Semi-empirical Interatomic Potentials Research Articles

Primary radiation damage in tungsten-based high-entropy alloy: Interatomic potential and collision cascade simulations

Tungsten (W)-based high-entropy alloys (HEAs) have shown promising properties as nuclear fusion materials. Characterizing the primary damage is a critical step in describing and revealing the irradiation-induced damage and radiation resistance mechanism. However, there are a limited number of studies on collision cascades and primary radiation damage in W-based HEAs, owing to the large amount of calculations involved and a lack of appropriate interatomic interaction potentials. In this work, we developed a semi-empirical interatomic potential for W–Ta–Cr–V. By using the developed potential, molecular dynamics simulations of collision cascades in W-based HEAs were performed to assess the primary damage due to irradiation. Based on experimental samples, we reported defect production in W38Ta36Cr15V11 and compared it to pure W for primary knock-on atom with energies ranging from 1 keV to 100 keV. Our findings showed that the number of FPs at the thermal spike and the number of surviving FPs at the end of the cascade in W38Ta36Cr15V11 are more than those in pure W, mainly due to the lower threshold displacement energy, melting temperature, and formation energy of point defects. Collision cascades in the W38Ta36Cr15V11 are less likely to result in the formation of dislocation loops compared to pure W. After collision cascade, in W38Ta36Cr15V11, the concentrations of Cr and V atoms in defects is significantly higher than their corresponding concentrations in the system, showing an aggregation tendency. The current collision cascade results provide insights into the primary damage of W-based HEA system under irradiation and should provide reliable guidance for describing the primary damage source terms needed in the kinetic models used to simulate radiation-induced microstructural evolution.

Classical and machine learning interatomic potentials for BCC vanadium

BCC transition metals (TMs) exhibit complex temperature and strain-rate dependent plastic deformation behavior controlled by individual crystal lattice defects. Classical empirical and semiempirical interatomic potentials have limited capability in modeling defect properties such as the screw dislocation core structures and Peierls barriers in the BCC structure. Machine learning (ML) potentials, trained on DFT-based datasets, have shown some successes in reproducing dislocation core properties. However, in group VB TMs, the most widely used DFT functionals produce erroneous shear moduli ${C}_{44}$ which are undesirably transferred to machine-learning interatomic potentials, leaving current ML approaches unsuitable for this important class of metals and alloys. Here, we develop two interatomic potentials for BCC vanadium (V) based on (i) an extension of the partial electron density and screening parameter in the classical semiempirical modified embedded-atom method (XMEAM-V) and (ii) a recent hybrid descriptor in the ML Deep Potential framework (DP-HYB-V). We describe distinct features in these two disparate approaches, including their dataset generation, training procedure, weakness and strength in modeling lattice and defect properties in BCC V. Both XMEAM-V and DP-HYB-V reproduce a broad range of defect properties (vacancy, self-interstitials, surface, dislocation) relevant to plastic deformation and fracture. In particular, XMEAM-V reproduces nearly all mechanical and thermodynamic properties at DFT accuracies and with ${C}_{44}$ near the experimental value. XMEAM-V also naturally exhibits the anomalous slip at 77 K widely observed in group VB and VIB TMs and outperforms all existing, publically available interatomic potentials for V. The XMEAM thus provides a practical path to developing accurate and efficient interatomic potentials for nonmagnetic BCC TMs and possibly multiprincipal element TM alloys.

Machine learning for metallurgy V: A neural-network potential for zirconium

The mechanical performance---including deformation, fracture and radiation damage---of zirconium is determined at the atomic scale. With Zr and its alloys extensively used in the nuclear industry, understanding that atomic scale behavior is crucial. The defects controlling that performance are at size scales far larger than accessible by first principles methods, necessitating the use of semiempirical interatomic potentials. Existing potentials for Zr are not sufficiently quantitative, nor easily extendable to alloys, oxides, or hydrides. To overcome these issues, a neural network machine learning potential (NNP) is developed here within the Behler-Parrinello framework for Zr. With a careful choice of descriptors of the atomic environments and the creation of a first-principles training dataset that includes a wide spectrum of configurations of metallurgical relevance, a very accurate NNP is demonstrated. Specifically, the Zr NNP yields a good description of dislocation structures and their relative energies and fracture behavior, along with bulk, surface, and point-defect properties and structures, and significantly outperforms the best available traditional potentials. Results here will enable large-scale simulations of complex processes and provide the basis for future extensions to alloys, oxides, and hydrides.

