vineyard attempt frequencies and the (static) energy barriers are reported. Then a comparison is made with the results of more realistic classical molecular dynamic simulations which also exhibit an Arrhenius-type behavior. It is concluded that the corresponding energy barriers are completely consistent with the static ones within the statistical errors and that the diffusion barrier along step $B$ is significantly larger than along step $A$. In contrast the prefactors are very different from the Vineyard frequencies. They increase with the static energy barrier in agreement with the Meyer-Neldel compensation rule and this increase is well approximated by the law proposed by Boisvert et al. [Phys. Rev. Lett. 75, 469 (1995)]. As a consequence, the remaining part of this work is devoted to the determination of static energy barriers for a large number of diffusion events that can occur in the presence of an adisland. In particular, it is found that the corner crossing diffusion process for triangular adislands is markedly different for the two types of borders ($A$ or $B$). From this set of results the diffusion rates of the most important atomic displacements can be predicted and used as input in kinetic Monte Carlo simulations.

Global minima of AlN, AuN and PtN, N ⩽ 80, clusters described by the Voter–Chen version of embedded-atom potentials

We report the global minima for aluminium, gold and platinum metal clusters modelled by the Voter–Chen version of the embedded-atom model potential containing up to 80 atoms using the basin-hopping Monte Carlo minimization approach. The results show that the global minima of the Al, Au and Pt clusters have structures based on either octahedral, decahedral, icosahedral or a mixture of decahedral and icosahedral packing. The 54-atom icosahedron without a central atom is found to be more stable than the 55-atom complete icosahedron for all of the elements considered in this work. Most of the Al global minima are identified as face-centred cubic structures and many of the Au global minima are found to be low symmetric structures, both of which are in agreement with the previous theoretical and experimental studies. Although many of the Pt global minima are identical with the global minima of the corresponding Au clusters, the most stable sizes of the Pt clusters correspond to the same sizes of the Al clusters.

Atomistic simulations of kinks in1/2a〈111〉screw dislocations in bcc tantalum

Two types of equilibrium core structures (denoted symmetric and asymmetric) for $1/2a〈111〉$ screw dislocations in bcc metals have been found in atomistic simulations. In asymmetric (or polarized) cores, the central three atoms simultaneously translate along the Burgers vector direction. This collective displacement of core atoms is called polarization. In contrast, symmetric (nonpolarized) cores have zero core polarization. To examine the possible role of dislocation core in kink-pair formation process, we studied the multiplicity, structural features, and formation energies of $1/3a〈112〉$ kinks in $1/2a〈111〉$ screw dislocations with different core structures. To do this we used a family of embedded atom model potentials for tantalum (Ta) all of which reproduce bulk properties (density, cohesive energy, and elastic constants) from quantum mechanics calculations but differ in the resulting polarization of $1/2a〈111〉$ screw dislocations. For dislocations with asymmetric core, there are two energy equivalent core configurations [with positive (P) and negative (N) polarization], leading to 2 types of (polarization) flips, 8 kinds of isolated kinks, and 16 combinations of kink pairs. We find there are only two elementary kinks, while the others are composites of elementary kinks and flips. In contrast, for screw dislocations with symmetric core, there are only two types of isolated kinks and one kind of kink pair. We find that the equilibrium dislocation core structure of $1/2a〈111〉$ screw dislocations is an important factor in determining the kink-pair formation energy.

Role of core polarization curvature of screw dislocations in determining the Peierls stress in bcc Ta: A criterion for designing high-performance materials

We use a family of embedded atom model potentials all based on accurate quantum-mechanical calculations to study the relation between Peierls stress and core properties of the $1/2a〈111〉$ screw dislocation in bcc tantalum (Ta). We find that the Peierls stress $({\ensuremath{\sigma}}_{P})$ is a function of the core-polarization curvature (\ensuremath{\Pi}) near the equilibrium core configuration. Our results suggest that the computationally available quantity \ensuremath{\Pi} is a useful criterion for designing high-performance materials.

