N-body Potential Research Articles

Formation and structure of Al-Zr metallic glasses studied by Monte Carlo simulations

Based on the recently constructed n-body potential, both molecular dynamics and Monte Carlo simulations revealed that the Al-Zr amorphous alloy or metallic glass can be obtained within the composition range of 24–66 at. % Zr. The revealed composition range could be considered the intrinsic glass-forming range and it quantitatively indicates the glass-forming ability of the Al-Zr system. The underlying physics of the finding is that, within the composition range, the amorphous alloys are energetically favored to form. In addition, it is proposed that the energy difference between a solid solution and the amorphous phase could serve as the driving force of the crystalline to amorphous transition and the driving force should be sufficiently large for amorphization to take place. The minimum driving forces for fcc Al-based and hcp Zr-based Al-Zr solid solutions to amorphize are calculated to be about −0.05 and −0.03 eV/atom, respectively, whereas the maximum driving force is found to be −0.23 eV/atom at the alloy stoichiometry of Al60Zr40. A thermodynamics parameter γ¯, defined as the ratio of the driving force to the formation energy of the solid solution, is further proposed to indicate the glass-forming ability of an Al-Zr alloy. Thermodynamics calculations show that the glass-forming ability of the Al56Zr44 alloy is the largest, implying that the Al56Zr44 amorphous alloy is more ready to form than other alloys in the Al-Zr system. Besides, Voronoi analysis found that there exists a strong correlation between the coordinate number and structure. Amorphization could result in increase of coordinate numbers and about 1.5% volume-expansion. The volume-expansion induced by amorphization can be attributed to two factors, i.e., the total bond number of the Al-Zr amorphous phase is greater than that of the corresponding solid solution, and the averaged bond length of the Al-Zr amorphous phase is longer than that of the corresponding solid solution. For the Al-Zr alloys, especially for the Al-Zr amorphous phase, there exists a negative chemical micro-inhomogeneity in the alloys, suggesting that metallic bonds prefer to be formed between the atoms of dissimilar species. Finally, it is found that there is a weak correspondence between the bond-angle distributions of Al-Zr amorphous alloys and the solid solutions. It is further suggested that the configuration of Al-Zr amorphous alloys embodies some hybrid imprint of bcc, fcc, and hcp structures. More interestingly, the short-range order is also observed in the bond-angle distributions.

Scaling behavior of quantum nanosystems: Emergence of quasi-particles, collective modes, and mixed exchange symmetry states

Examples of quantum nanosystems are graphene nanoribbons, molecular wires, and superconducting nanoparticles. The objective of the multiscale theory presented here is to provide a new perspective on the coupling of processes across scales in space and time underlying the dynamics of these systems. The long range objective for this multiscale approach is to serve as an efficient computational algorithm. Long space-time dynamics is derived using a perturbation expansion in the ratio ɛ of the nearest-neighbor distance to a nanometer-scale characteristic length and a theorem on the equivalence of long time-averages and expectation values. This dynamics is shown to satisfy a coarse-grained wave equation (CGWE) which takes a Schrödinger-like form with modified masses and interactions. The scaling of space and time is determined by the orders of magnitude of various contributions to the N-body potential. If the spatial scale of the coarse-graining is too large, the CGWE would imply an unbounded growth of gradients; if it is too short, the system's size would display uncontrolled growth inappropriate for the bound states of interest, i.e., collective motion or migration within a stable nanoassembly. The balance of these two extremes removes arbitrariness in the choice of the scaling of space-time. Since the long-scale dynamics of each Fermion involves its interaction with many others, we hypothesize that the solutions of the CGWE have mean-field character to good approximation, i.e., can be factorized into single-particle functions. This leads to a coarse-grained mean-field approximation that is distinct in character from traditional Hartree-Fock theory. A variational principle is used to derive equations for the single-particle functions. This theme is developed and used to derive an equation for low-lying disturbances from the ground state corresponding to long wavelength density disturbances or long-scale migration. An algorithm for the efficient simulation of quantum nanosystems is suggested.