Pressure dependence of thermodynamic interaction parameters for binary solid solution phases: An atomistic simulation study

The effect of pressure on the interaction parameters (enthalpy of mixing) of face-centered cubic (FCC) and body-centered cubic (BCC) binary solid solution phases has been investigated using atomistic simulations at 0 K based on semi-empirical interatomic potentials (the second nearest-neighbour modified embedded-atom method: 2NN MEAM). First, it is confirmed that the 2NN MEAM interatomic potentials reproduce the pressure dependence of enthalpy and molar volume of pure elements in excellent agreement with thermodynamic modelling and experimental data. The prediction of pressure dependence is then extended to binary solid solutions. It is shown that the pressure dependence of binary interactions is clearly correlated with the sign of excess volume of corresponding solid solution phases. That is, the enthalpy of mixing shifts toward the positive direction with pressure if the excess volume shows a positive deviation from the linear average of constituent elements, while it shifts toward the negative direction in the opposite case. The results can be interpreted well by the functional form for the pressure dependence of Gibbs free energy of solution phases. An atomistic computational approach to estimate the pressure dependence of the excess volume of solution phases is also proposed.

Theoretical investigation of the 70.5[formula omitted] mixed dislocations in body-centered cubic transition metals

The low-temperature plasticity of body-centered cubic (bcc) metals is governed by 12〈111〉 screw dislocations due to their compact, non-planar core. It has been proposed that 70.5° mixed (M111) dislocations may also exhibit special core structures and comparably large Peierls stresses, but the theoretical and experimental evidence is still incomplete. In this work, we present a detailed comparative study of the M111 dislocation in five bcc transition metals on the basis of atomistic simulations. We employ density functional theory and semi-empirical interatomic potentials to investigate both the core structure and the Peierls barrier of the M111 dislocation. Our calculations demonstrate that reliable prediction of M111 properties presents not only a very stringent test for the reliability of interatomic potentials but is also challenging for first-principles calculations for which careful convergence studies are required. Our study reveals that the Peierls barrier and stress vary significantly for different bcc transition metals. Sizable barriers are found for W and Mo while for Nb, Ta and Fe the barrier is comparably small. Our predictions are consistent with internal friction measurements and provide new insights into the plasticity of bcc metals.

A modified embedded-atom method interatomic potential for bismuth

A semi-empirical interatomic potential for the post-transition metal, bismuth, is developed based on the second nearest-neighbor modified embedded-atom method (MEAM). The potential reproduces a range of physical properties, such as the lattice constant, cohesive energy, elastic constants, vacancy formation energy, surface energy, and the melting point of pure bismuth. The calculations are done for the rhombohedral ground state of Bi. The results show good agreement with density functional theory and experimental data. The developed MEAM potential for bismuth is useful for material and mechanical behavior studies of the pure material at different conditions and sets the stage for the development of interatomic potentials for bismuth alloys or other bismuth compounds.

Diffusion-mediated processes in Pt/Cu(001) surface alloy

In this paper we present the investigation of the diffusion-mediated processes in a Pt/Cu(001) surface alloy. We use the interatomic semiempirical TB-SMA interatomic potentials and the self-learning kinetic Monte Carlo method to investigate the following processes: order-disorder phase transition in the Pt/Cu(001) surface alloy, dissolution of small Pt clusters, and electromigration of small vacancy clusters in the topmost layer of the Pt/Cu(001) surface alloy. We have fitted the universal parameters of the interatomic TB-SMA potentials for the Pt–Cu system. The potentials reproduce bulk properties of copper and platinum as well as properties of the Pt/Cu(001) and Pt/Cu(111) surface alloys.

