Interatomic Interaction Potentials Research Articles

Change in the melting temperature baric dependence during the transition from macro to nanocrystal

In this work we present new analytical (i.e., without computer modeling) method for calculating the dependence of the nanocrystal melting temperature both on pressure and on the size (number of atoms N) and surface shape of the nanocrystal. This method is based on the paired Mie–Lennard-Jones interatomic interaction potential, and takes into account the dependence of both the state equation and other lattice properties on the size and shape of the nanocrystal. For the first time, the dependences of the melting temperature on the pressure P, size N, and shape f of the nanocrystal were obtained. Calculations have been performed for gold, platinum and iron. It is shown that at any pressure, the melting point Tm(P, N, f) decreases both with an isomorphic-isobaric (f, P – const) decrease in the number of N atoms, and with an isomeric-isobaric (N, P – const) deviation of the nanocrystal shape from the energy-optimal shape. It is shown that the value of the baric derivative of the melting temperature Tm′(P) for a nanocrystal at low pressures is greater, and at high pressures less than the Tm′(P) value for a macrocrystal. At this, the dependence of the Tm′(P) function on the nanocrystal size is insignificant, i.e., at constant N-f-arguments, the baric dependences Tm(P, ∞) and Tm(P, N, f) are practically parallel. It is indicated how this method can be applied for experimental evaluation of the pressure under which a nanocrystal is located in a refractory matrix.

Existence state of Ti in diamond-like carbon coatings and its effects on hybrid structure and residual stress: Molecular dynamics simulations

In this study, the modified embedded atom method potential function is selected via the LAMMPS platform and OVITO interface software to describe the interatomic interaction potential, which is used to simulate the existence states of doped Ti in Ti-doped diamond-like coatings as well as their effect on the hybrid structure, hardness, and residual stress of the coatings. The results indicate that Ti atoms preferentially combine with C atoms to form Ti–C bonds, thus rendering it difficult to form metallic Ti clusters. The formation of Ti-C bond clusters with high extent of ordering (nanoc-TiC) in the coating is related to the density (or sp3C fraction) of the coating; the higher the density, the higher is the critical content of Ti (CV-Ti) required to form nanoc-TiC. When the density of the coating ranges from 2.4 to 3.6 g/cm3, the CV-Ti is 2–6 at.%. When the Ti content in the coating is less than CV-Ti, Ti atoms existed only in amorphous Ti–C clusters, which is not conducive to the stability of the sp3C phase and significantly reduces the residual stress and hardness of the coating. When the CV-Ti is exceeded, nanoc-TiC formed and grew until the hybrid C–C bonds in the coating disappeared completely, thus increasing the residual stress of the coating.

The role of the atom-atomic interactions depth on the metallic nanofilms structure evolution

Stochastic methods of modeling slow–moving processes controlled by diffusion make it possible to analyze the order-disorder phase transitions. The features of the kinetics of these transformations can also be identified due to these methods. Most of the investigations were made for binary alloys, taking into account the interaction of atoms in the first two coordination spheres. There is evidence that in real alloys the influence of the interatomic potential trimming radius is significant. The computer simulation results from the process of isothermal annealing of a binary metal nanofilm by a vacancy mechanism at various temperatures and the extent of the interatomic potential are presented. It has been established that with an increase in the extent of interatomic interaction potential, effects similar to those of temperature disordering a ear.

Interatomic force fields for zirconium based on the embedded atom method and the tabulated Gaussian Approximation Potential

