N-body Interatomic Potentials Research Articles

Atomic-Scale Surface Segregation in Copper-Gold Nanoparticles.

We combine electron microscopy measurements of the surface compositions in Cu-Au nanoparticles and atomistic simulations to investigate the effect of gold segregation. While this mechanism has been extensively investigated within Cu-Au in the bulk state, it was never studied at the atomic level in nanoparticles. By using energy dispersive x-ray analysis across the (100) and (111) facets of nanoparticles, we provide evidence of gold segregation in Cu_{3}Au and CuAu_{3} nanoparticles in the 10nm size range grown by epitaxy on a salt surface with high control of the nanoparticles morphology. To get atomic-scale insights into the segregation properties in Cu-Au nanoparticles on the whole composition range, we perform MonteCarlo calculations employing N-body interatomic potentials highlighting a complete segregation of Au in the (100) and (111) facets for gold nominal composition above 70% and 60%, respectively. Furthermore, we show that there is no size effect on the segregation behavior since we evidence the same oscillating concentration profile from the surface to the nanoparticle's core as in the bulk. These results shed new light on the interpretation of the enhanced reactivity, selectivity, and stability of Cu-Au nanoparticles in various catalytic reactions.

Prediction of the diffusion characteristics of the V-Cr system by molecular dynamics based on N-body interatomic potentials

Molecular dynamics (MD) is a promising method for predicting the diffusion characteristics of materials. However, the reliability of MD simulation results is largely determined by the technique of their interpretation and the interatomic potentials used. In this work, interatomic potentials are constructed for calculating the diffusion characteristics in alloys of the V-Cr system. We employed an approach that accurately takes into account the angular dependence of the potential energy of the atomic system. For monoatomic systems V and Cr, we used interatomic potentials that predict thermal expansion and melting point in good agreement with experimental values, along with good reproduction of BCC lattice parameters, sublimation energies, equations of state, elastic constants, and several other properties. The cross potential functions of the V-Cr binary system are optimized with using DFT calculations and experimental formation enthalpy values. The resulting V-Cr potential predicts the dependence of the BCC lattice parameter, the elastic constants of V-Cr solid solutions on the concentration of components and the thermal expansion of the stoichiometric V50Cr50 alloy in good agreement with the known experimental data. The constructed potentials were utilized to calculate the diffusion coefficients in V, Cr, V90Cr10 and V95Cr05 by the molecular dynamics method. We identified that the diffusion coefficient of V exceeds the diffusion coefficient of Cr in solid solutions of Cr in V. The calculated diffusion coefficients are consistent with the known results of diffusion experiments in V, Cr and Cr diffusion in V within the error of measurements. Inclusion of the temperature dependencies of the vacancy formation enthalpy and vacancy formation entropy into calculations of the diffusion coefficient leads to its deviation from the Arrhenius equation and improves the agreement with the experimental data.The good agreement between the independent results of the MD simulation and diffusion experiments confirms both the reliability of the experiment and the MD simulation.

Development of n-body interatomic potentials for calculating the thermodynamic characteristics of V-Nb-Mo-W alloys

New interatomic potentials for Mo and binary systems V-Nb, V-Mo, Nb-Mo, Nb-W and Mo-W are constructed taking into account the angular dependencies of interatomic interactions. Together with the potentials constructed earlier in the same approach, a complete set of potentials for modeling alloys of the V-Nb-Mo-W system at any component concentrations is obtained. A tendency to narrow the range of values of the calculated enthalpy of formation and the volume of formation in equiatomic alloys of the V-Nb-Mo-W system with an increase in the number of components was found. Deviations from the Vegard’s rule in the volume of formation of these alloys are shifted to the negative range of values when the number of components is more than two.

Direct Measurement of the Surface Energy of Bimetallic Nanoparticles: Evidence of Vegard's Rulelike Dependence.

