Two-dimensional Lennard-Jones System Research Articles

Inherent Structures and Two-Stage Melting in Two Dimensions

A large-scale study of the {open_quotes}inherent structures{close_quotes} (IS) associated with equilibrium two-dimensional Lennard-Jones systems is presented. The results validate, for simple 2D fluids, an essential premise of inherent-structures theory: there are consistent, {ital qualitative} differences between the IS associated with distinct equilibrium phases. The hexatic IS show free dislocations plus some nonpercolating grain boundaries. The liquid IS always contain percolating grain boundaries, but no evidence of free disclinations. Our results are consistent with the dislocation-unbinding scenario for the hexatic phase, but leave open the question of the microscopic melting mechanism leading to the isotropic liquid. {copyright} {ital 1997} {ital The American Physical Society}

Thermodynamic shift from three- to two-dimensional systems

The main thermodynamic properties of a two-dimensional Lennard-Jones system, the Helmholtz free energy and the pressure, are obtained by using accurate analytical equations for the corresponding three-dimensional system. The thermodynamic shift from three- to two-dimensional properties is made by scaling the temperature and simultaneously adding an analytical expression to the three-dimensional Helmholtz free energy.

Symmetry-breaking density profiles in confined liquids.

Density profiles of a liquid confined between two parallel plates are studied near a liquid-gas transition. The system is additionally exposed to an external field depending on the coordinate perpendicular to the plates that possesses a discrete left-right symmetry with respect to the midplane between the plates. It is found that the equilibrium density profiles can be symmetry breaking, i.e., they do not possess the discrete left-right symmetry of the external field. Explicit results are obtained within a simple double-slit model consisting of two layers of two-dimensional Lennard-Jones systems using both computer simulation and density-functional theory. Such symmetry-breaking profiles should be observable in confined colloidal suspensions.

Molecular dynamics simulation of atomic intermixing in microclusters

A molecular dynamics simulation was carried out using the two-dimensional Lennard-Jones system to study the mechanism of atomic intermixing in crystalline microclusters consisting of 127, 217, 331 and 469 atoms. The simulation was performed under the NVE constant condition after the temperature was adjusted. The temperature is aimed at0.375 ε/k B so that the clusters consist of a soiid-like core region and a region of surface melting. It is found that the collective motion of atoms amplified by the presence of a free surface causes atomic intermixing in the solid-like core region through the creation and motion of a dislocation or a vacancy or by the collective motions themselves. When the size becomes large, the role of dislocations diminishes in comparison with that of vacancies. For clusters with nominal size of 217 or smaller, atomic intermixing results from the collective motions themselves. The rate per atom of atomic intermixing in the solid-like core is found to be three to four orders of magnitude larger than that in the bulk crystal.

Molecular dynamics of the particle/substrate contact rupture in a liquid medium

The influence of a surrounding liquid on the process of rupture of contact between a solid particle and a flat surface has been studied by molecular dynamics simulations of a two-dimensional Lennard-Jones system. The computer experiments showed spontaneous particle escape and facilitation of contact rupture, i.e. less work had to be done to induce the rupture when a liquid was present. The adhesive force was, however, not reduced in the systems under investigation. The results show the role of the molecular structure of the liquid and solid phases, the shape of solid surfaces in the contact zone and especially the impossibility of liquid molecules penetrating into very narrow gaps between solid surfaces in the course of contact rupture. The increased role of the disjoining pressure fluctuations in the escape of the very small (molecular size) particles has been elucidated. These peculiarities set the limits for a continuous thermodynamic approach to microscopic systems of this kind.

Effect of the attractive forces in determining the critical point of a two-dimensional Lennard-Jones system

In order to calculate the thermodynamic properties of a two-dimensional Lennard-Jones system, we have carried out computer simulations to obtain its radial distribution function. The relative dependence between the repulsive and attractive intermolecular forces on the thermodynamics of these systems is modeled through the separation of the intermolecular potential proposed by Weeks, Chandler and Andersen. We simulated a large number of states and we obtain exact expressions for the thermodynamic properties by fitting to an analytical expression. The results extrapolated to the critical region permit us to propose a simple method to determine the critical properties of these systems. Despite the approximate nature of this method, its predictions are in agreement with previously published results for the full Lennard-Jones system. When the intensity of the attractive forces relative to the repulsive forces is changed, we found that the critical point varies linearly. These results could be important in applications where the repulsive forces have a different intensity such as is the case of the Lennard-Jones neutral molecules and in the adsorption of rare gases under an electric field caused by a solid surface.

