Lennard-Jones Interatomic Potential 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.

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.

Exact solutions of nonlinear dynamical equations for large-amplitude atomic vibrations in arbitrary monoatomic chains with fixed ends

Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classical work by Fermi, Pasta, Ulam, and Tsingou (FPUT) in the middle of the last century. However, symmetry selection rules for the energy transfer between nonlinear vibrational modes of different symmetry, which lead to the possibility of excitation of some bushes of such modes, were not revealed. Each bush determines an exact solution of nonlinear dynamical equations of the considered system. The collection of modes of a given bush does not change in time, while there is a continuous energy exchange between these modes. Bushes of nonlinear normal modes (NNMs) are constructed with the aid of group-theoretical methods and therefore they can exist for the case of large amplitude atomic vibrations and for any type of interatomic interactions. In most publications, bushes of NNMs or similar dynamical objects in one-dimensional systems are investigated under periodic boundary conditions. In this paper, we present a detailed study of the bushes of NNMs in monoatomic chains for the case of fixed boundary conditions, which sheds light on a series of new properties of the intermode interactions in such systems. We prove some theorems that justify a method for constructing bushes of NNMs by continuation of conventional normal modes to the case of large atomic oscillations. Our study was carried out for FPUT chains, for the chains with the Lennard-Jones interatomic potential, as well as for the carbon chains (carbynes) in the framework of the density functional theory. For one-dimensional bushes (Rosenberg nonlinear normal modes), the amplitude–frequency diagrams are presented and the possibility of their modulational instability is briefly discussed. We also argue in favor of the fact that our methods and main results are valid for any monoatomic chain.

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.

Parameters of the vacancy formation and self-diffusion in the iron

The parameters of the electroneutral vacancy formation and self-diffusion of atoms in iron have been calculated by the analytical method based on the paired four-parameter Mie–Lennard-Jones interatomic interaction potential. For the first time, all activation process parameters were calculated within the framework of a single method: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The isobaric temperature dependences of the indicated activation parameters for bcc and fcc iron structures from T = 10 K–1810 K along two isobars: P = 0 and 10 GPa were calculated. 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. 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 isobaric 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.

Dependencies of the parameters of vacancy formation and self-diffusion in a single-component crystal on temperature and pressure

An analytical method for calculating the parameters of electroneutral vacancy formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the four-parameter pairwise Mie–Lennard-Jones interatomic interaction potential. The method allows calculation of all activation process parameters, that is, Gibbs energy, enthalpy, entropy, and volume, for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependences of the activation process parameters for gold have been calculated from T = 10 K–1330 K along two isobars, P = 0 and 24 GPa. 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 has a negative value. In the high-temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependences, with a weakly temperature-dependent enthalpy and a positive value of the activation process entropy. Good agreement has been obtained with estimated activation parameters for gold in the literature. It is shown that at T = 0 K the activation process parameters reach their minima: the Gibbs energy, enthalpy, and volume of the activation process all become zero, and the minimum of the activation process entropy lies in the negative region. The connection of the proposed calculation method with the Varotsos cBΩ model is discussed.

Changing the Parameters of Vacancy Formation and Self-Diffusion in a Crystal with Temperature and Pressure

An analytical method for calculating the parameters of the electroneutral vacancies formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the 4-parameters pairwise Mie--Lennard-Jones interatomic interaction potential. The method allows calculating all the activation processes parameters: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependencies of the activation processes parameters for gold are calculated from T=10 K to 1330 K along two isobars P=0 and 24 GPa. 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 has a negative value. In the high temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependencies with a weakly temperature-dependent enthalpy and with a positive value of the activation process entropy. Good agreements were obtained with the estimates of activation parameters for gold known from the literature. The values of activation parameters at T=0 K were discussed. Keywords: vacancy, self-diffusion, interatomic potential, gold, state equation, thermal expansion.

Изменение параметров образования вакансий и самодиффузии в кристалле с температурой и давлением

An analytical method for calculating the parameters of the electroneutral vacancies formation and self-diffusion of atoms in a single-component crystal is proposed. The method is based on the 4-parameters pairwise Mie–Lennard-Jones interatomic interaction potential. The method allows calculating all the activation processes parameters: Gibbs energy, enthalpy, entropy and volume for both the vacancy formation process and the self-diffusion process. The method is applicable at any pressure (P) and temperature (T). The temperature dependencies of the activation processes parameters for gold are calculated from T = 10 K to 1330 K along two isobars P = 0 and 24 GPa. 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 has a negative value. In the high temperature region, the probability of vacancy formation and the self-diffusion coefficient pass into classical Arrhenius dependencies with a weakly temperature-dependent enthalpy and with a positive value of the activation process entropy. Good agreements were obtained with the estimates of activation parameters for gold known from the literature. The values of activation parameters at T = 0 K were discussed.

