Pairwise Interatomic Potential Research Articles

Changes in the structure of the Au–Fe alloy with a change in the concentration and with a decrease of the nanocrystal size

An analytical method is proposed for calculating the properties of a disordered Au–Fe substitution alloy both with fcc and with bcc structures. The parameters of the Mie–Lennard-Jones pairwise interatomic potential for the fcc and bcc structures of Au and Fe are determined. Based on these parameters, the concentration dependences of the properties of the fcc and bcc structures of the Au–Fe alloy are calculated. It is shown that the concentration dependences are nonlinear and agree with the results obtained for fcc-Au-Fe by using density functional theory method. The changes in the lattice properties of the Au–Fe alloy under the fcc-bcc structural phase transition at a pressure of P = 0 and a temperature of T = 300 K are calculated. Based on the changes in the properties at the fcc-bcc transition, it is concluded that iron plays a major role in the phase transition in the Au–Fe alloy. The appearance of a metastable amorphous structure in a wide range of concentrations around the fcc-bcc transition in an Au–Fe alloy was explained. In the framework of the RP-model of a nanocrystal, the displacement of the iron concentration (Cf), at which the fcc-bcc phase transition occurs, due to a decrease in the nanocrystal size was calculated. It is shown that at an isochoric-isothermal decrease of the atoms number (N) in an Au–Fe nanocrystal, the Cf value increases. For a nanocrystal with a fixed of atoms number and a constant surface shape, the Cf value increases at an isochoric increase in temperature, and the Cf value decreases at an isothermal decrease in density. Calculations have shown that at N < 59 900 for the Au1–CFeC alloy at P = 0, T ≤ 300 K and at any iron concentration, the fcc structure of the nanocrystal is more stable than the bcc structure.

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.

On the properties of the amorphous state of a single-component substance

It is shown that on the nonlinear dependence of the first coordination number (kn) versus the packing coefficient (kp) of the structure of a single-component substance, three special points corresponding to the amorphous structures can be distinguished. Based on the pairwise interatomic potential of Mie–Lennard-Jones, the state equation and properties of iron for both these three amorphous structures and the crystal state are calculated. It is shown that at kp = 0.45556 and kn = 6.2793 the minimum chemical potential is reached, i.e. this point is corresponding a thermodynamically stable amorphous structure into the liquid phase. An energetically equivalent point with the same kn value, but with kp = 0.6237, is a thermodynamically unstable amorphous structure corresponding to the solid phase. The following properties are calculated for amorphous iron: specific volume, chemical potential, entropy, Debye temperature, elastic modulus, thermal expansion coefficient, isobaric heat capacity, surface energy, and Poisson's ratio. It is shown that the specific surface energy of an amorphous solid metal is greater than that of an amorphous liquid phase, but less than that of a metal in the crystalline state. This should lead to the fact that the surface of the crystal metal should tend to amorphization.

Compaction simulation of crystalline nano-powders under cold compaction process with molecular dynamics analysis

In this paper, the uniaxial cold compaction process of metal nano-powders is numerically analyzed through the Molecular Dynamics (MD) method. The nano-powders consist of nickel and aluminum nano-particles in the pure and mixed forms with distinctive contributions. The numerical simulation is performed using the different number of nano-particles, mixing ratios of Ni and Al nano-particles, compaction velocities, and ambient temperatures in the canonical ensemble until the full-dense condition is achieved. In the MD analysis, the inter-atomic interaction between metal nano-particles is modeled by the many-body EAM potential, and the interaction between frictionless rigid die-walls and metal nano-particles is modeled by the pairwise Lennard-Jones inter-atomic potential. The mechanical behavior of metal nano-powders under the compaction process is numerically studied by plotting the relative density–pressure, mean stress-strain, and material characteristics–strain curves. Moreover, the nano-powder behavior is visualized by means of the centro-symmetry contour at various stages of the forming process. Finally, the evolution of top-punch velocity on the final stage of compaction process is studied by plotting the compaction pressure against the total energy at various compaction velocities.

A Method for the Parametrization of the Pairwise Interatomic Potential

Drawbacks of some methods known from the literature for determining four parameters of the Mie–Lennard-Jones pairwise interatomic potential as applied to crystals are pointed out. A new method for parametrization of the potential by thermoelastic properties of the crystal is proposed. The method determines the parameters by the best agreement of the calculated values with experimental data such as (1) the sublimation energy of the crystal at the zero values of the temperature (T = 0 K) and pressure (P = 0), (2) the thermal expansion coefficient and the isothermal modulus of elasticity measured at P = 0 and T = 300 K, and (3) the dependence of the isotherm curve T = 300 K of the equation of state on the volume P(300 K, V). The method was verified for iron and gold and showed good results. Further, the proposed method was applied to determine the parameters of the interatomic potential for refractory metals, viz., Nb, Ta, Mo, and W. The results obtained also allowed for more accurate determination of the sublimation energy, the Debye temperature, and the surface energy of the above metals.