Accurate method to calculate liquid and solid free energies for embedded atom potentials

Using a perturbation theory with a hard-sphere reference system we have directly calculated free energies of fluid and solid phases of aluminum with an embedded atom model potential. Unlike other approaches such as thermodynamic integration, we do not require any simulations. Moreover, the free energies of the two different phases are calculated in a single approach, unlike approximations like the quasi-harmonic solid approach. The calculated free energies are with an average relative error 0.55% of the simulation values and the resulting melting temperature is within 5% of the simulation value.

MODIFIED EAM POTENTIALS FOR MODELLING STACKING–FAULT BEHAVIOR IN Cu, Al, Au, AND Ni

In this paper we have developed empirical Embedded Atom Model potentials, following the fitting scheme proposed by Chantasiriwan and Milstein, in order to describe the stacking fault behaviour of copper, gold, nickel and aluminium. We show that the potentials based on this scheme can be modified to provide reasonable stacking-fault energy values and consequently a better description of the plastic properties. Modifications were done by changing the cut-off distance in case of aluminium and nickel, and in case of gold and copper by also modifying the functional form of the pair-potential. In order to validate these modified potentials we have tested them by studying various properties, such as structural, defect, and surface energies, and phonon spectra and comparing results with those from experiments and other model potentials.

Small Ni clusters at the (1 1 0) and (1 1 1) surfaces of Al: structures and lack of magnetic moment

Using the Voter and Chen embedded atom model potential for the Ni–Al system, we performed quenched molecular dynamics simulations to compute the ground-state structures of small Ni n clusters ( n⩽10) at the (1 1 0) and (1 1 1) surfaces of Al. Determination of spin-polarized electronic structure using a self-consistent tight-binding method showed that, due to hybridization between the Al sp and Ni d states, the Ni clusters are nonmagnetic.

Double Lattice Inversion Technique ? Application to the EAM Potential Construction

The embedded atom model (EAM) has been proved to be a very effective and powerful approach to energy calculation in metals. In the current work, we present a new approach to the construction of the EAM potential. The EAM functions are determined in a way to reproduce exactly two state equations defined for unit cells of two different metal structures. Our method is in some sense an extension of the lattice inversion algorithm proposed by Carlsson et al. (Phil Mag. A 41, 241 (1980)), where the resulting pair potential reconstructs only one given state equation. The inversion technique has been applied before to the construction of a pair potential and embedded atom potential from a single state equation. Using two input state equations we can determine only two functions, thus, we construct the pair potential and embedding function. The atomic charge density is taken from first-principle calculation. As an example, we apply our method to the determination of the EAM potential for solid lead. In order to estimate the quality of this potential, some bulk and defect properties are also calculated.

A computer simulation study of the ground-state configurations of Fe and Fe-Al clusters

Using the noncentral embedded atom model potential recently proposed by Besson and Morillo for \(\) bulk alloys (\(\)), we performed computer simulations to predict the ground-state configurations of \(\) and \(\) clusters (\(\)). The computed structures of \(\) clusters are in general agreement with such theoretical results as have been obtained by density functional calculations (i.e. for \(\)). The results for Fe-rich \(\) clusters show surface segregation of Al, which is in keeping with the findings of a previous study of \(\) clusters.

Stacking-fault energy of copper from molecular-dynamics simulations

The behavior of the energy of stacking fault defects in copper as a function of external strain and temperature is investigated making use of molecular-dynamics simulations. Atomic interactions are modeled by an effective-medium theory potential. Intrinsic, extrinsic, and twinning faults are considered. Our results suggest that the stability of stacking-fault defects in copper increases with temperature and decreases with applied compressive strain. In addition, we point out some difficulties posed by the application of finite range model potentials to the study of low-energy defects. To show that these difficulties are quite general in nature we also compute the stacking-fault energy (SFE) from an embedded atom model potential. Our results indicate that the SFE computed from model potentials displays a spurious change of sign with increasing compressive strain.

