Pairwise Interatomic Interactions Research Articles

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.

Field-theoretic simulations beyond δ-interactions: Overcoming the inverse potential problem in auxiliary field models.

Modern field-theoretic simulations of complex fluids and polymers are constructed around a particle-to-field transformation that brings an inverse potential u-1 in the model equations. This has restricted the application of the framework to systems characterized by relatively simple pairwise interatomic interactions; for example, excluded volume effects are treated through the use of δ-function interactions. In this study, we first review available nonbonded pair interactions in field-theoretic models and propose a classification. Then, we outline the inverse potential problem and present an alternative approach on the basis of a saddle-point approximation, enabling the use of a richer set of pair interaction functions. We test our approach by using as an example the Morse potential, which finds extensive applications in particle-based simulations, and we calibrate u-1 with results from a molecular dynamics simulation. The u-1 thus obtained is consistent with the field-theoretic model equations, and when used in stand-alone self-consistent field simulations, it produces the correct fluid structure starting from a random initial state of the density field.

Vibrational model of thermal conduction for fluids with soft interactions.

A vibrational model of heat transfer in simple liquids with soft pairwise interatomic interactions is discussed. A general expression is derived, which involves an averaging over the liquid collective mode excitation spectrum. The model is applied to quantify heat transfer in a dense Lennard-Jones liquid and a strongly coupled one-component plasma. Remarkable agreement with the available numerical results is documented. A similar picture does not apply to the momentum transfer and shear viscosity of liquids.

Calculation of the Surface Energy of a Crystal and its Temperature and Pressure Dependence

A method for calculating the specific surface energy σ, the isochoric and isobaric derivatives of the function σ with respect to the temperature, and the isothermal derivative of the function σ with respect to the pressure is developed proceeding from the parameters of the Mie–Lennard-Jones pairwise interatomic interaction potential. It is shown that this method is applicable for both macrocrystals and nanocrystals with specified numbers of atoms and with definite surface shapes. To implement this method, the parameters of the pair interatomic potential are determined using a self-consistent method based on the thermoelastic properties of a crystal. This method is tested using Fe, Au, Nb, Ta, Mo, and W macrocrystals at different temperatures and shows good agreement with experimental data. As the nanocrystal size is decreased along the isotherms T = 10, 300, and 2500 K, changes in the surface properties are studied using body-centered cubic (bcc) Ta as an example. It is shown that, at high pressures and low temperatures, the function σ can increase in the case of an isomorphic-isothermal-isobaric decrease in the nanocrystal size.

Pairwise interatomic interaction in alloys

The concepts of the physics of metallic alloys regarding the driving forces of diffusion phase transformations, the nature of solid solutions, the chemical interatomic interaction energy, the principles of plotting phase diagrams, and the principles of heat treatment of alloys are critically reviewed. The ordering–separation phase transition, which is caused by the recently detected property of alloys to change the sign of chemical interatomic interaction when temperature changes, is shown to change these concepts radically. The experimental data that fully support the ideas advanced in this review are presented (comprehensive experimental data for Ni–Cr and Co3V alloys are presented). The problem of the diffusion processes in multicomponent alloys is considered in detail. They are shown to occur according to the model of pairwise chemical interatomic interaction. The formation of diffusion couples in a multicomponent alloy begins in its liquid state. When temperature decreases, this process occurs in each diffusion couple similarly to the phase formation in the corresponding binary alloys.

Force Based Canonical Approximation of Molecular Potentials: Average Force versus Pointwise Force.

This work presents a new force-based canonical approach that utilizes the average force rather than the pointwise force, on which previously developed canonical approaches were based. Advantageously, the average force based method only requires the evaluation of the potential function and not its derivative. The average force and the pointwise force based methods are applied to a variety of diatomic molecules, and their accuracy is compared. It is demonstrated that the average force based method gives an improved accuracy compared to the pointwise force based method. This improved accuracy is attributed to the fact that the average force based method eliminates the need to use the numerical approximation of the derivative of the potential function that, in practice, is only known at discrete points. In addition, an algorithm is developed to apply the average force based method as a practical tool for generating potential curves for pairwise interatomic interactions utilizing the classical Lennard-Jones potential as reference. Moreover, application of the average force based method leads to a new canonical approximation paradigm. In this new paradigm, only the coordinates of the equilibrium configuration (the bottom of the potential well) of a molecule are required for accurate generation of the potential function. Moreover, theoretical results are presented, demonstrating the effectiveness of the canonical transformation procedure in producing highly accurate potential approximations. In particular, it is proved that a certain general set of qualitative conditions on potential-like functions are sufficient for a given potential function to be in the same canonical transformation class as a (dimensionless) Lennard-Jones potential. For functions satisfying these assumptions, it is shown that they have canonical approximations with arbitrarily small approximation errors.