The accuracy of interatomic interaction potentials – also known as force fields – is the main factor determining the physical soundness of classical molecular dynamics (MD) simulations. Here, we present a multi-objective framework to generate embedded-atom-method (EAM) force fields using ab initio data. The EAM force fields were tuned via particle swarm optimization to capture the non-linear association between atomic structures and system energies. Using this framework, 95 standard EAM force fields for zirconium were developed and 45 physical features for each developed force field were tracked. Principal component analysis (PCA) was performed to provide insights into the compromises that must be made when generating EAM force fields. Of note, by assigning large fitting weights to generalized stacking fault energy (GSFE) surfaces, there exist EAM force fields with properly positioned minima on prismatic GSFE surfaces and containing no spurious minima in basal GSFE surfaces. However, while standard EAM force fields achieved this without explicitly taking the angular dependence of atomic interactions into account, they led to a severe mismatch between other important physical properties and benchmarks. Hence, we also constructed two machine-learned tabulated Gaussian approximation potentials (tabGAP) with an additional three-body term, which successfully tackled the aforementioned issue and exhibit acceptable prediction accuracy across many physical properties (lattice parameters, elastic properties, dimer potential energies, melting temperatures, phase stability, point defect formation energies, point defect migration energies, and free surface energies) of Zr. Remarkably, its computational efficiency is only 6 times slower than standard EAM force fields.

Accuracy, Performance, and Transferability of Interparticle Potentials for Al–Cu Alloys: Comparison of Embedded Atom and Deep Machine Learning Models

In several recent years, a significant progress has been made in atomistic simulation of materials, involving the application of machine learning methods to constructing classical interatomic interaction potentials. These potentials are many-body functions with a large number of variable parameters whose values are optimized with the use of energies and forces calculated for various atomic configurations by ab initio methods. In the present paper a machine learning potential is developed on the basis of deep neural networks (DP) for Al–Cu alloys, and the accuracy and performance of this potential is compared with the embedded atom potential. The analysis of the results obtained implies that the DP provides a sufficiently high accuracy of calculation of the structural, thermodynamic, and transport properties of Al–Cu alloys in both solid and liquid states over the entire range of compositions and a wide temperature interval. The accuracy of the embedded atom model (EAM) in calculating the same properties is noticeably lower on the whole. It is demonstrated that the application of the potentials based on neural networks to the simulation on modern graphic processors allows one to reach a computational efficiency on the same order of magnitude as those of the embedded atom calculations, which at least four orders of magnitude higher than the computational efficiency of ab initio calculations. The most important result is that about the possibility of application of DP parameterized with the use of configurations corresponding to melts and perfect crystals to the simulation of structural defects in crystals and interphase surfaces.

Universal machine learning for the response of atomistic systems to external fields

Machine learned interatomic interaction potentials have enabled efficient and accurate molecular simulations of closed systems. However, external fields, which can greatly change the chemical structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into atomic descriptors to represent system-field interactions with rigorous rotational equivariance. This “all-in-one” approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in molecular and periodic systems in the presence of electric fields. Especially for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training atomic forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.

Anisotropic diffusion of radiation-induced self-interstitial clusters in HCP zirconium: A molecular dynamics and rate-theory assessment

Under irradiation, Zr and Zr alloys undergo growth in the absence of applied stress. This phenomenon is thought to be associated with the anisotropy of diffusion of either or both radiation-induced point defects and defect clusters. In this work, molecular dynamic simulations are used to study the anisotropy of diffusion of self-interstitial atom clusters. Both near-equilibrium clusters generated by aggregation of self-interstitial atoms and cascade-induced clusters were considered. The cascade-induced clusters display more anisotropy than their counterparts produced by aggregation. In addition to 1-dimensional diffusing clusters, 2-dimensional diffusing clusters were observed. Using our molecular dynamic simulations, the input parameters for the “self-interstitial atom cluster bias” rate-theory model were estimated. The radiation-induced growth strains predicted using this model are largely consistent with experiments, but are highly sensitive to the choice of interatomic interaction potential.

Gas Barrier Properties of Multilayer Polymer–Clay Nanocomposite Films: A Multiscale Simulation Approach

The paper discusses the development of a multiscale computational model for predicting the permeability of multilayer protective films consisting of multiple polymeric and hybrid layers containing clay minerals as fillers. The presented approach combines three levels of computation: continuous, full atomic, and quantitative structure–property correlations (QSPR). Oxygen and water are chosen as penetrant molecules. The main predictions are made using the continuum model, which takes into account the real scales of films and nanoparticles. It is shown that reliable predictions of the permeability coefficients can be obtained for oxygen molecules, which is not always possible for water. The latter requires the refinement of existing QSPR methods and interatomic interaction potentials for the atomistic level of calculations. Nevertheless, we show that the maximum effect on permeability reduction from the addition of clay fillers to the hybrid layer can be achieved by using nanoparticles with large aspect ratios and a high degree of orientational order. In addition, the use of the hybrid layer should be combined with the use of polymer layers with minimal oxygen and water permeability. The constructed model can be used to improve the properties of protective coatings for food and drug storage and to regulate the gas permeability of polymeric materials.