Kajian Simulasi Dinamika Molekul Adsorpsi Hidrogen pada Carbone Nanotube dengan Variasi Chirality dan Temperatur Menggunakan Kode LAMMPS

Hydrogen adsorption has been simulated on carbon nanotubes for optimum hydrogen absorption. Parameters that affect the amount of hydrogen absorbed have been studied, such as the effect of chirality and temperature on hydrogen absorption in CNTs. The simulation method of hydrogen adsorption on carbone nanotubes uses molecular dynamics simulation code LAMMPS, applies Lennard-Jones interatomic potential and hydrogen atom movement using Van Der Waals force with Microcanonical Ensemble. Data analysis is the output of LAMPS in the form of data in XYZ format. The data contains information in the form of integration steps, number of atoms, temperature, pressure, potential energy, kinetic energy, volume, van der Waals energy, total simulation time and hydrogen absorption. The simulation results show that the optimum absorption occurs at run 10000 and a temperature of 100 K, for armchair chirality of 10 atoms, chirality of 12 atoms and zigzag chrality of 5 atoms. Formation of hydrogen coordinates with Avogadro software, formation of CNT coordinates with VMD software and visualization of hydrogen adsorption on CNTs using VMD software.

Two-dimensional mobile breather scattering in a hexagonal crystal lattice.

We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an "egg-box" harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to 60^{∘} scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.

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.

Size Dependence of the Surface Tension of a Small Droplet under the Assumption of a Constant Tolman Length: Critical Analysis

Convincing arguments have been presented testifying that that the surface tension of a small spherical droplet must decrease upon diminishing droplet radius in correspondence with a positive constant Tolman length. The solution of the Gibbs–Tolman–Koenig–Buff equation has been found in the most compact form. The surface tension of a small spherical droplet has been calculated within the framework of the continual approximation using the Mie–Lennard-Jones interatomic pair potential.

Change in Thermophysical Properties and Melting Temperature of Niobium with Increasing Pressure

Based on the Mie–Lennard-Jones interatomic pair potential and the Einstein crystal model, the thermal equation of state and the pressure dependences of the thermophysical properties of niobium are obtained. The pressure dependences of the Debye temperature, the first, second, and third Gruneisen parameters, isothermal compression modulus, isochoric and isobaric heat capacity, thermal expansion coefficient, and the pressure derivatives of these parameters along the 300 and 3000 K isotherms are studied. The calculations showed good agreement with experimental data. Based on the results obtained, the pressure dependence of the melting point of niobium and its pressure derivative are calculated.

A computational modeling of Raman radial breathing-like mode frequencies of fullerene encapsulated inside single-walled carbon nanotubes.

Raman radial breathing-like mode (RBLM) frequencies of an infinite nanopeapods are calculated within the framework of a continuum-molecular based model. The nanotube-fullerene interaction is modeled via the Lennard-Jones interatomic potential. An analytical formulation is developed and is justified due to its good agreement with the experimental and atomistic-based results. Furthermore, we propose new relationships for the van der Waals (vdW) interaction coefficients between the atoms of this hybrid nanostructure. Numerical results are also obtained for various nanopeapods on the basis of the present formulation. The RBLM frequency upshifts are predicted for small single-walled carbon nanotubes (SWCNTs). The frequency shifts can be adequately explained by the vdW intermolecular interactions acting between the fullerene and the SWCNTs atoms. To the best of our knowledge, a simple theoretical method which can predict the Raman RBLM frequencies of the nanopeapods with high precision has not been provided hitherto. We believe that the present study is likely to fill the gap.

Numerical modeling of adhesion and adhesive failure during unidirectional contact between metallic surfaces

Abstract In this work, we developed a finite element modeling approach to study adhesion during unidirectional contact between a two-dimensional plane-strain square and a flat slab. The surfaces were metallic or ceramic, and we analyzed different pairs of materials and their adhesion intensity using a FORTRAN subroutine (DLOAD) connected to a commercial finite element code Abaqus, which provided the surface attractive forces based on the Lennard-Jones interatomic potential using Hamaker constants. We considered adhesive loads during both the approach and separation of the surfaces. During the separation step, we modeled the material transfer between surfaces due to adhesion with respect to damage initiation and propagation at the flat slab. The parameters considered in the simulations include normal load, chemical affinity, and system size, and we analyzed different conditions by comparing the interaction forces during approach and withdrawal. This work also presents: (i) a description of the evolution of energy dissipation due to adhesion hysteresis, (ii) the formation–growth–breakage process of the adhesive junctions and the material transfer between surfaces, and (iii) an adhesive wear map based on a proposed novel equation that correlates the material parameters and material loss due to adhesion. The results indicate that the chemical affinity between bodies in contact is more related to adhesion than the applied load. In addition, the ratio between the material strength and elastic modulus seems to be an important factor in reducing adhesive wear.

