Effective Interatomic Potentials Research Articles

Development of the RF-MEAM Interatomic Potential for the Fe-C System to Study the Temperature-Dependent Elastic Properties.

One of the major impediments to the computational investigation and design of complex alloys such as steel is the lack of effective and versatile interatomic potentials to perform large-scale calculations. In this study, we developed an RF-MEAM potential for the iron-carbon (Fe-C) system to predict the elastic properties at elevated temperatures. Several potentials were produced by fitting potential parameters to the various datasets containing forces, energies, and stress tensor data generated using density functional theory (DFT) calculations. The potentials were then evaluated using a two-step filter process. In the first step, the optimized RSME error function of the potential fitting code, MEAMfit, was used as the selection criterion. In the second step, molecular dynamics (MD) calculations were employed to calculate ground-state elastic properties of structures present in the training set of the data fitting process. The calculated single crystal and poly-crystalline elastic constants for various Fe-C structures were compared with the DFT and experimental results. The resulting best potential accurately predicted the ground state elastic properties of B1, cementite, and orthorhombic-Fe7C3 (O-Fe7C3), and also calculated the phonon spectra in good agreement with the DFT-calculated ones for cementite and O-Fe7C3. Furthermore, the potential was used to successfully predict the elastic properties of interstitial Fe-C alloys (FeC-0.2% and FeC-0.4%) and O-Fe7C3 at elevated temperatures. The results were in good agreement with the published literature. The successful prediction of elevated temperature properties of structures not included in data fitting validated the potential's ability to model elevated-temperature elastic properties.

Probing precise interatomic potentials by nonadiabatic nonlinear phonons

Accurately probing the interatomic potential (IP) in crystals is essential for understanding the dynamic mechanisms in phase transitions and chemical reactions. Here, by interrogating laser-induced coherent phonon dynamics, we propose a new kind of optical microscopy for determining effective interatomic potentials beyond the harmonic and adiabatic approximation. This technique is tested against available experimental and first-principles data, by which the interatomic potential of graphene and a few other materials are successfully reconstructed in a large configuration space and beyond the ground state. A significant nonadiabatic effect emerges in nonlinear phonon dynamics and the IP reconstruction, which corrects the anharmonic part of IP much stronger (up to 50%) than the harmonic part. The nonadiabaticity-modulated potentials can lead to ∼10% correction on thermal expansion coefficients and ∼0.3 eV on phase transition barriers. This work offers a new strategy for probing complex interactions in quantum materials and exemplifies the universality of nonadiabaticity, which deserves a full consideration for precisely determining physical properties of quantum many-body systems.

The incompressibility of atoms at high pressures

Abstract The structures of the silica polymorphs α-quartz and stishovite have been geometry optimized at highly simulated isotropic pressure within the framework of Density Functional Theory. The atoms of the high-pressure polymorph stishovite are virtually incompressible with the bonded radii for Si and O atoms decreasing by only 0.04 and 0.08 Å, respectively, at 100 GPa. In compensating for the increase in the effective interatomic potential associated with the compression of the Si-O bonded interactions, the electron density at the bond critical point between the bonded pair increases from 0.69 to 0.89 e/Å 3. The bonded radii of the Si and O atoms for α-quartz decrease by 0.006 and 0.008 Å, respectively, between 1 bar and 26.4 GPa. The impact of simulated, isotropic pressure on the bonded radii of the atoms for three perovskites YAlO3, LaAlO3, and CaSnO3 was also examined at high pressure. For the YAlO3 perovskite, the bonded radii for Y and Al decrease by 0.06 and 0.05 Å, respectively, at 80 GPa, while the electron density between the bonded atoms increases by 0.12 and 0.15 e/Å3, on average. The calculations also show that the coordination number of the Y atom increases from 9 to 10 while the coordination number of the O1 atom increases concomitantly in the structure from 5 to 6 at 20 GPa. Hence pressure not only promotes an increase in the coordination number of the metal atoms but also a necessary concomitant increase in the coordination number of the O atoms. The bonded radii, determined at a lower pressure between 0.0 and 15 GPa for LaAlO3 and CaSnO3, decrease a smaller amount with the radii for the La and Ca atoms decreasing by 0.03 and 0.04 Å, respectively, while the radii for the smaller Al and Sn atoms decrease by 0.01 and 0.02 Å, respectively. In general, O atoms are more compressible than the metal atoms, but overall the calculations demonstrate that the bonded radii for the atoms in crystals are virtually incompressible when subjected to high pressure. The reason that the bonded radii change little when subjected to high pressure is ascribed to the changes in the effective interatomic potentials that result in increased repulsion when the atoms are squeezed together.