Уравнение состояния и поверхностные свойства аморфного железа

It is shown that on the nonlinear dependence of the first coordination number (kn) versus the packing coefficient (kp) of the structure of a mono-component substance, three special points corresponding to the amorphous structure can be distinguished. Based on the pairwise interatomic potential of Mie–Lennard-Jones, the state equation and properties of iron for both these three amorphous structures and the crystal state are calculated. It is shown that at kp = 0.45556 and kn = 6.2793 the minimum chemical potential is reached, i.e. this point is corresponding a thermodynamically stable amorphous structure into the liquid phase. An energetically equivalent point with the same kn value, but with kp = 0.6237, is a thermodynamically unstable amorphous structure corresponding to the solid phase. It is shown that the specific surface energy of an amorphous solid metal is greater than that of an amorphous liquid phase, but less than that of a metal in the crystalline state. This should lead to the fact that the surface of the crystal metal should tend to amorphize.

Изучение свойств сплава золото-железо в макро- и нанокристаллических состояниях в различных P-T-условиях

For a disordered fcc-Au-Fe substitution alloy, the parameters of the Mie–Lennard-Jones pairwise interatomic potential are determined. Based on these parameters, the concentration dependencies of lattice properties for the macrocrystal of this alloy are calculated. Calculations of 20 properties of macrocrystals fcc-Au, fcc-Fe and fcc-Au0.5Fe0.5 are showed good agreement with experimental data. Using the RP-model of the nanocrystal, the state equation P(v, T; N) and baric dependences of both lattice and surface properties of the fcc-Au0.5Fe0.5 alloy are calculated. Calculations were performed at temperatures T = 100, 300 and 500 K for both a macrocrystal (N = Macro) and a cubic nanocrystal with N = 306 atoms. It is shown that with an isothermal-isobaric (P = 0) decrease in the size of a nanocrystal, its the Debye temperature, elastic modulus, and specific surface energy decrease, while its the specific volume, thermal expansion coefficient, specific heat capacity, and Poisson's ratio increase. At low temperatures in a certain pressure region, the specific surface energy increases at an isothermal-isobaric decrease in the number of atoms in the nanocrystal. As the temperature increases, this pressure region disappears.

Change in baric properties with decreasing size of germanium nanocrystal

The equation of state P(v/vo) and the baric dependences of both the lattice and the surface properties for germanium macro- and nanocrystals were calculated using the Mie-Lennard-Jones pairwise interatomic potential and the RP-model of a nanocrystal. It is shown that at a certain value of the relative volume (v/vo)0, the isothermal dependences P(v/vo) for the macro- intersect with those for the nanocrystal. At the intersection point (at (v/vo)0), the surface pressure becomes zero. The value (v/vo)0 decreases both with an isomorphic-isomeric rise in temperature, and with an isomorphically-isothermal decrease in the number of atoms in a nanocrystal, or with an isomeric-isothermal deviation of the shape of the nanocrystal from the energy-optimal shape (a cube for the RP-model). Based on the equation of state obtained, the change in 23 properties of Ge was studied both at an isochoric (v/vo = 1) and at an isobaric (P = 0) decrease in the number of atoms in a nanocrystal at temperatures of 100, 300, and 1000 K.

Изменение термодинамических свойств при уменьшении размера нанокристалла германия в различных Р-Г-условиях

The equation of state P ( v / v o ) and the baric dependences of both the lattice and the surface properties for macro- and nano- crystals germanium were calculated by means of the method with using the Mie-Lennard-Jones pairwise interatomic potential and by of the RP-model of a nanocrystal. It is shown that at a certain value of the relative volume ( v / v o ) 0 , the isothermal dependences P ( v / v o ) for the macro- and nano-crystal intersect. At the intersection point (at ( v / v o ) 0 ), the surface pressure becomes zero. The value ( v / v o ) 0 decreases both with an isomorphic-isomeric rise in temperature, and with an isomorphically-isothermal decrease in the number of atoms in a nanocrystal, or with an isomeric-isothermal deviation of the shape of the nanocrystal from the energy-optimal shape (for the RP-model it is a cube). Based on the obtained equation of state, the change in 23 properties of germanium was studied both at an isochoric ( v / v o = 1) and at an isobaric ( P = 0) decrease in the number of atoms in a nanocrystal at temperatures of 100, 300, and 1000 K. It is shown that at an isobaric ( P = 0) decrease in size, the specific volume of the germanium nanocrystal increases the more, the higher the temperature of the nanocrystal.