Drag on a sphere in a slow flow of a binary mixture of rarefied gases

The drag force on a sphere in an isothermal binary mixture of rarefied gases is calculated on the basis of the McCormack model for the linearized Boltzmann equation. The diffuse scattering of the gas–surface interaction law is assumed as the boundary condition. The rigid-spheres model of interatomic interaction potential is used as well as ab initio potentials for helium, argon, and krypton gases. The force is obtained in a wide range of the gas rarefaction, which covers the free molecular, transition, and slip regimes of the gas flow. In the free molecular and slip flow regimes, the problem is solved analytically, while in the transition regime, the system of kinetic equations is solved numerically via the discrete velocity method optimized to overcome the problem of discontinuity of the distribution function of molecular velocities on the convex surface. The calculations are carried out for the mixtures helium–argon and helium–krypton at 300 K. In the slip flow regime, the data available in the literature for the viscous slip coefficient of the helium–argon mixture are used, while for the mixture helium–krypton, it is calculated. The influence of the interatomic interaction potential, molar fraction, and ratio of atomic mass of species in the mixture on the drag force is analyzed.

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.

Puzzles of Surface Segregation in Binary Pt–Pd Nanoparticles: Molecular Dynamics and Thermodynamic Simulations

Up till now, there have been extremely contradictory opinions and inadequate results concerning surface segregation in binary platinum–palladium (Pt–Pd) nanoparticles, including the problems regarding segregating components, as well as the size and temperature dependences of segregation. Taking into account such a situation, we investigated the surface segregation in Pt–Pd nanoparticles by combining atomistic (molecular dynamics) and thermodynamic simulations. For molecular dynamics experiments, the well-known program LAMMPS and the embedded atom method were employed. In the course of the atomistic simulations, two different sets of parameterizations for the Pt–Pt, Pd–Pd, and Pt–Pd interatomic interaction potentials were used. The thermodynamic simulation was based on solving the Butler equation by employing several successive approximations. The results obtained via atomistic simulation and thermodynamic simulation on the basis of the Butler equation were compared with each other, as well as with predictions that were based on the Langmuir–McLean equation and some experimental data. Both simulation methods (atomistic and thermodynamic) predicted the surface segregation of Pd, which diminishes with the nanoparticle size and with increasing temperature. Our simulation results do not confirm the predictions of some authors on surface segregation inversion, i.e., the reversal from the surface segregation of Pd to the surface segregation of Pt when diminishing the nanoparticle size.

Study of the melting temperature baric dependence for Au, Pt, Nb

In this work we present new analytical (i.e., without computer modeling) method for calculating the dependence of the melting temperature (Tm) on pressure (P) for a single-component crystal. The method is based on the paired four–parameter Mie–Lennard-Jones interatomic interaction potential, and the delocalized criterion of melting. This method was used to calculate the baric dependences of the melting temperature Tm(P) and its pressure derivative Tm′(P) for gold, platinum and niobium in the pressure range: P = 0–1000 GPa. It has been shown that the dependences calculated by this method for gold and platinum are in better agreement with experimental data than the dependences obtained by computer modeling methods: the molecular dynamics simulations and the ab initio Z-method calculations. For niobium, the calculated Tm(P) dependence turned out to be steeper, i.e. the Tm′(P) values turned out to be greater than the experimental data obtained in [D. Errandonea et al. Communications Materials 1, 1 (2020)]. It has been indicated that this deviation can be caused both by a decrease in the Lindemann parameter with an increase in pressure, and by the redistribution of electrons in the s-to-d orbitals during compression of transition metals with a bcc structure. Furthermore, the discrepancy may also be due to the highly-correlated chain-like self-diffusion, which is inherent in bcc metals before melting.