We use insitu transmission electron microscopy to monitor in real time the evaporation of gold, copper, and bimetallic copper-gold nanoparticles at high temperature. Besides, we extend the Kelvin equation to two-component systems to predict the evaporation rates of spherical liquid mono- and bimetallic nanoparticles. By linking this macroscopic model to experimental TEM data, we determine the surface energies of pure gold, pure copper, Cu_{50}Au_{50}, and Cu_{25}Au_{75} nanoparticles in the liquid state. Our model suggests that the surface energy varies linearly with the composition in the liquid Cu-Au nanoalloy; i.e., it follows a Vegard's rulelike dependence. To get atomic-scale insights into the thermodynamic properties of Cu-Au alloys on the whole composition range, we perform MonteCarlo simulations employing N-body interatomic potentials. These simulations at a microscopic level confirm the Vegard's rulelike behavior of the surface energy obtained from experiments combined with macroscopic modeling.

Primary radiation damage of Zr-0.5%Nb binary alloy: atomistic simulation by molecular dynamics method

Ab initio calculations predict high positive binding energy (∼1 eV) between niobium atoms and self-interstitial configurations in hcp zirconium. It allows the expectation of increased niobium fraction in self-interstitials formed under neutron irradiation in atomic displacement cascades. In this paper, we report the results of molecular dynamics simulation of atomic displacement cascades in Zr-0.5%Nb binary alloy and pure Zr at the temperature of 300 K. Two sets of n-body interatomic potentials have been used for the Zr-Nb system. We consider a cascade energy range of 2–20 keV. Calculations show close estimations of the average number of produced Frenkel pairs in the alloy and pure Zr. A high fraction of Nb is observed in the self-interstitial configurations. Nb is mainly detected in single self-interstitial configurations, where its fraction reaches tens of percent, i.e. more than its tenfold concentration in the matrix. The basic mechanism of this phenomenon is the trapping of mobile self-interstitial configurations by niobium. The diffusion of pure zirconium and mixed zirconium-niobium self-interstitial configurations in the zirconium matrix at 300 K has been simulated. We observe a strong dependence of the estimated diffusion coefficients and fractions of Nb in self-interstitials produced in displacement cascades on the potential.

Surface segregation in AuPd alloys: Ab initio analysis of the driving forces

In order to determine the energetic driving forces for surface segregation in AuPd alloys, we use a combined approach coupling ab initio calculations and an analysis via an effective Ising model. Previously, this approach has been used successfully in the framework of N-body interatomic potentials to study the surface segregation in both semi-infinite alloys and nanoparticles, allowing one to determine the relative contributions of the different elementary driving forces. Here, we go beyond the use of N-body interatomic potentials by using ab initio calculations to evaluate the segregation enthalpy and the effective pair interactions, the contribution due to the size difference between the constituants being still obtained by N-body interatomic potentials. We show that the decomposition of the segregation enthalpy into its different elementary contributions is still valid at this level of description. This allows us to analyze the segregation driving forces in the two infinite dilute limits of the Au–Pd system, for both (100) and (111) surfaces. Finally, between the two infinite dilute limits, we find that our results are consistent with existing experimental data.

MD simulation of atomic displacement cascades in Fe–10 at.%Cr binary alloy

Molecular dynamics simulation of atomic displacement cascades up to 20 keV has been performed in Fe–10 at.%Cr binary alloy at a temperature of 600 K. The N-body interatomic potentials of Finnis–Sinclair type were used. According to the obtained results the dependence of “surviving” defects amount is well approximated by power function that coincides with other researchers’ results. Obtained cascade efficiency for damage energy in the range from 10 to 20 keV is ≈0.2 NRT that is slightly higher than for pure α-Fe. In post-cascade area Cr fraction in interstitials is in range 2–5% that is essentially lower than Cr content in the base alloy. The results on size and amount of vacancy and interstitial clusters generated in displacement cascades are obtained. For energies of 2 keV and higher the defect cluster average size increases and it is well approximated by a linear dependence on cascade energy both for interstitials and vacancies.