Estimation of the Critical Temperatures of Order-Disorder Phase Transitions in Cu-Au Alloys Using Short-Range Order Parameters

An expression for calculating the critical temperature of order-disorder transition in face-centered cubic alloys is developed with accounting of pairwise interatomic potential in the first eleven shells. Obtained expression was applied for the estimation of critical temperatures at Cu3Au, CuAu, and CuAu3 alloys in comparison with experimental data from phase diagram of Cu-Au system. Magnitudes of the pairwise interatomic potential in considered alloys was computed using values of the short-range order parameters which were experimentally obtained from X-ray diffuse scattering intensity. In this computation, the Krivoglaz-Clapp-Moss approximation and Cowley equations were applied.

The Changes in the Thermodynamic Properties of a Germanium Nanocrystal with a Decrease in Its Size under Various P–T-Conditions

The equation of state P(v/vo) and the baric dependences of both the lattice and surface properties of germanium macro- and nanocrystals have been determined on the basis of the Mie–Lennard–Jones pairwise interatomic potential and the RP-model of a nanocrystal. It has been shown that the isothermal dependences P(v/vo) of macro- and nanocrystals intersect each other at a certain value of the relative volume (v/vo)0. The surface pressure becomes zero at the intersection point (at (v/vo)0). The relative volume (v/vo)0 decreases with both an isomorphic–isomeric increase in the temperature and an isomorphic–isothermic decrease in the number of atoms in a nanocrystal or upon the isomeric–isothermic deviation of a nanocrystal from its energetically optimal shape (a cube for the RP-model). Based on the derived equation of state, the changes in 23 properties of germanium with both an isochoric (v/vo = 1) and isobaric (P = 0) decrease in the number of atoms in a nanocrystal at temperatures of 100, 300, and 1000 K have been studied. It has been shown that the higher the temperature of a nanocrystal is, the greater the increase is in the specific volume of a germanium nanocrystal under an isobaric (P = 0) decrease in its size.

BARIC DEPENDENCE OF LATTICE PROPERTIES FOR DIAMOND

Based on the pairwise interatomic potential of Mi-Lennard-Jones and the Einstein's model of crystal the state equation P(V/V0, T) and the baric dependencies of the lattice properties for diamond were obtained. The calculations were performed along two isotherms: T = 300 and 3000 K and until to P = 10000 kbar (i.e. until to the relative volume V/V0 = 0.5). The baric dependencies for the following properties were obtained: isothermal elastic modulus, isochoric and isobaric heat capacities and thermal expansion coefficient. Good agreement with experimental data was obtained.

Effect of wetting on nucleation and growth of D2 in confinement.

We have performed a computational study to determine how the wetting of liquid deuterium to the walls of the material influences nucleation. We present the development of a pair-wise interatomic potential that includes zero-point motion of molecular deuterium. Deuterium is used in this study because of its importance to inertial confinement fusion and the potential to generate a superfluid state if the solidification can be suppressed. Our simulations show that wetting dominates undercooling compared to the pore geometries. We observe a transition from heterogeneous nucleation at the confining wall to homogeneous nucleation at the bulk of the liquid (and intermediate cases) as the interaction with the confining wall changes from perfect wetting to non-wetting. When nucleation is heterogeneous, the temperature needed for solidification changes by 4 K with decreasing deuterium-wall interaction, but it remains independent (and equal to the one from bulk samples) when homogeneous nucleation dominates. We find that growth and quality of the resulting microstructure also depends on the magnitude of liquid deuterium-wall interaction strength.

Procedure for pseudopotential calculations of alkali metal elastic constants

A procedure for pseudopotential calculations of the elastic constants of BCC alkali metals is developed using radial and tangential force constants obtained from the dependence of the pairwise interatomic potential on distance. The equations for calculating elastic constants are derived using the Delaunay algorithm based on elements of a dynamic matrix defined by radial and tangential force constants and a subsequent long-wavelength approximation whose results are compared with the elements of a dynamic matrix expressed within a similar approximation in the Born-Begbie model through elastic constants c11, c12, and c44. The calculations for elastic constants of alkali metals performed using the proposed procedure agree satisfactorily with the experimental data.