Glass-forming ability and atomic-level structure of the ternary Ag–Ni–Zr metallic glasses studied by molecular dynamics simulations

Based on the recently proposed long-range empirical potential formulism, an n-body potential is constructed for the Ag–Ni–Zr ternary metal system and verified to be realistic by reproducing some important properties of the pure metals as well as of some equilibrium compounds of the system. Applied the constructed Ag–Ni–Zr potential, molecular dynamics simulations and Voronoi tessellations are then carried out to study the effect of alloying composition on glass-forming ability and atomic-level structure of the ternary Ag–Ni–Zr metallic glasses. For the Ag50−x/2 NixZr50−x/2 alloys, with increasing Ni concentration, distortion of the crystalline structure becomes significant, implying a disordering process going on, and at the same time, the number of {0, 0, 12, 0} icosahedrons increases remarkably and the {0, 0, 12, 0} icosahedrons are almost Ni-centered. When the Ni concentration is increased up to 20 atom %, the ternary Ag–Ni–Zr solid solution collapses and turns into a disordered state, suggesting that increasing the Ni concentration could enhance the glass-forming ability of the system. For the Ag30Ni40Zr30 ternary metallic glass, it is found that most of the polyhedrons with coordinate number (CN < 13) are Ni-centered, whereas most of polyhedrons with CN > 14 are either Ag or Zr centered.

Metallic glass-forming composition range of the Cu–Zr–Ti ternary system determined by molecular dynamics simulations with many-body potentials

Abstract

Thermodynamic calculation and interatomic potential to predict the favored composition region for the Cu–Zr–Al metallic glass formation

For the Cu-Zr-Al system, the glass forming compositions were firstly calculated based on the extended Miedema's model, suggesting that the amorphous phase could be thermodynamically favored over a large composition region. An n-body potential was then constructed under the smoothed and long-range second-moment-approximation of tight-binding formulism. Applying the constructed Cu-Zr-Al potential, molecular dynamics simulations were conducted using solid solution models to compare relative stability of crystalline solid solution versus its disordered counterpart. Simulations reveal that the physical origin of metallic glass formation is crystalline lattice collapsing while solute concentration exceeding the critical value, thus predicting a hexagonal composition region, within which the Cu-Zr-Al ternary metallic glass formation is energetically favored. The molecular dynamics simulations predicted composition region is defined as the quantitative glass-forming-ability or glass-forming-region of the Cu-Zr-Al system.

Local structure of the Zr–Al metallic glasses studied by proposed n-body potential through molecular dynamics simulation

An n-body potential is first constructed for the Zr–Al system and proven to be realistic by reproducing a number of important properties of the system. Applying the constructed potential, molecular dynamics simulations, chemical short-range order (CSRO) calculation, and Honeycutt and Anderson (HA) pair analysis are carried out to study the Zr–Al metallic glasses. It is found that for the binary Zr–Al system, metallic glasses are energetically favored to be formed within composition range of 35–75 at.% Al. The calculation shows that the CSRO parameter is negative and could be up to −0.17, remarkably indicating that there exists a chemical short-range order in the Zr–Al metallic glasses. The HA pair analysis also reveals that there are diverse short-range packing units in the Zr–Al metallic glasses, in which icosahedra and icosahedra/face-centered cubic (fcc)-defect structures are predominant.

Glass Forming Region of Cu−Ti−Hf Ternary Metal System Derived from the n-Body Potential through Molecular Dynamics Simulation

An n-body potential is constructed for the Cu-Ti-Hf ternary metal system under a recently proposed formalism named long-range empirical potential. Applying the proven relevant Cu-Ti-Hf potential, molecular dynamics simulations are carried out using solid solution model to compare the relative stability of the crystalline solid solution versus its disordered counterpart as a function of solute concentration. The simulation results not only reveal that the physical origin of the crystal-to-amorphous transition is the collapse of the crystalline lattice, while the solute atoms exceed the critical value, but also predict a region in the composition triangle energetically favored for the Cu-Ti-Hf ternary metallic glass formation. Interestingly, the prediction directly from the n-body potential is supported by the experimental observations and is in accordance with the so-called structural difference rule.

Analytic calculation of formation enthalpies directly from interatomic potentials for binary and ternary refractory metal systems

An analytic method is proposed to calculate the formation enthalpy directly from empirical n-body potential and applied to the binary and ternary systems consisting of the refractory metals Mo, Nb, Ta and W. It turns out that the calculated enthalpies are in overall agreement with experimental observations and some other theoretical calculations. Interestingly, it shows that the formation enthalpies of the ternary systems are significantly affected by those of the constituent binary systems.

Model calculations of edge dislocation defects and vacancies in α-Iron lattice

Two models of defects in perfect α-iron lattice were discussed. In the perfect bcc iron lattice 42×42×42 ao (ao = 2,87 Å) an edge dislocation was created, moving the second half of the bulk on one ao distance. This action generates a little volume in the middle of the bulk witch increases of the positron lifetime (PLT) calculated using the superimposed-atom method of Puska and Nieminen [1]. The result of 118 ps PLT in simple edge dislocation's model is in a good concurrence with earlier publications and experimental data [2]. Through the dislocation line one, two and three vacancies were localized. These models give the results for PLT of 146, 157 and 167 ps respectively. The computer simulations were performed using Finnis–Sinclair (FS) N-body potential.