Compaction simulation of nano-crystalline metals with molecular dynamics analysis

The molecular-dynamics analysis is presented for 3D compaction simulation of nano-crystalline metals under uniaxial compaction process. The nano-crystalline metals consist of nickel and aluminum nano-particles, which are mixed with specified proportions. The EAM pair-potential is employed to model the formation of nano-particles at different temperatures, number of nano-particles, and mixing ratio of Ni and Al nano-particles to form the component into the shape of a die. The die-walls are modeled using the Lennard-Jones inter-atomic potential between the atoms of nano-particles and die-walls. The forming process is model in uniaxial compression, which is simulated until the full-dense condition is attained at constant temperature. Numerical simulations are performed by presenting the densification of nano-particles at different deformations and distribution of dislocations. Finally, the evolutions of relative density with the pressure as well as the stress-strain curves are depicted during the compaction process.

Change in the thermophysical properties of BCC iron during isothermal compression

Equation of state P(V/V 0, T) and baric dependences of the thermodynamic properties of bcc iron are obtained using the Mie–Lennard-Jones interatomic pair potential and the Einstein model of a crystal without any adjustable parameters. The calculations performed along two isotherms at 300 and 1500 K from P = 0 to 8000 kbar = 800 GPa (i.e., to V/V 0 = 0.5) show good agreement with the experimental data. Baric graphical dependences are obtained for the following properties: isothermal bulk modulus B T and B′(P), isochoric specific heat C v and C v ′ (P), isobaric specific heat C p , thermal expansion coefficient α p and α p ′ (P), and specific surface energy of (100) face σ and σ′(P). Analytical approximations are obtained for baric dependences B′(P), α p (P), and σ′(P). It is shown that, at P → ∞, functions B T (P) and σ(P) for bcc iron change linearly and function α p ′ (P) tends toward zero.

Contributions of mass and bond energy difference and interface defects on thermal boundary conductance

The impact of mass and bond energy difference and interface defects on thermal boundary conductance (TBC) is investigated using non-equilibrium molecular dynamics (NEMD) with the Lennard-Jones (L-J) interatomic potential. Results show that the maximum TBC is achieved when the mass and bond energy of two dissimilar materials are matched, although the effective thermal conductivity is not necessarily a maximum due to the contributions of the thermal conductivity of the constituent materials. Mass and bond energy differences result in a mismatch between phonon dispersions, limiting high frequency phonon transport at the interface. This frequency mismatch is defined by a frequency ratio, which is a ratio of the characteristic frequencies of the two materials, presented in the discussion section, and is a reference of the level of phonon dispersion mismatch. Inelastic scattering may result at higher temperatures, especially when there exists a bond energy difference, resulting in strain in the lattice, which would allow phonons outside the allowable frequency range to contribute to transport. TBC decreases abruptly with small mass differences, but at which point larger differences in mass have no impact. In addition, interdiffusion across the interface further reduces the TBC between the frequency ratios of 0.79 and 1.26 while vacancies have negligible impact.

Thermal Stability of Nanoporous Raney Gold Catalyst

Nanoporous “Raney gold” sponge was prepared by de-alloying an Au-Al precursor alloy. Catalytic tests using a micro-reactor confirmed that Raney gold can serve as an active heterogeneous catalyst for CO oxidation, reduction of NO to N2, and oxidation of NO to NO2. In general, the specific surface area of a heterogeneous catalyst has an influence on its catalytic efficacy. Unfortunately, gold sponges coarsen readily, leading to sintering of their structure and reduction in surface area. This potentially places constraints on their upper operating temperature in catalytic reactors. Here we analyzed the behavior of Raney gold when the temperature was raised. We examined the kinetics and mechanism of coarsening of the sponge using a combination of in situ optical measurements and Metropolis Monte Carlo modeling with a Lennard-Jones interatomic potential. Modeling showed that the sponges started with an isotropic “foamy” morphology with negative average “mean curvature” but that subsequent thermally activated coarsening will drive the morphology through a bi-continuous fibrous state and on, eventually, to a sponge consisting of sintered blobs of predominantly positive “mean curvature”.

Impact of Mass and Lattice Difference on Thermal Boundary Conductance

ABSTRACTThe impact of mass and lattice difference on thermal boundary conductance is investigated using non-equilibrium molecular dynamics with the Lennard-Jones interatomic potential. Results show that the maximum thermal boundary conductance is achieved when the mass and the lattice of two dissimilar materials are matched, although the composite thermal conductance is not necessarily a maximum. It is observed that the small difference in mass and potential well depth has as significant an impact as large differences, and that the frequency mismatch is an important factor that affects thermal boundary conductance. It is, also, found that inelastic scattering begins to play a role at the interface as the temperature increases.