Structure, energetics, and electronic properties of stacking fault defects in ilmenite-structured ZnTiO3

The stacking fault behaviors on ilmenite ZnTiO3 were investigated by calculating the generalized stacking fault (GSF) energies using density functional theory (DF T) based on first principles calculations and classical calculations employing effective partial charge interatomic potentials. The results show that stable and unstable stacking fault energies are in qualitative agreement and provide the same sequence of stacking fault energies, although there exist quantitative differences with DFT providing lower stable and unstable stacking fault energy values than those from classical potential calculations. The γ-surfaces of two low energy surfaces, (1 1 0) and (1 0 4), of ZnTiO3 were fully mapped together with ideal shear stress (ISS) calculations. It was found that stacking faults along 〈〉/{1 0 4} are preferred energetically and are most probable to nucleate dislocations due to their significantly lower γsf/ γusf values. The atomic structures of the low energy stacking faults were analyzed and their electronic structures calculated and compared with bulk ZnTiO3 structures. It was found that stacking fault formation led to narrowing of the band gap and creating inter-bandgap states, mainly due to the dangling bonds and bonding defects, as compared to the bulk structures.

MEAMfit: A reference-free modified embedded atom method (RF-MEAM) energy and force-fitting code

Ab initio modeling of materials has become routine in recent years, largely due to the success of density functional theory (DFT). However, for many processes in materials, realism is achieved only when millions of atoms are considered. Currently, such large scale simulations are beyond ab initio capabilities so that one has to resort to effective interatomic potentials that well represent ab initio data on smaller scales. Two of the more widely used types of interatomic potentials are embedded atom method (EAM) and modified embedded atom method (MEAM) potentials. Here we present a code that can use ab initio generated energies and forces to obtain representative EAM and reference-free MEAM type effective interatomic potentials. We illustrate the use of this code with ab initio computed thermal excitations in ZrC. Program summaryProgram title: MEAMfitCatalogue identifier: AEWY_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEWY_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4467841No. of bytes in distributed program, including test data, etc.: 56403685Distribution format: tar.gzProgramming language: Fortran.Computer: Linux based workstations.Operating system: Linux.RAM: 120 MegabytesClassification: 16.1.External routines: TOMS611 Unconstrained Minimization [1] included in the MEAMfit code.Nature of problem: Fitting embedded atom method (EAM) and reference-free modified embedded atom method (RF-MEAM) potentials [2-3] to energies and forces produced by VASP [4-7].Solution method: A computer program is presented which uses a conjugate-gradient minimizer paired with a genetic algorithm to fit EAM and RF-MEAM potentials to energies and/or atomic forces read directly from VASP output files. Potentials produced by the code are directly usable with the LAMMPS [8] or Camelion [9] molecular-dynamics packages.Additional comments: User manual provided.!!!!! The distribution file for this program is over 56 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. !!!!!Running time: The run-time depends on the required level of accuracy of the final potential. For an EAM potential fit to 670 energies, a few hours on a single core is usually sufficient to produce a potential with R=12%–13% (see Equation. 9 in main-text for definition). To ensure a maximally optimized potential however (R=12%), a run-time of 24 hours is recommended. To optimize a RF-MEAM potential, a further 24 hours should be allowed. One will already find an improvement over the EAM using just a single core, however to ensure a maximally optimized potential, one should run several instances of MEAMfit in parallel.