Twenty five years of Finnis–Sinclair potentials

In 1984, the paper, entitled A simple empirical N-body potential for transition metals by M.W. Finnis and J.E. Sinclair appeared in Philosophical Magazine A 1. Twenty five years later, with more th...

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.

Long-range empirical potential model: extension to hexagonal close-packed metals

An n-body potential is developed and satisfactorily applied to hcp metals, Co, Hf, Mg, Re, Ti, and Zr,in the form of long-range empirical potential. The potential can well reproduce the lattice constants,c/a ratios, cohesive energies, and the bulk modulus for their stable structures (hcp) andmetastable structures (bcc or fcc). Meanwhile, the potential can correctly predict the orderof structural stability and distinguish the energy differences between their stable hcpstructure and other structures. The energies and forces derived by the potential cansmoothly go to zero at cutoff radius, thus completely avoiding the unphysicalbehaviors in the simulations. The developed potential is applied to study thevacancy, surface fault, stacking fault and self-interstitial atom in the hcp metals. Thecalculated formation energies of vacancy and divacancy and activation energies ofself-diffusion by vacancies are in good agreement with the values in experiments and inother works. The calculated surface energies and stacking fault energies are alsoconsistent with the experimental data and those obtained in other theoreticalworks. The calculated formation energies generally agree with the results in otherworks, although the stable configurations of self-interstitial atoms predicted in thiswork somewhat contrast with those predicted by other methods. The proposedpotential is shown to be relevant for describing the interaction of bcc, fcc andhcp metal systems, bringing great convenience for researchers in constructingpotentials for metal systems constituted by any combination of bcc, fcc and hcpmetals.

Molecular Dynamics Study of Stability of Solid Solutions and Amorphous Phase in the Cu–Al System

The relative stability of fcc and bcc solid solutions and amorphous phase with different compositions in the Cu–Al system is studied by molecular dynamics simulations with n-body potentials. For Cu1−xAlx alloys, the calculations show that the fcc solid solution has the lowest energies in the composition region with x < 0.32 or x > 0.72, while the bee solid solution has the lowest energies in the central composition range, in agreement with the ball-milling experiments that a single bcc solid solution with 0.30 < x < 0.70 is obtained. The evolution of structures in solid solutions and amorphous phase is studied by the coordination number (CN) and bond-length analysis so as to unveil the underlying physics. It is found that the energy sequence among three phases is determined by the competition in energy change originating from the bond length and CNs (or the number of bonds).

Proposed Long-Range Empirical Potential To Study the Metallic Glasses in the Ni−Nb−Ta System

An n-body potential is constructed for the Ni-Nb-Ta ternary metal system in the newly proposed form of long-range empirical potential. The constructed Ni-Nb-Ta potential can well reproduce the lattice constants, cohesive energies, and elastic modulus of the metals and some compounds as well as the equations of state of the system. Applying the constructed Ni-Nb-Ta potential, molecular dynamics simulations and Voronoi tessellations are carried out to study the issues related to the Ni-Nb-Ta metallic glasses. It is found that increasing the Ni content can obviously improve the glass-forming ability of the binary Nb-Ta system, which features a isomorphous phase diagram unfavoring for forming glass, indicating that the Ni solute plays a decisive role in forming the Nb-based or Ta-based Ni-Nb-Ta metallic glasses. Concerning the atomic structure, the Voronoi cell volume and coordination number (CN) of Ta are generally larger than those of Ni in the binary Ni-Ta metallic glasses. With increasing the Ni concentration, the fraction of icosidihedron (CN=13) increases, while the fractions of icosihexahedron (CN=15) and icosioctahedron (CN=16) decrease. Meanwhile, with increasing the Ni concentration, the dominating coordination numbers of Ta atoms increase. Interestingly, similar feature in the atomic structure with variation of Ni concentration is also observed in the Ni-Nb metallic glasses. For the ternary Ni-Nb-Ta alloys, it is observed from the CN distributions that the structure of the metallic glasses is mostly affected by the Ni concentration.