Neural network aided development of a semi-empirical interatomic potential for titanium

Artificial neural networks, utilizing machine learning techniques to uncover subtle and complex patterns in big data problems, are able to condense large amounts of computationally expensive density functional theory and ab initio results into classical force field potentials. However, in order to produce a computationally efficient network, with minimal network architecture, a structural fingerprint whose components are highly correlated to the per atom energy is necessary. In this paper, we demonstrate the effectiveness a structural fingerprint motivated by the highly successful MEAM formalism by creating an artificial neural network containing a single hidden layer of 20 nodes which provides a semi-empirical force field potential for elemental titanium. This potential is suitable for dynamic calculations of α-, β-, and ω-titanium at a variety of temperatures. This potential is able to achieve a number of results in agreement with DFT calculations which surpass classical potential formalisms with comparable computational performance.

A Novel Identification of the Extended-Rydberg Potential Energy Function

The Extended-Rydberg potential has wide applicability in determining the properties of diatomic molecules. In this paper, we estimate the Extended-Rydberg potential using a novel approach based on the objective least square functions of differential, integral-differential and integral approaches for the estimation of the potential. Interesting research results are obtained as the numerical differentiation (differential approach), integration (integral-differential and integral approach) are in agreement with the experimental data sets of gold atoms. It is a well-known fact that the more parameters a semiempirical interatomic potential has, the more flexible and accurate it is for experimental curve fitting but it takes longer computational time. We establish via CPU time the efficiency and novelty of our approach for the five-parameter Extended-Rydberg potential.

Static and dynamical isomerization of Cu38 cluster

The lowest-energy geometrical and electronic structures of Cu38 cluster are investigated by density-functional calculations combined with a genetic algorithm based on a many body semi-empirical interatomic potential, the traditional FCC-truncated Octahedron (OH) and an incomplete-Mackay icosahedron (IMI) are recognized as the two lowest energy structures (energetically degenerate isomers) but with different electronic structures: a semiconductor-type with the energy-gap of 0.356 eV for the IMI and a metallic-type with negligible gap for the OH, which is in good agreement with the experimental results. The electron affinity and ionization potential of Cu38 are also discussed and compared with the observations of the ultraviolet photoelectron spectroscopy experiments. The dynamical isomerization of the OH-like and IMI-like structures of Cu38 is revealed to dominate the pre-melting stage through the investigation by the molecular dynamics annealing simulations.

Accurate interatomic force field for molecular dynamics simulation by hybridizing classical and machine learning potentials

Full atom simulations have demonstrated the scalability for billions of atoms, but still suffered from the transferability of semi-empirical interatomic potentials. We propose a dynamic multiscale molecular dynamics (MD) simulation method with both high accuracy and efficiency in interatomic force field calculation by hybridizing both classical and machine learning (ML) potentials. A dynamic procedure has been adopted by evaluating the centro-symmetry parameter of evolving microstructures during MD simulations and accordingly modifying the highly distorted regions depicted by ML potentials. Atomic force field calculation in near-perfect or perfect lattices remain sticking to the fast EAM potential, which precisely captures the long range elastic interactions. A handshaking region is introduced in order to enforce the continuity in atomic interactions. The MD simulations using a dynamic multiscale scheme can achieve the ab-initio accuracy without raising considerable computational cost. The foundation of this approach deeply roots in the facts that the ML method has comparable accuracy to ab-initio MD simulations and possesses the same order of computation complexity to the classical MD (O(N)). The proposed multiscale method, attaining both high accuracy and efficiency simultaneously, will pave the way for solving many material science problems involving complex interactions of both long range elastic forces and short range chemical bonding/debonding processes.

Theoretical study of xenon adsorption on UO2 surfaces

During in-pile operation, fission gases such as xenon are produced and precipitates in nuclear fuel as nano-bubbles, modifying the thermomechanical properties of UO2 fuel matrix. This work aims at precising the nature and the scope of the xenon—UO2 matrix interaction. To this end, we present a theoretical study of xenon adsorption on UO2 surfaces, based on Monte Carlo simulation and semi-empirical interatomic potential. We determine xenon adsorption isotherms on previously relaxed (111) and (100) UO2 surfaces, and we compare them to the incorporation ones inside an empty box in order to isolate interface effects. A specific attention is given to the microstructure of xenon in these systems. Finally, an analysis of the mechanical properties (pressure and stress profiles near by the surface) is achieved in order to investigate the sensitivity to surface orientation and to get pertinent quantities that will supply micromechanical models at higher scale.