Beyond Born−Oppenheimer: A canonical perspective

By using the classic Lennard-Jones potential as reference, inverse canonical transformations allow for the accurate generation of post Born−Oppenheimer potentials in the ground and excited electronic states for H2, He dimer, LiH, CH+, Mg2, HF, and OH radical. The two parameters in the reference Lennard-Jones potential are set to one. The studied potentials include corrections for adiabatic, nonadiabatic, relativistic, and quantum electrodynamics effects. The relative error in the generated potentials are less than 0.01. Application of canonical approaches with the algebraic Lennard-Jones potential accurately reproduces the best post Born−Oppenheimer potential curves of pairwise interatomic interactions.

Парное межатомное взаимодействие в сплавах

Парное межатомное взаимодействие в сплавах

Is there any fundamental difference between ionic, covalent, and others types of bond? A canonical perspective on the question.

The concept of chemical bonding is normally presented and simplified through two models: the covalent bond and the ionic bond. Expansion of the ideal covalent and ionic models leads chemists to the concepts of electronegativity and polarizability, and thus to the classification of polar and non-polar bonds. In addition, the intermolecular interactions are normally viewed as physical phenomena without direct correlation to the chemical bond in any simplistic model. Contrary to these traditional concepts of chemical bonding, recently developed canonical approaches demonstrate a unified perspective on the nature of binding in pairwise interatomic interactions. This new canonical model, which is a force-based approach with a basis in fundamental molecular quantum mechanics, confirms much earlier assertions that in fact there are no fundamental distinctions among covalent bonds, ionic bonds, and intermolecular interactions including the hydrogen bond, the halogen bond, and van der Waals interactions.

Statistical theory of diffusion in concentrated bcc and fcc alloys and concentration dependencies of diffusion coefficients in bcc alloys FeCu, FeMn, FeNi, and FeCr

The statistical theory of diffusion in concentrated bcc and fcc alloys with arbitrary pairwise interatomic interactions based on the master equation approach is developed. Vacancy–atom correlations are described using both the second-shell-jump and the nearest-neighbor-jump approximations which are shown to be usually sufficiently accurate. General expressions for Onsager coefficients in terms of microscopic interatomic interactions and some statistical averages are given. Both the analytical kinetic mean-field and the Monte Carlo methods for finding these averages are described. The theory developed is used to describe sharp concentration dependencies of diffusion coefficients in several iron-based alloy systems. For the bcc alloys FeCu, FeMn, and FeNi, we predict the notable increase of the iron self-diffusion coefficient with solute concentration c, up to several times, even though values of c possible for these alloys do not exceed some percent. For the bcc alloys FeCr at high temperatures T ≳ 1400 K, we show that the very strong and peculiar concentration dependencies of both tracer and chemical diffusion coefficients observed in these alloys can be naturally explained by the theory, without invoking exotic models discussed earlier.

Canonical Force Distributions in Pairwise Interatomic Interactions from the Perspective of the Hellmann-Feynman Theorem.

Force-based canonical approaches have recently given a unified but different viewpoint on the nature of bonding in pairwise interatomic interactions. Differing molecular categories (covalent, ionic, van der Waals, hydrogen, and halogen bonding) of representative interatomic interactions with binding energies ranging from 1.01 to 1072.03 kJ/mol have been modeled canonically giving a rigorous semiempirical verification to high accuracy. However, the fundamental physical basis expected to provide the inherent characteristics of these canonical transformations has not yet been elucidated. Subsequently, it was shown through direct numerical differentiation of these potentials that their associated force curves have canonical shapes. However, this approach to analyzing force results in inherent loss of accuracy coming from numerical differentiation of the potentials. We now show that this serious obstruction can be avoided by directly demonstrating the canonical nature of force distributions from the perspective of the Hellmann-Feynman theorem. This requires only differentiation of explicitly known Coulombic potentials, and we discuss how this approach to canonical forces can be used to further explain the nature of chemical bonding in pairwise interatomic interactions. All parameter values used in the canonical transformation are determined through explicit physical based algorithms, and it does not require direct consideration of electron correlation effects.