Performance Evaluation on Several Exchange-correlation Functional Ap-proximations in Calculations of Alkali-metals and IB Group Metals Pair Potentials

In the present paper, inter-atomic pair potentials in alkali-metals and IB group metals, in crystal state and dia- tomic system, respectively, are systematically calculated by means of electronic density functional theory with several ex- change-correlation (EC) functional approximations. In the absence of experimental potential function information, exper- imentally available bonding length and binding energy of crystal lattice structure, and equilibrium separation and potential minimum of diatomic systems, are used for the first time in the context of potential energy as a function of atom separa- tion, to evaluate the performance of the EC approximations considered in calculating the main properties of neutral atom potential energy curve. Comparison between the experiment measures and first-principle calculations indicates that (i) all EC functional approximations show great changes in their performances for different systems, and the performances of a given EC functional approximation are variable even for the same element but different structures. (ii) The EC functional approximations considered show relatively stronger adaptability in calculations for the crystal lattice structures of both al- kali-metals and IB metals, but the performances for the IB metals Cu, Ag, Au diatomic systems degrade somewhat; more than that, the alkali-metal Li, Na, K, Rb, and Cs diatomic systems are inexorably the most difficult to be dealt with by all EC approximations considered. (iii) Although the calculated inter-atomic pair potentials in the diatomic system comprised of the IB metals and alkali-metals, respectively, display unmistakable deviations from the experimental measures, they still constitute specific empirical materials on which effective inter-atomic pair potentials are constructed to take into ac- count the three-body interactions in the statistical mechanics theory considering only two-body interactions.

Structural investigations on an amorphous Se90Te10 alloy produced by mechanical alloying using EXAFS, cumulant expansion and RMC simulations

We investigated an amorphous Se90Te10 alloy produced by mechanical alloying using two different approaches. First, we used extended x-ray absorption fine structure (EXAFS) spectroscopy and the cumulant expansion method using the Einstein model for the temperature dependence of the cumulants to obtain the cumulants , and . From these, we found information about the structure of the alloy as well as the thermal and structural disorder, anharmonicity of the effective interatomic pair potentials, thermal expansion of the Se–Se and Se–Te bonds and asymmetry of the partial distribution functions gSe−Se(r) and gSe−Te(r). The cumulants , and also allowed us to reconstruct the functions from EXAFS. Then, we made reverse Monte Carlo (RMC) simulations using the total structure factor \U0001d4ae(K) obtained from synchrotron x-ray diffraction and the EXAFS oscillations χ(k) on the Se K edge as input data to obtain the functions. Both methods furnished very similar gij(r) functions, and the structural data obtained from them were also very similar. The results obtained from both methods showed the presence of Se–Te pairs indicating that there is alloying at the atomic level. In addition, we could not find any evidence of the presence of Te clusters in the alloy.

Development of a Software to Optimize Parameters of Interatomic Potentials for Solid Systems

Generally, it is difficult to develop practical interatomic potentials which can be used in classical molecular dynamics calculations, since a method for development had not been established. In order to solve such problems, we had proposed a framework to develop interatomic potentials. However, the framework had not been widely used due to the difficulty of coding a process to optimize potential-parameters, which was involved in the framework. In this work, a practical software to optimize potential-parameters for solid systems, was developed based on real-coded genetic algorithm (GA). Fitness (=optimization-function) in GA for potential-parameter optimization could be calculated in practical time, and a concept of the corresponded module in GA-code was proposed. The developed software has an extensible structure: a user can define a new crystal-structure, or a new potential function to use in potential-parameter optimization by defining a corresponded class for that in separated header files. Convenient interfacial class to calculate equilibrium material properties of crystals and that to calculate material properties of user-inputted atomic-structures were prepared to define optimization-function. Several sample input files and header files were available for easy starting. As a result of distribution, several effective interatomic potentials were developed by using the software. As a sample of the development of interatomic potential, Tersoff-type potential for SiO2 systems were shown.

Effective Interatomic Potentials Based on The First-Principles Material Database

Effective interatomic potentials are frequently utilized for large-scale simulations of materials. In this work, we generate an effective interatomic potential, with Niobium as an example, using the force-matching method derived from a material database which is created by the first-principle molecular dynamics. It is found that the potentials constructed in the present work are more transferable than other existing potential models. We further discuss how the first-principles material database should be organized for generation of additional potential.