Experimental and theoretical study of the morphology of commensurate and incommensurate graphene layers on Ni single-crystal surfaces

The paper reports on a scanning tunneling microscopy (STM) study and computer simulation with an N-body interatomic interaction potential of a graphite monolayer (i.e., graphene) on the Ni(111), (110), (755), and (771) single-crystal surfaces. Unlike the case of graphene on Ni(111), which forms a solid single-crystal coating with $(1\ifmmode\times\else\texttimes\fi{}1)$ structure, graphene on the Ni(110) surface forms a complex crystal structure distorted substantially by interaction with the substrate. Calculations of the graphene/Ni(110) system have revealed that the strong chemical interaction of carbon with nickel gives rise to a noticeable curving of the graphene layer on a scale of a few angstroms. The model thus derived has permitted proper interpretation of the experimental data obtained by STM, as well as prediction of the main result of studies of graphene formed on faceted surfaces, which have revealed the ability of graphene to coat geometrically nonuniform surfaces in the form of a curved continuous film.

Effect of a size mismatch on bulk and surface alloy interactions: The illustrative example of the Cu–Ag system

Alloy effective pair interactions (EPIs) are crucial quantities to characterize the bulk and surface thermodynamical properties of alloys. In this paper we focus on the influence of a size mismatch between the components of an alloy, by considering the illustrative example of the Cu–Ag system. Using N-body interatomic potentials derived from the second-moment approximation of the tight-binding scheme, we compute the EPIs in the bulk and in the (001) surface for the two infinitely dilute limits. Both the bulk and the surface EPIs obey a two-domain rule. The first two EPIs hold a specific behaviour that depends linearly on the value of the mixed interaction, while the others originate in elasticity and hold a behaviour that can be made general by an appropriate normalization. We observe that a dilatation as well as a contraction of the lattice parameter can reverse the sign of the first two bulk EPIs. Moreover, the observed sign reversal between the bulk and the surface first EPI is due to an additive factor (and not a multiplicative one) induced by the size mismatch. The elasticity-related surface EPIs hold a very anisotropic behaviour, as significant values are restricted to the close-packed directions of the (001) surface. These values decay exponentially with the distance along these directions, in a direct relation with the exponential decay of the surface relaxations. These EPIs have also been computed for the non-equivalent sites of the c(10×2) superstructure of an Ag-pure plane on a Cu(001) substrate. They reveal a very large heterogeneity between the sites which accompanies the one due to the permutation enthalpy, the second energetic quantity involved in the determination of the 2D phase diagram.

Site segregation in size-mismatched nanoalloys: Application to Cu–Ag

In order to determine the energetic driving forces for surface segregation in bimetallic clusters, we use a combined approach coupling numerical simulations within an N-body interatomic potential and a lattice-gas model. This approach, which has been used successfully to study both the superficial segregation in semi-infinite alloys and the intergranular segregation, allows us to determine the relative contributions of the three elementary driving forces for the different sites of the cluster surface (vertices, edges and facets) in both dilute limits for the Cu–Ag system. We show that the segregation hierarchy based on broken-bond arguments (preferential segregation to the vertex sites, less to edge sites, and least to facet sites) is not at all universal. In particular, unusual hierarchies are predicted when the sizes of the constituents are strongly different. Furthermore, we compare the segregation driving forces for cubo-octahedral and icosahedral clusters. They are similar for the vertex sites and edge sites, whereas they differ significantly for the sites of the triangular facets. The segregation of the species with the largest atomic radius (Ag) is indeed largely enhanced in the icosahedral structure due to dilations of the orthoradial distances.