Viscosity calculations at molecular dynamics simulations

Viscosity and diffusion are chosen as an example to demonstrate the universality of diagnostics methods in the molecular dynamics method. To emphasize the universality, three diverse systems are investigated, which differ from each other drastically: liquids with embedded atom method and pairwise interatomic interaction potentials and dusty plasma with a unique multiparametric interparticle interaction potential. Both the Einstein-Helfand and Green-Kubo relations are used. Such a particular process as glass transition is analysed at the simulation of the aluminium melt. The effect of the dust particle charge fluctuation is considered. The results are compared with the experimental data.

A general transformation to canonical form for potentials in pairwise interatomic interactions.

A generalized formulation of explicit force-based transformations is introduced to investigate the concept of a canonical potential in both fundamental chemical and intermolecular bonding. Different classes of representative ground electronic state pairwise interatomic interactions are referenced to a chosen canonical potential illustrating application of such transformations. Specifically, accurately determined potentials of the diatomic molecules H2, H2(+), HF, LiH, argon dimer, and one-dimensional dissociative coordinates in Ar-HBr, OC-HF, and OC-Cl2 are investigated throughout their bound potentials. Advantages of the current formulation for accurately evaluating equilibrium dissociation energies and a fundamentally different unified perspective on nature of intermolecular interactions will be emphasized. In particular, this canonical approach has significance to previous assertions that there is no very fundamental distinction between van der Waals bonding and covalent bonding or for that matter hydrogen and halogen bonds.

A Unified Perspective on the Nature of Bonding in Pairwise Interatomic Interactions

Different classes of ground electronic state pairwise interatomic interactions are referenced to a single canonical potential using explicit transformations. These approaches have been applied to diatomic molecules N2, CO, H2(+), H2, HF, LiH, Mg2, Ca2, O2, the argon dimer, and one-dimensional cuts through multidimensional potentials of OC-HBr, OC-HF, OC-HCCH, OC-HCN, OC-HCl, OC-HI, OC-BrCl, and OC-Cl2 using accurate semiempirically determined interatomic Rydberg-Klein-Rees (RKR) and morphed intermolecular potentials. Different bonding categories are represented in these systems, which vary from van der Waals, halogen bonding, and hydrogen bonding to strongly bound covalent molecules with binding energies covering 3 orders of magnitude from 84.5 to 89,600.6 cm(-1) in ground state dissociation energies. Such approaches were then utilized to give a unified perspective on the nature of bonding in the whole range of diatomic and intermolecular interactions investigated.

Hybrid native partitioning of interactions among nonconserved residues in chimeric proteins

Given any operational criterion for pairwise interatomic interactions, for a pair of structurally homologous proteins there exists for both proteins a unique equivalent partitioning of the nonconserved residue positions into mutually non-interacting clusters. In the formation of a chimeric protein derived from these two parental sequences, if nonnative-like interactions are to be avoided in its tertiary structure, then all of the nonconserved residues of each cluster must necessarily be either maintained or interchanged simultaneously. This hybrid native partitioning criterion is applied to known gene shuffling results. When the degree of estimated disruption is modest, the HybNat algorithm provides an efficient predictor of structural integrity. This supports the expectation that a substantial fraction of sequences that conform to the hybrid native partitioning criterion will yield tertiary structures that largely preserve the native-like interactions of the parental proteins.

Discrete and continuum models for calculating the phonon spectra of carbon nanotubes

The vibration spectrum of perfect carbon nanotubes is studied using a two-parametric potential which includes pairwise and three-particle interatomic interactions. This potential was proposed by Keating and allows one to take into account the elasticity of pairwise interatomic bonds and the elasticity associated with a change in the angle between directional interatomic bonds in covalent crystals. Using the Keating potential, the vibration spectrum of a graphite monolayer is calculated and fitted to the vibration spectrum of crystalline graphite, thereby determining the parameters of the potential. With these parameters, the phonon spectra of perfect monolayer graphite nanotubes are calculated. A continuum model, in which a monolayer nanotube is represented as an elastic cylindrical shell of a finite thickness, is also discussed. Within this model, the vibration spectrum of a nanotube is calculated numerically in the long-wavelength limit as a function of the radius and thickness of the nanotube.