Interaction potentials for alumina and molecular dynamics simulations of amorphous and liquid alumina

Structural and dynamical properties of crystalline alumina α-Al2O3 and amorphous and molten alumina are investigated with molecular dynamics simulation based on an effective interatomic potentials consisting of two- and three-body terms. Structural correlations are examined through pair distribution functions, coordination numbers, static structure factors, bond angle distributions, and shortest-path ring analyses. The calculated results for neutron and x-ray static structure factors are in good agreement with experimental results. Dynamical correlations, such as velocity autocorrelation function, vibrational density of states, current-current correlation function, and frequency-dependent conductivity, are also discussed.

First-principles study of the adhesive and mechanical properties of the O-terminated α-Al2O3(0001)/Cu(111) interfaces

Adhesive and mechanical properties of the O-terminated (O-rich) α-Al2O3(0001)/Cu(111) interface have been examined by the first-principles pseudopotential method. Strong Cu–O covalent and ionic interactions exist, such as Cu3d–O2p hybridization and substantial electron transfer from Cu to O, which result in larger adhesive energy, greater tensile strength and larger interfacial Young's moduli than the Al-terminated (stoichiometric) interface with electrostatic–image and Cu–Al hybridization interactions. Substantial effects of interfacial Cu–O coordination are also present. Changes in the interface electronic structure for cleavage have been examined. Cu–O interlayer potential curves have been analyzed using the universal binding energy relation and compared with Cu–Al and Cu–Cu curves, which is valuable for the development of effective interatomic potentials in large-scale simulations.

Interatomic potentials and the simulation of fracture: C15 NbCr2

The discrete nature of solids and the interatomic interactions strongly influence crack propagation. Lattice trapping results in stable cracks above and below the critical Griffith load. Local atomic arrangements near the crack front define fracture behaviour. The analysis of these processes on an atomic scale helps to understand principle mechanisms and their consequences, which also have to be incorporated in more coarse-grained descriptions to get reliable results. Large-scale molecular dynamics simulations of fracture on the atomic level can supply information not accessible to experiment. But to simulate a specific material reasonable effective interatomic potentials are needed. In this paper, we report on the fitting and validation of potentials specifically generated for the fracture of C15 NbCr2. Results are compared to those derived with potentials for the elements from the literature. The comparison indicates that interactions fitted to elemental metals are not sufficient to determine alloy properties.

First-principles study on the tensile strength and fracture of the Al-terminated stoichiometric α-Al2O3(0001)/Cu(111) interface

The first-principles tensile tests have been applied to the Al-terminated stoichiometric α-Al2O3(0001)/Cu(111) interface by using the ab initio pseudo-potential method based on the density-functional theory. Firstly, the Cu/Al and Cu/Cu interlayers have been examined by the rigid-type tensile test. The interlayer potential curves derived from the first-principles calculations are well fitted by the universal binding-energy relation (UBER) curves. The Cu–Al adhesion is weaker than the back Cu–Cu adhesion. Secondly, the relaxed-type tensile test has revealed the tensile strength and features of interfacial fracture. The ideal tensile strength is about 10 GPa, and the local Young's modulus is about 40 GPa, which means that the Cu/Al interface is quite weak and soft compared with the bulk regions and the O-terminated interface. The failure is initiated from the charge depletion region near the interfacial O atoms when the interlayer stretching exceeds about 30%, and the behaviour of electrons and ions indicates no strong Cu–O bond compared with substantial Cu–Al interactions. The present ab initio data are useful for the construction of effective interatomic potentials at the interface.

Computation of the Peierls stress in tantalum with an extended-range modified embeddedatom method potential

When computing the Peierls stress of screw dislocations in tantalum by means of classicalmolecular dynamics (CMD), we have observed that a suitable potential should be able toreproduce the complicated angular dependence of forces arising in the core structure ofdislocations. This prevents the use of simple embedded atom potentials, but we notice thatmore generally, effective interatomic potentials tend to overestimate the Peierls stress.Since the Peierls–Nabarro model of dislocation requires an accurate description ofthe generalized stacking fault (GSF) energy surface, we have decided to use themodified embedded atom method (MEAM) potential, which explicitly incorporatesangular terms, whose coefficients are constrained to reproduce ab initio GSF data.Calculations with our new tantalum empirical model show the importance of hardcore screw dislocations and underline the problem of kinetics in Peierls stresscalculations.