Melting in Two-Dimensional Lennard-Jones Systems: Observation of a Metastable Hexatic Phase.

Large scale molecular dynamics simulations of two-dimensional melting have been carried out using a recently revised Parrinello-Rahman scheme on massively parallel supercomputers. A metastable state is observed between the solid and liquid phases in Lennard-Jones systems of 36 864 and 102 400 atoms. This intermediate state shows the characteristics of the hexatic phase predicted by the theory of Kosterlitz, Thouless, Halperin, Nelson, and Young.

Shape of hexatic domains of a two-dimensional Lennard-Jones system

We determine the shape of an hexatic inclusion surrounded by an isotropic medium using the Wulff construction to obtain the minimal surface energy. The thermodynamic states (hexagonal solid and hexatic and liquid phases) are obtained via Monte Carlo simulations in the NVT ensemble, and the surface energy as a function of orientation is derived from the general Gibbs formulation. We find that the shape of the hexatic domain changes with temperature from an irregular hexagon to a shape where more facets are developed, becoming closer to a circular one

Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis

The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionPL(ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities . Particular attention is paid to the question whether accurate estimates of critical temperatureTc and critical density ρc can be obtained. In the lattice gas model these critical parameters are known exactly and the limitations of the approach can thus be definitively asserted. The final estimates for the Lennard Jones problem areTc=0.47±0.01 (in units of the Lennard Jones energy e) and ρc (in units of σ2), a comparison with previous estimates is made.

Two-dimensional compressed liquid: a molecular dynamics study

Extensive molecular-dynamics computer simulation results are presented for a two-dimensional (2D) Lennard-Jones system as it is compressed isothermally well beyond its normal liquid state. They show systematic changes in the pair distribution function and some of the time correlation functions as the system is transformed from a normal liquid into an amorphous state. The density correlation functions, however, start to exhibit a two-step relaxation process, a rapidly decaying component and a slowly decaying component indicating a structural slowdown, as the system is compressed. The density at which the transition to an amorphous state takes place has been estimated. The results, when compared with those of three-dimensional systems, indicate that while the general behaviour is similar, the changes in 2D take place over a much smaller range of density. Implications of the results for localization and the Lindemann criterion are discussed.

Crystal to Glass Transition and Melting in Two Dimensions

ABSTRACTThermodynamic properties, structures, defects and their configurations of a two-dimensional Lennard-Jones (LJ) system are investigated close to crystal to glass transition (CGT) via molecular dynamics simulations. The CGT is achieved by saturating the LJ binary arrays below glass transition temperature with one type of the atoms which has different atomic size from that of the host atoms. It was found that for a given atomic size difference larger than a critical value, the CGT proceeds with increasing solute concentrations in three stages, each of which is characterized by distinct behaviors of translational and bond-orientational order correlation functions. An intermediate phase which has a quasi-long range orientational order but short range translational order has been found to exist prior to the formation of the amorphous phase. The destabilization of crystallinity is observed to be directly related to defects. We examine these results in the context of two dimensional (2D) melting theory. Finite size effects on these results, in particular on the intermediate phase formation, are discussed.

Dynamical block analysis in a non-equilibrium system

We present molecular dynamics simulation results of quenches into the unstable region of a two-dimensional Lennard-Jones system. The evolution of the system from the non-equilibrium state into equilibrium was analyzed with a dynamical block analysis. This can lead to a new approach in the study of non-equilibrium phenomena. We show that with such an analysis one can obtain results on the dynamic evolution as the system evolves, consistent with those obtained from and analysis of the pair-distribution function, structure factor and excess energy. The simulations were carried out on the parallel computer of the condensed matter theory group at the University of Mainz.

Dodecagonal order in a two-dimensional Lennard-Jones system.

We investigate a two-dimensional Lennard-Jones mixture with the interaction parameters chosen so as to favor configurations where the large atoms form squares and equilateral triangles. Many such configurations are possible which by our choice of interactions are nearly degenerate in energy. It is hypothesized that a thermal equilibrium state with 12-fold orientational order exists. Several Monte Carlo simulations were performed to cool the system to a temperature approaching zero. The ordering process was studied by following the evolution of the configurations with temperature. The onset of ordering seemed to be very diffuse in space rather than nucleated at a point. The resulting configurations consist of squares and triangles, except for a few dislocations, and thus have perfect orientational order. We also characterized the deviation from ideal quasiperiodicity in terms of the ``phason strain''; this was analyzed both by fitting a linear relation between the physical space coordinates of the atoms and the corresponding ``perpendicular space'' coordinates, and also by calculating the diffraction peaks. The latter are shifted and broadened, relative to an ideal 12-fold diffraction pattern, as in real quasicrystals.