Interstitial distribution in Fe–Al and Fe–Cr quenched and aged alloys:: Computer simulation and internal friction study

Two types of physical approaches for simulation of the Snoek-type relaxation in low and high alloyed iron are examined to explain the experimental results obtained for Fe–Al–C and Fe–C–Cr alloys. The first approach developed by Smirnov–Tomilin is to calculate all octahedral positions available for interstitial atoms with different amount of substitute atoms in the first coordination shell and to simulate the loss maximum as a sum of all partial peaks according to the above mentioned interstice positions. The second approach takes into account the all pairwise interatomic interaction between solute atoms in a few coordination shells due to their interatomic elastic and ‘chemical’ interaction according to Khachaturyan–Blanter theory. The change of activation energy of ‘diffusion under the stress’ for interstitial atoms in that case is not a linear function of substitutional concentration in solution. Both physical models (short- and long-range interatomic interaction) for the Snoek-type relaxation in quenched ternary alloys (Fe–C–Me) are examined from the viewpoint of a distance of interatomic interaction taken into account and checked using experiments. It is shown that contrary to the second approach, the first type of calculations is reasonable for relatively low alloyed solid solution only. Decomposition (Fe–Cr) and ordering (Fe–Al) change the parameters of atomic distribution in bcc solid solution and lead to the corresponding change in the Snoek relaxation parameters. The use of an adequate physical model and structure parameters allows to explain corresponding effects and, vice versa, the internal friction spectrum allows to estimate quantitatively atom redistribution in alloyed ferrite.

Towards molecular dynamics simulation of large proteins with a hydration shell at constant pressure

Molecular dynamics simulation of a large protein in explicit water with periodic boundary conditions is extremely demanding in terms of computation time. Consequently, we have sought approximations of the solvent environment that model its important features. Here, we describe our SAPHYR (Shell Approximation for Protein HYdRation) model in which the protein is surrounded by a shell of water molecules maintained at constant pressure. In addition to the usual pairwise interatomic interactions, these water molecules are subjected to forces approximating van der Waals and dipole–dipole interactions with the implicit surrounding bulk solvent. The SAPHYR model is tested for a system of one argon atom in water and for the protein ubiquitin, and then applied to cytochrome P450cam, a protein with over 400 residues. The results demonstrate that structural and dynamic properties of the simulated systems are improved by use of the SAPHYR model, and that this model provides a significant computational saving over simulations with periodic boundary conditions.

The effect of substitutional impurities on the evolution of Fe-Al diffusion layer

The formation and growth characteristics of Fe based aluminide diffusion layers at the Fe-Al interface have been analysed in terms of interfacial interaction potentials based on the statistico-thermodynamical theory of multicomponent alloys combined with electronic theory in the pseudopotential approximation. The pairwise interatomic interaction potentials and partial ordering energies have been calculated to predict the effect of various alloying additions on the activity coefficient of Al atoms in α-Fe0.95(AlI − nXn)0.05 alloys where X = Si, Ge, Sb, Mg, Cu, Ca, Ag, Cd, Cr, Co, Zn, Mn, Ni, Pb or Bi and considered up to 1 at.%. The results of calculation show that the impurity elements with regard to their effect on the activity coefficient of Al atoms may be classified into two groups; I-group impurity elements, XI = Si, Ti, Ge, Sb, Mg, Cu, Ca, Ag, Cd, and Cr which decrease the activity coefficient of Al atoms, reduce the thickness of the Fe-Al intermetallic diffusion layer and II-group impurity elements, XII = Co, Zn, Mn, Ni, Pb and Bi, which increase the activity coefficient of Al atoms, tend to increase the thickness of diffusion layer at the Fe-Al interface. It has been established, in agreement with experimental observation, that the value of activity coefficient of Al atoms in α-Fe0.95(AlI − nXn)0.05 alloys has a strong influence on the formation and growth kinetics of interfacial diffusion layers at the Fe-Al interface. The analysis of the effects of type and content of XI and XII impurity elements on the activity coefficients of Al atoms, γAlγoAl, in α-Fe0.95(Al1 − nXn)0.05 alloys is in good qualitative agreement with the experimental results reported in the literature.

Convergence of symmetry-adapted perturbation theory expansions for pairwise nonadditive interatomic interactions

Convergence properties of symmetry-adapted perturbation expansions for nonadditive interactions are tested by performing high-order calculations for three spin-aligned hydrogen atoms. It is shown that the strong symmetry forcing characteristic of the Hirschfelder–Silbey theory leads to a rapidly convergent perturbation series. The symmetrized Rayleigh–Schrödinger perturbation theory employing a weak symmetry forcing is shown to provide in low orders accurate approximations to the nonadditive part of the interaction energy. In very high orders the convergence of this perturbation expansion becomes very slow, and the series converges to an unphysical limit, very close to the exact interaction energy. The nonadditive part of the interaction energy for the lowest quartet state of H3 is interpreted in terms of the first-order exchange, induction, exchange-induction, exchange-dispersion, induction-dispersion, and dispersion contributions. It is shown that even for such a simple trimer the correct description of these components is necessary to obtain quantitative agreement with variational full configuration interaction results.