1401 アルミナ/金属界面の機械的性質の第一原理計算と原子間ポテンシャルの検討(キーノート講演,OS-14A 電子・原子・マルチスケールシミュレーションに基づく材料特性評価(第一原理計算),OS-14 電子・原子・マルチスケールシミュレーションに基づく材料特性評価)

1401 アルミナ/金属界面の機械的性質の第一原理計算と原子間ポテンシャルの検討(キーノート講演,OS-14A 電子・原子・マルチスケールシミュレーションに基づく材料特性評価(第一原理計算),OS-14 電子・原子・マルチスケールシミュレーションに基づく材料特性評価)

Composition dependence of the low-temperature magnetic ordering and the hyperfine interactions in Fe–N austenite

The electronic structure of two model structures of stoichiometry Fe8N with different types of ordering of the nitrogen atoms are calculated using the ab initio FLAPW method. To first approximation these structures can be treated as a prototype of Fe–N austenite. The influence of the nitrogen atoms on the electronic structure and magnetic properties of γ iron and on the components of the Mössbauer spectrum is investigated, permitting a detailed interpretation of the experimental data. The dependence of the exchange integral on the concentration of nitrogen atoms is obtained, clarifying the influence of nitrogen on the magnetic properties of fcc iron. The effective interatomic interaction potentials of nitrogen atoms in fcc iron in six coordination spheres is calculated using the ab initio FLAPW method and the cluster expansion technique. The potentials thus obtained are used in a Monte Carlo investigation of the temperature dependence of the short-range order in the Fe–N system. The temperature dependence of the heat capacity and short-range order parameters is calculated. It is established that a transition from the disordered state to the nitride Fe4N is observed at 830 K.

Calculation of thermodynamic quantities of metals and alloys by statistical moment method

The thermodynamic quantities of metals and alloys are studied using the moment method in the quantum statistical mechanics, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the free energy, specific heats Cv and Cp, mean square atomic displacements and thermal lattice expansion coefficients are derived explicitly in terms of the second and fourth order vibrational coupling constants. The thermodynamic quantities are calculated both for cubic (fcc and bcc) and closed packed hexagonal (hcp) metals. The Lennard–Jones type of potentials as well as the effective interatomic potentials derived from the tight-binding (TB) total energy calculation scheme are used. The calculated thermodynamic quantities are favorably compared with the experimental results. For the calculations of alloys, we investigate the effects of thermal lattice vibration on the long range order (LRO) parameter and order–disorder transitions of the ordered binary alloys.

Atomistic simulations of dislocation processes incopper

We discuss atomistic simulations of dislocation processes incopper based on effective medium theory interatomic potentials. Results on screw dislocation structures and processes arereviewed with particular focus on point defect mobilities andprocesses involving cross slip. For example, the stability ofscrew dislocation dipoles is discussed. We show that thepresence of jogs will strongly influence cross slip barriers anddipole stability.We furthermore present some new results on jogged edgedislocations and edge dislocation dipoles. The jogs are found tobe extended, and simulations of vacancy controlled climb showthe jogs to climb easily in their extended form. The stabilityof small vacancy dipoles is discussed and it is seen that theintroduction of jogs may lead to the formation of Z-type faultedvacancy dipoles.

Interatomic potentials and atomistic calculations of some metal hydride systems

The effective interatomic pair potentials for Ti, Zr, Hf, V, Nb, Ta and their hydrides are obtained by inverting the ab initio cohesive energy curves based on the lattice inversion method, and then the inverted pair potentials are used to calculate the mechanical and thermal properties of these hydrides.

Modeling of the sliding resistance of ∑3〈111〉 tungsten grain boundary: influence of boron additive

We performed total energy calculations for extremely dilute disordered W–B solid solutions using the Linear Muffin-Tin Orbitals (LMTO) method within the framework of the Coherent Potential Approximation (CPA). From the obtained values of the total energies of the alloy and the total energies of the pure compounds we calculated the mixing energy as a function of the lattice parameter. Effective interatomic potentials were calculated by means of a recursion procedure. Interatomic potentials were applied in Monte Carlo simulations in order to calculate the elastic properties of ∑3〈111〉 tungsten grain boundary with and without boron atoms.