Orientational order and solid-liquid coexistence in the two-dimensional Lennard-Jones system.

There exist large discrepancies between the results of different techniques used to locate the melting point of a two-dimensional Lennard-Jones system. In particular, the melting line determined by Barker et al [Physica 106A, 226 (1981)] through thermodynamic integration differs from the limit of mechanical stability of the two-dimensional (2D) solid which follows from recent simulations on very large systems. This discrepancy is puzzling because in the latter simulations no hysteresis was observed. We report a new calculation of the relevant part of the melting line of a 2D Lennard-Jones system by thermodynamic integration. Our results differ significantly from the results reported by Barker et al. and agree well with the simulations on large systems. We note that the structural properties of the two-phase region for a large system [O${(10}^{4}$) particles] exhibit all the characteristics of a bond-orientational order-disorder transition. This suggests that solid-liquid coexistence in 2D may differ qualitatively from its three-dimensional counterpart.

Monte Carlo study of glassy order in two-dimensional Lennard-Jones systems.

The presence of disordered states in quenched Lennard-Jones systems in two dimensions is investigated by use of Monte Carlo simulations. No glassy state is observed in the one-component Lennard-Jones system; for all the (N,V,T) ensembles studied, the quenched system evolves readily into the ordered solid. When the two-component Lennard-Jones fluid is quenched to a low temperature, depending on the ratios of the concentration ${N}_{A}$/${N}_{B}$ and ``sizes'' ${\ensuremath{\sigma}}_{\mathrm{AA}}$/${\ensuremath{\sigma}}_{\mathrm{BB}}$, it may evolve into either a fairly well-ordered solid, a microcrystalline state, or a disordered solid which may or may not be glassy. The two-component glasses are highly disordered with well-localized particles and have the characteristic split-second peak in the partial pair distribution function ${g}_{\mathrm{BB}}$, which is found in scattering experiments for metallic glasses and previous three-dimensional computer simulations of glasses. The authors propose that these glasses are only metastable and the phase-separated ordered lattice is the ground state. There is no hexatic order in the two-dimensional glasses; they have only short-range bond orientational correlation.

Determination of the algebraic exponents near the melting transition of a two-dimensional Lennard-Jones system.

Determination of the algebraic exponents near the melting transition of a two-dimensional Lennard-Jones system.

Computer simulation of a phase transition at constant temperature and pressure.

The dynamical equations for the motion of classical mechanical particles at constant temperature T and pressure p, derived by Nos\'e and by Hoover, are solved for a two-dimensional Lennard-Jones system. The molecular-dynamics isothermal-isobaric (MDTP) simulations of the solid-fluid transition show that the T-p thermostat works well. The MDTP results agree with the corresponding MD data and the pressure thermostat does not destroy the long-range bond correlation in the fluid near the freezing point.

Method of determining parameters of lattice models.

We propose a general method of determining parameters of lattice models by integrating out approximately the fluctuations that are expected to affect the thermodynamic properties only quantitatively. The method is based on a bond-moving transformation, which gives a rigorous upper bound on the exact partition function if the interactions are of sufficiently short range. As an example we consider an Ising-lattice-gas model of the two-dimensional Lennard-Jones system and find good agreement, outside the melting region, with computer simulations.

Isothermal molecular-dynamics calculations.

We have performed long-time runs of molecular-dynamics computer simulations of a two-dimensional Lennard-Jones system, without any scaling procedure. The thermodynamic properties show spontaneous fluctuations except when the system is far from the melting zone.

Monte Carlo Simulation of Growth of Crystalline and Amorphous Silicon

ABSTRACTThe authors have previously introduced a method, based on Monte Carlo techniques, for simulation of crystal growth processes in a continuous space. We have applied the method, initially used to simulate growth of two-dimensional Lennard-Jones systems, to treat growth of silicon in three dimensions. The interaction model for silicon is taken to be the recently introduced Stillinger-Weber (S-W) potential, which is a two- and threebody classical potential. Although the early stages of growth seem to be well modelled by the S-W potential, growth of even a single monolayer of epitaxial (111) silicon does not seem to be possible. Modifications to the S-W potential were considered, and found to be unacceptable physically. More accurate treatment of non-ideal atomic configuration energies is necessary to arrive at physically realistic growth simulations.