Ab initio calculations of the interaction potentials and thermodynamic functions for ArN and ArN.

Argon compounds play an important role in the mass spectrometry with inductively coupled plasma and other applications. At the same time, there is a little knowledge of their electronic terms and thermodynamic functions due to the complexity of experimental observations. In this work, the ab initio simulations are performed to obtain the interatomic interaction potentials for the ground and excited states of ArN and ArN+ . Using these potentials, the vibrational-rotational partition functions and thermodynamic properties in the gas phase are calculated for these molecules at the temperature range of 298.15-10,000 K. The errors of the thermodynamic functions associated with the approximation of interatomic interaction potentials are estimated.

Effect of Interatomic Potential on Simulation of Fracture Behavior of Cu/Graphene Composite: A Molecular Dynamics Study

Interatomic interaction potentials are compared using a molecular dynamics modeling method to choose the simplest, but most effective, model to describe the interaction of copper nanoparticles and graphene flakes. Three potentials are considered: (1) the bond-order potential; (2) a hybrid embedded-atom-method and Morse potential; and (3) the Morse potential. The interaction is investigated for crumpled graphene filled with copper nanoparticles to determine the possibility of obtaining a composite and the mechanical properties of this material. It is observed that not all potentials can be applied to describe the graphene–copper interaction in such a system. The bond-order potential potential takes into account various characteristics of the bond (for example, the angle of rotation and bond lengths); its application increases the simulation time and results in a strong interconnection between a metal nanoparticle and a graphene flake. The hybrid embedded-atom-method/Morse potential and the Morse potential show different results and lower bonding between graphene and copper. All the potentials enable a composite structure to be obtained; however, the resulting mechanical properties, such as strength, are different.

Changing the parameters of vacancy formation and self-diffusion in various polymorphic modifications of iron

The activation parameters for various iron structures were calculated by the analytical method based on the paired four-parameter Mie-Lennard-Jones interatomic interaction potential. Within the framework of a single method, all the activation processes parameters were calculated: Gibbs energy, enthalpy, entropy and volume for both the process of electroneutral vacancy formation and for the process of atom self-diffusion. The isobaric temperature dependences of the indicated activation parameters for BCC and FCC iron structures from T=10 to 1810 K along two isobars: P=0 and 10 GPa were calculated. It is shown that at the α-γ transition temperature (1184 K), the activation parameters decrease during the isobaric transition from the BCC to the FCC structure. At the γ-delta transition temperature (1667 K), the activation parameters increase during the transition from the FCC to the BCC structure. With increasing pressure, the jumps magnitude for the Gibbs energy and the enthalpy of the activation process increases, and for the entropy and volume of the activation process decreases. It is shown that, at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region is negative. In the high temperature region, a good agreement has been obtained with the experimental estimates of activation parameters for different iron structures known from the literature. Keywords: vacancy, self-diffusion, interatomic potential, iron, structure, phase transition.

On the brittleness of elementary semiconductors

It is shown that the brittleness of a single-component covalent crystal (diamond, Si, Ge) is due to the "duplicity" of the paired potential of interatomic interaction for elastic (reversible) and for plastic (irreversible) deformation. This leads to the fact that the specific surface energy during plastic deformation of a covalent crystal is more than two times less than the specific surface energy during elastic deformation. Therefore, with a small deformation of a covalent crystal, it is energetically more advantageous to create a surface by irreversible breaking than by reversible elastic stretching. It is indicated that the brittle-ductile transition in a single-component covalent crystal is accompanied by metallization of covalent bonds on the surface. It is shown that the brittle-ductile transition temperature (TBDT) for single-component covalent crystals under static load has an upper limit: TBDT/Tm<0.45, where Tm --- is the melting temperature. Keywords: interatomic covalent bond, brittleness, ductility, elementary semiconductors, brittle-ductile transition.