High-Pressure, High-Temperature Phase Diagram of Calcium Fluoride from Classical Atomistic Simulations

We study the phase diagram of calcium fluoride (CaF2) under pressure using classical molecular dynamics simulations performed with a reliable pairwise interatomic potential of the Born−Mayer−Huggins form. Our results obtained under conditions 0 ≤ P ≲ 20 GPa and 0 ≤ T ≲ 4000 K reveal a rich variety of multiphase boundaries involving different crystal, superionic, and liquid phases, for all of which we provide an accurate parametrization. Interestingly, we predict the existence of three special triple points (i.e., solid−solid−superionic, solid−superionic−superionic, and superionic−superionic−liquid coexisting states) within a narrow and experimentally accessible thermodynamic range of 6 ≤ P ≤ 8 GPa and 1500 ≤ T ≤ 2750 K. In addition, we examine the role of short-ranged repulsive (SR) and long-ranged van der Waals attractive (LA) interactions in the prediction of melting lines with the finding that SR Ca−F and LA F−F contributions are most decisive.

Computer simulation of the interaction of carbon atoms with self-interstitial clusters in α-iron

Static and dynamic properties of clusters of self-interstitial atoms and their complexes with carbon (C) atoms in α-iron are studied by molecular dynamics method using a pairwise interatomic potential for iron–carbon interaction and a many-body potential for iron. The effect of C atoms on the configuration, stability and migration of 1 2 〈 1 1 1 〉 , 1 2 〈 1 1 0 〉 and 〈1 0 0〉 interstitial clusters is investigated. In the framework of the simple model of interstitial solute used here, C atoms enhance the relative stability of 〈1 0 0〉 over 1 2 〈 1 1 1 〉 clusters, but not enough to explain their common occurrence under irradiation. Clusters of seven interstitials or smaller are able to co-migrate with C atoms with a reduced mobility compared with pure iron. Bigger clusters have dislocation structure and are immobilised: C migrates along the core of their periphery as in the core of a straight edge dislocation. C dissociates from all clusters at high enough temperature.

Melting and liquid structure of aluminum oxide using a molecular-dynamics simulation

The radial distribution function G(r) for liquid aluminum oxide (corundum) is calculated by means of the two-phase molecular-dynamics method utilizing a previously developed pairwise interatomic potential. Our results agree very well with the recent exper

Role of allowance for interaction of distant neighbors in loss of stability in an extended anharmonic atomic chain

We investigate the problem of loss of stability in an anharmonic atomic chain whose ends are subject to a constant tensile stress when we allow for interaction of not only immediate neighbors, but distant neighbors as well. Using the approximation of self-consistent phonons, we obtain general expressions for the law of dispersion for natural oscillations of the chain and the equilibrium interatomic distance. We perform a concrete analysis for the pairwise interatomic Morse potential. Together with the case of first and second neighbors, we consider the general case of interaction of all atoms with each other. We show that instability appears simultaneously in all oscillation modes. Allowance for the interaction of more distant neighbors as well as closer neighbors increases the domain of stability of a chain relative to external stresses.

Elastic and structural properties of zeolites: Sodalite and dehydrated zeolite A

A pairwise interatomic potential has been used to investigate elastic and structural properties of two cubic zeolites: sodalite and dehydrated zeolite A. Constant volume energy minimization has been used to determine the variation of lattice constants and atomic coordinates with pressure. The calculated structures of sodalite and dehydrated zeolite A obtained at zero pressure are in reasonably good agreement with the available experimental values. We find that the structures at zero pressure are largely determined by the Coulomb potential. The pressure dependence of bond lengths and bond angles show that both sodalite and dehydrated zeolite A are easily deformed by bending the Si–O–Al angles. As expected for a less dense crystal, the dehydrated zeolite A is softer than the sodalite. We have also obtained the equation of state of these materials.

Hybrid Monte Carlo simulation of silica

A novel Hybrid Monte Carlo simulation method is used in conjunction with an accurate pairwise additive interatomic potential (Tsuneyuki , 1988, Phys. Rev. Lett. 61, 869) to study the phase diagram of silica. In the Hybrid Monte Carlo formalism discussed in this work trial moves are proposed by resorting to molecular dynamics techniques. However, since hybrid methods do not suffer from the numerical instabilities associated with finite step sizes, we are able to use effectively time steps that are several times larger than those required for conventional molecular dynamics simulations. More importantly, such methods provide a means of conducting simulations of complex systems within a Monte Carlo framework, thereby facilitating the study of isothermal or isobaric ensembles and that of open systems and phase equilibria. To illustrate the applicability and the usefulness of the methods we use them to reproduce the various thermal- and pressure-induced solid—solid phase transitions undergone by silica over wide ranges of pressure and temperature. This is of particular interest for mineralogical research at extreme conditions such as those encountered in the Earth's interior.