Drastic changes for segregation and wetting between flat and vicinal surfaces of binary alloys

Segregation for the (3 1 0) surface in Cu(Ag) solid solution is studied by Monte Carlo simulations in conjunction with an N-body interatomic potential. Three stages occur according to the bulk concentration of Ag. At low concentration, only the surface plane is enriched by Ag atoms and no structural change is observed. In a second stage, three Ag planes form at the surface. These planes are strongly disordered due to the large size-mismatch between Ag and Cu atoms. Finally, a third stage occurs, in which a thick Ag film grows at the surface. This wetting behaviour is accompanied by a structural change, the Ag film becoming well ordered and growing along the 〈1 1 2〉 direction. Comparison is drawn up with segregation for the flat (0 0 1) surface on one hand and for the Σ=5(3 1 0)〈0 0 1〉 tilt grain boundary on the other hand.

Unexpected profiles of surface segregation vibrational entropies

Profiles of vibrational entropy of segregation are calculated as a function of distance from (0 0 1) and (3 1 0) free surfaces for the infinitely dilute Cu(Ag) system. The local vibrational densities of states are evaluated using the recursion method with the force-constant matrix generated from a N-body interatomic potential based on the second moment approximation of the tight-binding scheme. We show that the maximum of the segregation vibrational entropy is not located in the surface plane but in the first underlayer that recovers the bulk coordination number of nearest neighbours. Furthermore, we show that surface relaxations are essential to obtain this unexpected vibrational entropy profile. For the (3 1 0) surface, the maximum value of the segregation vibrational entropy is located on the third underlayer and is larger than for the (0 0 1) orientation. Moreover, we estimate the change in the segregation entropy due to the variation of the mean atomic positions with temperature.

Multilayer properties of superficial and intergranular segregation isotherms: A mean-field approach

Segregation is studied at the (001) and (310) surfaces, as well as for the $\ensuremath{\Sigma}=5$ (310) [001] tilt grain boundary (GB), in the Cu(Ag) system. Based on an effective Ising model with energetic parameters obtained from an N-body interatomic potential, we compare the segregation driving forces for the three interfaces in this system, which presents a strong tendency toward phase separation in the bulk. Within mean-field theory, we derive segregation isotherms, and we find an essential difference between the flat (001) surface and the open (310) surface. For the first one, the isotherm is characterized by a succession of monolayer phase transitions, whereas the isotherm of the (310) surface exhibits a multilayer phase transition, all these transitions occurring well within the domain of the Cu(Ag) solid solution. The segregation isotherm for the (310) [001] tilt grain boundary is similar to the (310) surface one, with the presence of a multilayer phase transition too. The behavior of the GB plane itself is rather intricate, a multireentrant phase transition being predicted. A ground-state analysis and a simple bilayer model allows us to detail the conditions for the existence of an interfacial multilayer phase transition, as a function of both the energetic and crystallographic parameters and the temperature.

Phase transition induced by superficial segregation: the respective role of the size mismatch and of the chemistry

Segregation at the (0 0 1) surface in Cu(Ag) alloys has been studied using Monte Carlo (MC) simulations in conjunction with a semi-empirical N-body potential. The simulations show that the surface undergoes a first order phase transition at 600 K. This phase transition corresponds to a discontinuous increase of the surface concentration of Ag from 0.3 to 0.9 for a critical value of the bulk concentration well within the domain of existence of the bulk Cu(Ag) solid solution. This chemical transition is coupled with a change of the surface structure. The Ag-rich phase presents a pseudo-hexagonal c(10×2) structure, in complete agreement with experiments. This structural transition requires that some of the surface atoms are squeezed out into adatom positions. We present also a matching of the MC results on a lattice gas model consistent with the N-body interatomic potential used in the simulations. This matching allows us to determine the segregation driving forces and to detail their dependence on the surface structure. Surprisingly, the presence of the superstructure does not change the main driving forces for the surface plane but has a large influence for the first underlayer. In addition, the matching allows a discussion on the respective role of the structure and of the chemistry for the occurrence of the surface phase transition.