О хрупкости элементарных полупроводников

It is shown that the brittleness of a single-component covalent crystal (diamond, Si, Ge) is due to the “duplicity” of the paired potential of interatomic interaction for elastic (reversible) and for plastic (irreversible) deformation. This leads to the fact that the specific surface energy during plastic deformation of a covalent crystal is more than two times less than the specific surface energy during elastic deformation. Therefore, with a small deformation of a covalent crystal, it is energetically more advantageous to create a surface by irreversible breaking than by reversible elastic stretching. It is indicated that the brittle-ductile transition in a single-component covalent crystal is accompanied by metallization of covalent bonds on the surface. It is shown that the brittle-ductile transition temperature (TBDT) for single-component covalent crystals under static load has an upper limit: TBDT/Tm < 0.45, where Tm is the melting temperature.

STRUCTURE AND VIBRATIONS OF FREE NIN CLUSTERS (N < 20)

The binding energy, equilibrium geometry, and vibration frequencies of small free Nin clusters (n < 20) were calculated using interatomic interaction potentials calculated in an embedded atom method. Calculations of the energy parameter of stability АЕ2 and dissociation energy showed that the most energetically stable clusters are those with the magic numbers of atoms n = 4, 6, 13, 19. Calculations of atomic vibrations revealed that the dynamic contribution to the stability of clusters is determined by the minimum vibration frequency, whose extreme values fall on clusters with the magic numbers of atoms n = 4, 6, 13, 19. The maximum vibration frequency varies nonmonotonically and for clusters with n < 19 it has no clear extreme values. This result is consistent with available experimental data on stable structures of small and medium-sized metal clusters.

Изменение параметров образования вакансий и самодиффузии в различных полиморфных модификациях железа

The activation parameters for various iron structures were calculated by the analytical method based on the paired four-parameter Mie–Lennard-Jones interatomic interaction potential. Within the framework of a single method, all the activation processes parameters were calculated: Gibbs energy, enthalpy, entropy and volume for both the process of electroneutral vacancy formation and for the process of atom self-diffusion. The isobaric temperature dependences of the indicated activation parameters for BCC and FCC iron structures from T = 10 K to 1810 K along two isobars: P = 0 and 10 GPa were calculated. It is shown that at the α-γ transition temperature (1184 K), the activation parameters decrease during the isobaric transition from the BCC to the FCC structure. At the γ-δ transition temperature (1667 K), the activation parameters increase during the transition from the FCC to the BCC structure. With increasing pressure, the jumps magnitude for the Gibbs energy and the enthalpy of the activation process increases, and for the entropy and volume of the activation process decreases. It is shown that, at low temperatures, due to quantum regularities, activation parameters strongly depend on temperature, and the entropy of activation processes in this region is negative. In the high temperature region, a good agreement has been obtained with the experimental estimates of activation parameters for different iron structures known from the literature.

THE EFFECTS OF PARTICLE SIZE AND TEMPERATURE ON THE STABILITY AND LOCAL STRUCTURAL EVOLUTIONS OF AMORPHOUS BULK AND NANOPARTICLES OF THE FeNI3 ALLOYS

The effects of particle size (2-6 nm) and temperature (300-1900 K) on the stability and local structural evolutions of amorphous bulk and nanoparticles of the FeNi3 alloys have been studied by using classical molecular dynamics (MD) simulation method combined with embedded atom model (EAM) in Largescale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The nanoparticles were obtained from the unstable amorphous bulk FeNi3 alloys. MD simulations have been performed for glassy FeNi3 intermetallic alloy by making use of pairwise interatomic interaction potentials and electron densities calculated via EAM method. The formation and evolution of structures and their stability have been analyzed at a wide temperature range (300-1900 K) by calculating radial distribution functions (RDF), interatomic distances (ID), coordination numbers (CN), core-to-surface concentration profiles, as well as Voronoi analysis. According to the results, although some deviations in the structural properties occurred during the heat treatment, the amorphous nanoparticles exhibited the same crystal structure and local atomic configuration with its bulk counterpart at room temperature.