Embedded atom model calculations of the structures of small Ni clusters and of a full Ni monolayer on the (001) surface of Al

Using the Voter and Chen embedded-atom model potential for the Ni–Al system, we performed quenched molecular dynamics simulations to obtain the structures and binding energies of small clusters and of a full monolayer of Ni atoms on the Al(001) surface. Our results show that both clusters and the monolayer undergo surface alloying, i.e., there is a tendency for the Ni atoms to be embedded in the substrate, displacing Al atoms from their initial positions. However, whereas the surface alloying of the clusters occurs rapidly, that of the monolayer requires an appreciable prior equilibration period at a temperature allowing atomic mobility; quenching without this equilibration period can freeze the system in a metastable state in which the Ni adlayer remains on an Al surface that is hardly altered. An analogous metastable state may have been achieved in experiments by other authors with ultrathin Ni films.

Embedded atom model calculations of the diffusion coefficient of Ni impurity in liquid Al

Using the embedded atom model potential for solid Ni–Al systems proposed by Voter and Chen, we performed molecular dynamics simulations to compute the diffusion coefficient of Ni impurity in liquid Al. Our results are in excellent agreement with available experimental data.

A many body potential for α-Zr. Application to defect properties

An embedded atom model (EAM) interatomic potential that reproduces room temperature elastic behavior for α-Zr is developed. At variance with previous potentials from the literature, the present one predicts a self-interstitial relaxation volume consistent with the relatively low measured value. A critical review of results for static and dynamic properties of point defects is undertaken by comparing with predictions from other potentials and with experimental findings. This survey allows us to conclude that most well fitted EAM potentials give low vacancy migration energies and a basal crowdion as the stable interstitial configuration with fast 1D migration.

Theembedded-atom model applied to vacancy formation in bulk aluminium andlithium

The embedded-atom model (EAM) is applied to the study of vacancy formation in bulk aluminium and lithium. A systematic study is undertaken into the sensitivity of the EAM potentials and embedding energy functionals as a function of the unrelaxed vacancy formation energy which is normally obtained via ab initio density functional calculations. The effect of this `empirical' input parameter on the vacancy relaxation energy, formation volume and structural relaxation is also investigated using super-cell sizes not normally accessible in orbital-based ab initio relaxation studies. We find that for aluminium, for which at most a fifth-nearest-neighbour model is required, the vacancy relaxation energy and formation volume are not sensitive functions of the unrelaxed vacancy formation energy. For lithium, for which at least a ninth-nearest-neighbour model is needed, the situation is somewhat different: both the vacancy relaxation energy and the formation volume are found to be a noticeably related to the unrelaxed vacancy formation energy. For both solids, the structural relaxation was found to be largely insensitive to the unrelaxed vacancy formation energy, agreeing well with previous ab initio calculations. In particular for aluminium, the EAM result agrees extremely well with recent orbital-free density functional calculations which use super-cell sizes approaching those used here. Finally, we find that for lithium, the embedding energy functional has negligible curvature for a wide range of local electronic densities, justifying the use of a simpler pair potential description for lithium in mildly inhomogeneous systems.

Vibrational states on vicinal surfaces of Al, Ag, Cu and Pd

We present the calculation of vibrational modes and lattice relaxation for the (110), (211), (311), (511), (331) and (221) surfaces of Al, Ag, Cu and Pd. The surface phonon frequencies and polarizations are obtained for relaxed and unrelaxed surfaces using embedded atom model potentials. On all surfaces studied step-localized vibrational modes and surface states localized on terrace atoms are found. It is shown that as the terrace width increases so does the number of surface phonons. It is found that interlayer relaxation leads to a shift in the frequencies of the surface states and to a change in the number and localization. In particular, it may cause the appearance or disappearance of step modes. It is shown that the character of relaxation on vicinal surfaces is determined by the number of atoms on a terrace. A comparison of the results with the available experimental data for the Al(221), Cu(211), and Cu(511) surfaces indicates that there is a good agreement with the experimental data.