How to compare superficial and intergranular segregation? A new analysis within the mixed SMA–TBIM approach

The driving forces for intergranular segregation are much less known than the ones for superficial segregation. In order to investigate the relation between grain-boundary and surface segregation, we have calculated the segregation energy for one impurity in both dilute limits for the Cu–Ag system. This is performed for the (001) surface on one hand and for the symmetrical tilt grain boundary Σ=5 (210) [001] on the other. These numerical results, obtained using N-body interatomic potentials derived from the second moment approximation (SMA) of the tight-binding scheme, are then discussed within an analytic model, the tight-binding Ising model (TBIM). This allows us to determine the relative role of the different driving forces in superficial and intergranular segregation. In particular competition or synergy between site and size effects strongly differ between surface and grain-boundary segregation. This study illustrates the efficiency of the mixed SMA–TBIM approach to predict and to analyse interfacial segregation.

Influence of Dislocations on Positron Lifetime in Iron

To clarify `medium' lifetimes of ∼150 ps in deformed iron, we calculate the positron lifetimes at the core of dislocations and related defects in iron. The calculations are based on an empirical N-body interatomic potential by Finnis and Sinclair for the atomic arrangements and the local-density approximation for the positron–electron correlation. We find the positron lifetime for vacancies associated with edge dislocation to be the medium lifetime, while that for vacancies associated with screw dislocation is almost the same as the single-vacancy value. The positron lifetimes for pure dislocations and for jogged dislocations are close to the perfect-lattice value.

Development of an N-body interatomic potential for hcp and bcc zirconium.

An interatomic potential based on the second-moment approximation of the tight-binding scheme is developed for zirconium, by fitting its four adjustable parameters to the cohesive energy, atomic volume, and elastic constants of the hcp phase. In this work we attempt to model realistically two different crystallographic phases of a solid with the same potential. The reliability of our potential is tested in both the hcp and the bcc phases with regard to defect properties, thermal expansion, phonon properties, and mean-square displacements. For this purpose, we perform quenched molecular-dynamics relaxations, quasiharmonic lattice-dynamics calculations, and molecular-dynamics simulations. The low vacancy-formation and migration energies found in the bcc phase are consistent with the fast diffusivity experimentally observed. Unlike some other N-body potentials recently proposed to model bcc transition metals, our potential is not affected by the flaw of unphysical or even negative thermal expansion. We obtain thermal expansions that agree well with experiments in both phases, although they turned out to be slightly too large. The phonon-dispersion curves and, in particular, the anomalies in the bcc phase are well reproduced. We emphasize the stabilization with temperature of the T1 N-point phonon of the bcc phase, which is related to the bcc- to hcp-phase transition. We obtain a temperature dependence of this mode much weaker than in the experimental case. This influences the temperature behavior of the vibrational properties: In particular the mean-square displacement is markedly higher than the one extracted from experiments in the bcc phase at high temperatures. On the other hand, mean-square displacements in the hcp phase are in excellent agreement with experiment. The results are quite satisfactory in view of the small number of fitting parameters and the difficulties commonly encountered in matching the properties of bcc metals.

Diffusion Mechanisms in Bcc-Zr:A Molecular Dynamics Approach

ABSTRACTBasing our calculations on a realistic N-body interatomic potential for Zr, we study the vacancy migration mechanism and determine the related diffusion coefficient in the bcc phase. The form of the potential energy along the nearest-neighborjump migration path is single-peaked. The vacancy jump rate determined by molecular dynamics simulations has a perfectly Arrhenian behavior and its activation energy is very close to the static value of the vacancy migration energy, both being very low (≈ 0.3 eV) . The diffusion coefficient is in very satisfactory agreement with experiments.

Defect clusters in vanadium modelled using n-body potentials

Abstract The geometry and energy of small clusters of interstitials and vacancies have been studied by computer simulation using an n-body interatomic potential for vanadium. Clusters of up to seven interstitials have been considered for the various configurations which may exist in the bcc structure, particularly in relation to the Eyre-Bullough mechanism of dislocation loop formation. For up to four defects, faulted platelets are most stable, but beyond this size the 1 2 111) form is favoured. Platelets of $ 10 vacancies do not readily collapse, but for larger sizes well-defined dislocation loops are observed with unexpected core geometries.