Free energy of the Lennard-Jones solid

Phase diagram of the Weeks-Chandler-Andersen potential from very low to high temperatures and pressures

A combination of two molecular simulation algorithms has been used to determine the solid-liquid coexistence of the Weeks-Chandler-Andersen (WCA) fluid from low temperatures up to very high temperatures. Values are reported for the coexistence pressure, temperature, energy, enthalpy change, and densities of both the liquid and solid phases. At very high temperatures, the coexistence pressure approaches the same 12th-power soft-sphere asymptote as the 12-6 Lennard-Jones potential. However, in contrast to the Lennard-Jones potential, which shows a discontinuity of pressure at low temperatures, the coexistence pressure of the WCA potential approaches the zero-temperature limit. Empirical relationships are determined to accurately reproduce the coexistence pressure and both solid and liquid phase densities from near zero temperature to very high temperatures. The simulation data are used to improve the accuracy of a WCA equation of state. The validity of common melting and freezing rules is tested.

Universal scaling law for energy and pressure in a shearing fluid

Using nonequilibrium molecular-dynamics simulation, we study the shear-rate dependence of pressure and potential energy in a liquid metal subjected to shear. We show that both thermodynamic properties vary according to a power law gamma[over ];{beta} of the shear rate gamma[over ] , in which the exponent beta is a simple linear function of temperature and density. Moreover, we establish that the coefficients for this linear law are the same as those previously obtained for a Lennard-Jones fluid by Ge [Phys. Rev. E 67, 061201 (2003)]. This is a strong indication that these coefficients, as well as the linear law for beta , could be applicable to any atomic fluid. It is also an important step toward the determination of a nonequilibrium equation of state, which would predict the value of pressure and energy of a shearing fluid for any state point and any value of the applied shear rate.

Monte Carlo simulation in the isobaric-multithermal ensemble of a bulk Lennard-Jones fluid system: thermodynamic quantities for pressure from P{ *}=2.42 to 7.25

A Monte Carlo (MC) simulation in the isobaric-multithermal (MuTh) ensemble has been carried out for a bulk Lennard-Jones fluid system that consists of 108 particles. The MuTh weight factor which we determined turned out to be reliable for the temperature and pressure range from (T{ *},P{ *})=(T_{0}{ *},P_{0}{ *})=(2.09,7.25) to (T{ *},P{ *})=(0.417,1.45) along P{ *}/T{ *}=P_{0}{ *}/T_{0}{ *} . Thermodynamic quantities calculated from the MuTh MC production run by the reweighting techniques showed the discontinuous change, which is the feature of the first-order phase transition. The radial distribution functions suggest that the transition takes place between liquid and solid states. Two distinct local maxima were observed in the obtained contour representations of the probability distribution at T{ *}=1.04 and P{ *}=3.63 , which is the phase transition point along P{ *}/T{ *}=P_{0}{ *}/T_{0}{ *} .

Melting line of the Lennard-Jones system, infinite size, and full potential

Literature estimates of the melting curve of the Lennard-Jones system vary by as much as 10%. The origin of such discrepancies remains unclear. We present precise values for the Lennard-Jones melting temperature, and we examine possible sources of systematic errors in the prediction of melting points, including finite-size and interaction-cutoff effects. A hypothetical thermodynamic integration path is used to find the relative free energies of the solid and liquid phases, for various system sizes, at constant cutoff radius. The solid-liquid relative free energy and melting temperature scale linearly as the inverse of the number of particles, and it is shown that finite-size effects can account for deviations in the melting temperature (from the infinite-size limit) of up to 5%. An extended-ensemble density-of-states method is used to determine free energy changes for each phase as a continuous function of the cutoff radius. The resulting melting temperature predictions exhibit an oscillatory behavior as the cutoff radius is increased. Deviations in the melting temperature (from the full potential limit) arising from a finite cutoff radius are shown to be of comparable magnitude as those resulting from finite-size effects. This method is used to identify melting temperatures at five different pressures, for the infinite-size and full potential Lennard-Jones system. We use our simulation results as references to connect the Lennard-Jones solid equation of state of van der Hoef with the Lennard-Jones fluid equation of state of Johnson. Once the references are applied the two equations of state are used to identify a melting curve. An empirical equation that fits this melting curve is provided. We also report a reduced triple point temperature T(tr)=0.694.

Characteristic temperatures of glassy behaviour in a simple liquid

A model for the metastable liquid in terms of holes present in the amorphous structure is considered using the classical density functional theory (DFT). For a one component Lennard-Jones liquid we obtain the temperature dependence of the free volume v(f) in the metastable state. A temperature T(0), similar to that of the characteristic transition of the free volume theory, is identified by extrapolating v(f)(T) to zero. The Kauzmann temperature T(K) is also obtained here by extrapolating the entropy difference between the supercooled state and that of the crystal to zero. We compare the temperatures T(0) and T(K) obtained in our model with other two characteristic temperatures for glassy behaviour, namely (a) the dynamic transition temperature T(c) of the mode coupling theory (MCT) and (b) the glass transition temperature T(g) which was obtained by Leonardo et al (2000 Phys. Rev. Lett. 84 6054) from studying the violation of the fluctuation-dissipation theorem. All the four temperatures, obtained from independent routes, are located with respect to the melting temperature T(m) in a manner which is in agreement with experiments.

Controlling polymorphism during the crystallization of an atomic fluid

We use molecular dynamics simulations to shed light on polymorph selection during the crystallization of the Lennard-Jones fluid. By varying pressure at fixed supercooling, we form large crystallites either of the stable face centered cubic form or of the metastable body centered cubic form and even fine-tune the fractions of stable and metastable polymorphs in the crystallite. We demonstrate that the conditions of crystallization, leading to large bcc crystallites, lie within the occurrence domain of the metastable bcc polymorph. We also find that the predominantly fcc crystallites contain a notable amount of the hexagonal close packed form, due to the cross nucleation of the hcp form on the fcc form. By varying temperature at fixed pressure, we prevent cross nucleation and form pure fcc crystallites. Our results reveal that polymorph selection may take place, and be controlled, during the growth step.