Influence of strain on dislocation core in silicon

First principles, density functional-based tight binding and semi-empirical interatomic potentials calculations are performed to analyse the influence of large strains on the structure and stability of a 60 dislocation in silicon. Such strains typically arise during the mechanical testing of nanostructures like nanopillars or nanoparticles. We focus on bi-axial strains in the plane normal to the dislocation line. Our calculations surprisingly reveal that the dislocation core structure largely depends on the applied strain, for strain levels of about 5%. In the particular case of bi-axial compression, the transformation of the dislocation to a locally disordered configuration occurs for similar strain magnitudes. The formation of an opening, however, requires larger strains, of about 7.5%. Furthermore, our results suggest that electronic structure methods should be favoured to model dislocation cores in case of large strains whenever possible.

Size-dependent plastic deformation of twinned nanopillars in body-centered cubic tungsten

Compared with face-centered cubic metals, twinned nanopillars in body-centered cubic (BCC) systems are much less explored partly due to the more complicated plastic deformation behavior and a lack of reliable interatomic potentials for the latter. In this paper, the fault energies predicted by two semi-empirical interatomic potentials in BCC tungsten (W) are first benchmarked against density functional theory calculations. Then, the more accurate potential is employed in large scale molecular dynamics simulations of tensile and compressive loading of twinned nanopillars in BCC W with different cross sectional shapes and sizes. A single crystal, a twinned crystal, and single crystalline nanopillars are also studied as references. Analyses of the stress-strain response and defect nucleation reveal a strong tension-compression asymmetry and a weak pillar size dependence in the yield strength. Under both tensile and compressive loading, plastic deformation in the twinned nanopillars is dominated by dislocation slip on {110} planes that are nucleated from the intersections between the twin boundary and the pillar surface. It is also found that the cross sectional shape of nanopillars affects the strength and the initial site of defect nucleation but not the overall stress-strain response and plastic deformation behavior.

Diffusion of small Cu islands on the Ni(111) surface: A self-learning kinetic Monte Carlo study

We elucidate the diffusion kinetics of a heteroepitaxial system consisting of two-dimensional small (1–8 atoms) Cu islands on the Ni(111) surface at (100–600) K using the Self-Learning Kinetic Monte Carlo (SLKMC-II) method. Study of the statics of the system shows that compact CuN (3≤N≤8) clusters made up of triangular units on fcc occupancy sites are the energetically most stable structures of those clusters. Interestingly, we find a correlation between the height of the activation energy barrier (Ea) and the location of the transition state (TS). The Ea of processes for Cu islands on the Ni(111) surface are in general smaller than those of their counterpart Ni islands on the same surface. We find this difference to correlate with the relative strength of the lateral interaction of the island atoms in the two systems. While our database consists of hundreds of possible processes, we identify and discuss the energetics of those that are the most dominant, or are rate-limiting, or most contributory to the diffusion of the islands. Since the Ea of single- and multi-atom processes that convert compact island shapes into non-compact ones are larger (with a significantly smaller Ea for their reverse processes) than that for the collective (concerted) motion of the island, the later dominate in the system kinetics -- except for the cases of the dimer, pentamer and octamer. Short-jump involving one atom, long jump dimer-shearing, and long-jump corner shearing (via a single-atom) are, respectively, the dominating processes in the diffusion of the dimer, pentamer and octamer. Furthermore single-atom corner-rounding are the rate-limiting processes for the pentamer and octamer islands. Comparison of the energetics of selected processes and lateral interactions obtained from semi-empirical interatomic potentials with those from density functional theory show minor quantitative differences and overall qualitative agreement.