Molecular dynamics study of Pb-substituted Cu(1 0 0) surface layers

Using molecular dynamics (MD) and phenomenological n-body potentials from the literature, we have studied the structure of the uppermost layers of low-index surfaces in copper after partial substitution of copper by lead atoms at randomly selected sites. We found that lead atoms substituting copper strongly perturb the positions of nearest and of next-nearest neighbors thus triggering the setup of a disordered, nanometer-thick amorphous-like surface layer. Equilibrium atomic density profiles, computed along the [1 0 0] crystallographic direction, show that amorphous overlayers are largely metastable whereas the system displays a structured compositional profile of lead segregating at the interfaces. Similarities between our results and experimental findings are briefly discussed.

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.

Development of n-body potentials for hcp–bcc and fcc–bcc binary transition metal systems

Within the framework of the second-moment approximation of the tight-binding theory, n-body potentials are proposed for hcp, fcc and bcc transition metals and their alloys. Both the energies and their derivatives calculated from the proposed potentials go smoothly to zero at cutoff radii, thus avoiding the unphysical behaviors that may emerge in simulations. With the assistances of ab initio calculations, the proposed potentials are then applied to Zr, Hf, Cu, V, Nb, Ta and their binary alloys. It turns out that the n-body potentials can well predict the energy sequence of stable and metastable structures of these metals. The vacancy formation energies, surface energies and melting points derived from the potentials also match well with experimental results. Based on the constructed potentials, molecular dynamics simulations reveal that Cu–Nb and Zr–Nb metallic glasses could be formed within the composition range of about 15–72 and 8–80at.% Nb, respectively, matching well with experimental observations. Voronoi analyses reveal that the dominating atomic packings in Cu–Nb metallic glasses are the icositetrahedron (CN=14), icosihexahedron (CN=15) and icosidihedron (CN=13) with fractions of 33%, 26% and 21%, respectively.

Computer modeling of diffusion in Ni-richNi3Al and compositiondependence of diffusion in γ′ Ni3Al

Atomistic simulations of diffusion in off-stoichiometric Ni-richNi3Al (Ni77Al23) at temperatures ranging from 1300 to 1550 K and comprehensiveanalysis of the composition dependence of Ni and Al diffusion inγ′ Ni3Al of threecompositions, 73, 75 and 77 at.% Ni, are presented. The interatomic forces are described by Finnis–Sinclairtype N-body potentials. The simulations reveal that Ni diffusion is dominated by Ni vacancy mechanisms;Al diffusion is via both the intrasublattice and antistructure bridge (ASB) mechanism inNi77Al23 at the temperatures investigated. The presence of an extra 2% of antisitedefects enhances diffusion of both Ni and Al at off-stoichiometric Ni-enrichedNi3Al via the vacancy–antisite interaction. The single vacancy diffusivity of Ni and Al inNi3Al of three compositions, 73, 75 and 77 at.% Ni, at the above temperatures are corrected withthermal equilibrium concentration of point defects. The corrected Ni and Al diffusion dataare in good agreement with available experimental data. The Ni diffusivity decreases withthe Ni concentration, while Al diffusivity has a minimum at the stoichiometric compositionin the simulated temperature range.

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.

Distinct atomic structures of the Ni-Nb metallic glasses formed by ion beam mixing

Four Ni-Nb metallic glasses are obtained by ion beam mixing and their compositions are measured to be Ni77Nb23, Ni55Nb45, Ni31Nb69, and Ni15Nb85, respectively, suggesting that a composition range of 23–85 at. % of Nb is favored for metallic glass formation in the Ni-Nb system. Interestingly, diffraction analyses show that the structure of the Nb-based Ni31Nb69 metallic glass is distinctly different from the structure of the Nb-based Ni15Nb85 metallic glass, as the respective amorphous halos are located at 2θ≈38 and 39 deg. To explore an atomic scale description of the Ni-Nb metallic glasses, an n-body Ni-Nb potential is first constructed with an aid of the ab initio calculations and then applied to perform the molecular dynamics simulation. Simulation results determine not only the intrinsic glass forming range of the Ni-Nb system to be within 20–85 at. % of Nb, but also the exact atomic positions in the Ni-Nb metallic glasses. Through a statistical analysis of the determined atomic positions, a new dominant local packing unit is found in the Ni15Nb85 metallic glass, i.e., an icositetrahedron with a coordination number to be around 14, while in Ni31Nb69 metallic glasses, the dominant local packing unit is an icosahedron with a coordination number to be around 12, which has been reported for the other metallic glasses. In fact, with increasing the irradiation dose, the Ni31Nb69 metallic glasses are formed through an intermediate state of face-centered-cubic-solid solution, whereas the Ni15Nb85 metallic glass is through an intermediate state of body-centered-cubic-solid solution, suggesting that the structures of the constituent metals play an important role in governing the structural characteristics of the resultant metallic glasses.