Molecular Simulation of Cross-Nucleation between Polymorphs

Recent experiments report that an early nucleating crystalline structure (or polymorph) may nucleate another polymorph. We use molecular dynamics simulations to model this phenomenon known as cross-nucleation. We study the onset of crystallization in a liquid of Lennard-Jones particles cooled at a temperature 22% below the melting temperature. We show that growth proceeds through the successive cross-nucleation of the metastable hexagonal close-packed (hcp) polymorph on the stable face-centered cubic (fcc) polymorph and of the stable fcc polymorph on the metastable hcp polymorph. This finding is in agreement with the experimental results which demonstrated that the cross-nucleation of a stable polymorph on a metastable polymorph is just as likely as the cross-nucleation of a metastable polymorph on a stable polymorph. We then extend our findings established in the case of the homogeneous crystal nucleation to a situation of practical interest, i.e., when a seed of the stable polymorph is used. By studying the crystal growth from the (111) plane of a perfect fcc crystal, we show that, again, growth proceeds through the cross-nucleation of the hcp and fcc structures.

Molecular Mechanism for the Cross-Nucleation between Polymorphs

We use molecular simulations to study the early stages of crystallization in a supercooled liquid of Lennard-Jones particles. We observe the onset of concomitant polymorphism and demonstrate that this phenomenon results from the cross-nucleation of a metastable polymorph on the stable polymorph. We also show that cross-nucleation is selective as it only takes place between polymorphs of almost equivalent free energy. Our simulations provide detailed insights into the molecular mechanism underlying concomitant polymorphism and cross-nucleation between polymorphs.

Interplay between structure and size in a critical crystal nucleus

We study the kinetics of crystal nucleation of an undercooled Lennard-Jones liquid using various path-sampling methods. We obtain the rate constant and elucidate the pathways for crystal nucleation. Analysis of the path ensemble reveals that crystal nucleation occurs along many different pathways, in which critical solid nuclei can be small, compact, and face centered cubic, but also large, less ordered, and more body centered cubic. The reaction coordinate thus includes, besides the cluster size, also the quality of the crystal structure.

Toward a robust and general molecular simulation method for computing solid-liquid coexistence

A rigorous and generally applicable method for computing solid-liquid coexistence is presented. The method overcomes some of the technical difficulties associated with other solid-liquid simulation procedures and can be implemented within either a molecular dynamics or Monte Carlo framework. The method consists of three steps: First, relative Gibbs free energy curves are created for the solid and liquid phases using histogram reweighting. Next, the free energy difference between the solid and liquid phases is evaluated at a single state point by integrating along a pseudosupercritical transformation path that connects the two phases. Using this result, the solid and liquid free energy curves are referenced to a common point, allowing a single coexistence point to be determined. Finally, Gibbs-Duhem integration is used to determine the full coexistence curve. To evaluate its utility, this method is applied to the Lennard-Jones and NaCl systems. Results for solid-liquid coexistence agree with previous calculations for these systems. In addition, it is shown that the NaCl model does not correctly describe solid-liquid coexistence at high pressures. An analysis of the accuracy of the method indicates that the results are most sensitive to the transformation free energy calculation.

Dislocation nucleation in shocked fcc solids: effects of temperature and preexisting voids

Quantitative behaviors of shock-induced dislocation nucleation are investigated by means of molecular dynamics simulations on fcc Lennard-Jones solids: a model argon. In perfect crystals, it is found that the Hugoniot elastic limit (HEL) is a linearly decreasing function of temperature: from near-zero to melting temperatures. In a defective crystal with a void, dislocations are found to nucleate on the void surface. Also, HEL drastically decreases to 15% of the perfect crystal when the void radius is 3.4 nanometers. The decrease of HEL becomes larger as the void radius increases, but HEL becomes insensitive to temperature.

Computer simulation study of the global phase behavior of linear rigid Lennard-Jones chain molecules: Comparison with flexible models

The global phase behavior (i.e., vapor-liquid and fluid-solid equilibria) of rigid linear Lennard-Jones (LJ) chain molecules is studied. The phase diagrams for three-center and five-center rigid model molecules are obtained by computer simulation. The segment-segment bond lengths are L = sigma, so that models of tangent monomers are considered in this study. The vapor-liquid equilibrium conditions are obtained using the Gibbs ensemble Monte Carlo method and by performing isobaric-isothermal NPT calculations at zero pressure. The phase envelopes and critical conditions are compared with those of flexible LJ molecules of tangent segments. An increase in the critical temperature of linear rigid chains with respect to their flexible counterparts is observed. In the limit of infinitely long chains the critical temperature of linear rigid LJ chains of tangent segments seems to be higher than that of flexible LJ chains. The solid-fluid equilibrium is obtained by Gibbs-Duhem integration, and by performing NPT simulations at zero pressure. A stabilization of the solid phase, an increase in the triple-point temperature, and a widening of the transition region are observed for linear rigid chains when compared to flexible chains with the same number of segments. The triple-point temperature of linear rigid LJ chains increases dramatically with chain length. The results of this work suggest that the fluid-vapor transition could be metastable with respect to the fluid-solid transition for chains with more than six LJ monomer units.

Entropic effects on the size dependence of cluster structure

We show that the vibrational entropy can play a crucial role in determining the equilibrium structure of clusters by constructing structural phase diagrams showing how the structure depends upon both size and temperature. These phase diagrams are obtained for example rare gas and metal clusters.