CT-MEAM interatomic potential of the Li-Ni-O ternary system for Li-ion battery cathode materials

Conventional interatomic potential methods for Li-ion battery cathode materials normally use fixed-charge models, which are not accurate enough to model the dynamical oxidation state change of transition metals during electrochemical reactions. In order to enable more accurate large-scale simulations for battery cathode materials, here we report a semiempirical interatomic potential of the Li-Ni-O ternary system based on an advanced dynamic charge method: Charge-Transfer Modified Embedded-Atom Method (CT-MEAM). The potential is parameterized by fitting the atomic Bader charges and energy-strain curves of the LiNiO2 cathode material under uniaxial, biaxial and hydrostatic strains to results obtained with ab initio density-functional theory (DFT) calculations. A variety of structural, electrochemical and dynamical properties derived from the fitted CT-MEAM potential are observed to be in excellent agreement with previous DFT and experimental data. The transferability of the potential is validated by comparing relative phase stabilities and charge distribution states within the ternary Li-Ni-O systems. Our results support the capability of the present CT-MEAM to model complex ternary transition metal oxides. This method will facilitate not only the optimal design of Lithium-ion battery cathode materials, but also other transition metal oxide-based applications involving electrochemical reactions.

Segregation, precipitation, andα−α′phase separation in Fe-Cr alloys

Segregation, precipitation, and phase separation in Fe-Cr systems is investigated. Monte Carlo simulations using semiempirical interatomic potential, first-principles total energy calculations, and experimental spectroscopy are used. In order to obtain a general picture of the relation of the atomic interactions and properties of Fe-Cr alloys in bulk, surface, and interface regions several complementary methods has to be used. Using Exact Muffin-Tin Orbitals method the effective chemical potential as a function of Cr content (0-15 at.% Cr) is calculated for a surface, second atomic layer and bulk. At ~10 at.% Cr in the alloy the reversal of the driving force of a Cr atom to occupy either bulk or surface sites is obtained. The Cr containing surfaces are expected when the Cr content exceeds ~10 at.%. The second atomic layer forms about 0.3 eV barrier for the migration of Cr atoms between bulk and surface atomic layer. To get information on Fe-Cr in larger scales we use semiempirical methods. Using combined Monte Carlo molecular dynamics simulations, based on semiempirical potential, the precipitation of Cr into isolated pockets in bulk Fe-Cr and the upper limit of the solubility of Cr into Fe layers in Fe/Cr layer system is studied. The theoretical predictions are tested using spectroscopic measurements. Hard X-ray photoelectron spectroscopy and Auger electron spectroscopy investigations were carried out to explore Cr segregation and precipitation in Fe/Cr double layer and Fe_0.95Cr_0.05 and Fe_0.85Cr_0.15 alloys. Initial oxidation of Fe-Cr was investigated experimentally at 10^-8 Torr pressure of the spectrometers showing intense Cr_2O_3 signal. Cr segregation and the formation of Cr rich precipitates were traced by analysing the experimental spectral intensities with respect to annealing time, Cr content, and kinetic energy of the exited electron.

Semi-empirical interatomic potentials: recent advances and challenges

Semi-empirical interatomic potentials: recent advances and challenges

First-principles study of point defects at a semicoherent interface.

Most of the atomistic modeling of semicoherent metal-metal interfaces has so far been based on the use of semiempirical interatomic potentials. We show that key conclusions drawn from previous studies are in contradiction with more precise ab-initio calculations. In particular we find that single point defects do not delocalize, but remain compact near the interfacial plane in Cu-Nb multilayers. We give a simple qualitative explanation for this difference on the basis of the well known limited transferability of empirical potentials.

Molecular dynamics simulations of the formation of 1D spin-valves from stretched Au-Co and Pt-Co nanowires

We have performed molecular dynamics (MD) simulations of stretched Aux-Co1 − x and Ptx-Co1 − x nanowires to investigate the formation of bimetallic monoatomic wires between two electrodes. We have considered nanowires with two concentrations x = 0.2 and 0.8, aspect ratio of 13, a cross section of 1 nm2 and a wide range of temperatures (from 10 to 400 K). For the MD simulations we have used a semi-empirical interatomic potential based on the second moment approximation (SMA) of the density of states to the tight-binding Hamiltonian.For Au-Co alloys, Au atoms tends to migrate towards the narrowed region to form almost pure Au wires. In the PtCo case the formed chains usually consist of Pt enriched alternating structures. The most striking result is probably the Au0.2-Co0.8 alloy where pure monoatomic Au chains form between two Co electrodes constituting a potential 1D spin valve. Despite the known ease with which the 5d metals (Pt, Ir, and Au) form monoatomic chains (MACS), our results show that in the presence of Co (x = 0.2), the percentage of chain formation is higher than in the Pt and Au rich cases (x = 0.8).