H.L. Tepper

Crystallization and melting in the Lennard-Jones system: Equilibration, relaxation, and long-time dynamics of the moving interface

Nonequilibrium molecular dynamics simulations have been carried out on the growth and melting of the Lennard-Jones (100) interface at small undercoolings and superheatings. Two regimes of linear growth rate were discovered: a short-time regime associated with interface relaxation and a long-time regime associated with the macroscopic limit of growth and melting. It was shown that, if system sizes or equilibration times are taken too small, one will find only the initial regime. On the basis of our very accurate results on the macroscopic growth rates close to equilibrium, the possibility of a discontinuity in the temperature dependence of growth and melting rates at the melting point was ruled out.

Transport diffusion of argon in AlPO4-5 from equilibrium molecular dynamics simulations

Transport diffusion of argon in the unidirectional channels of the molecular sieve AlPO4-5 has been studied using molecular dynamics simulations. Using the Green–Kubo formalism, this nonequilibrium property is, for the first time, extracted from just one equilibrium simulation. Apart from the computational advantages above nonequilibrium simulations, the new method also provides a way to check the validity of the assumption of linear response, which is at the basis of both methods. The transport diffusion coefficient for argon at 87 K and half the maximum loading is found to be equal to Dt = (1.4±0.1)×10–5 cm2/s, of which approximately 20% can be attributed to correlated, collective motion.

Unidirectional diffusion of methane in AlPO4-5

Tracer diffusion of methane molecules in the unidirectional channels of AlPO4-5 has been studied by means of molecular dynamics simulations. A one-dimensional hop-and-cross model is introduced and is shown to be able to reproduce the molecular dynamics results accurately and we profit by extensive speedup in computational time. After elimination of system size effects by using the new model, two regimes can be recognized: a short-time regime where the mean square displacement is proportional to t0.6, and a long-time regime where the proportionality is linear.

Simulations of crystallization and melting of the FCC (100) interface : the crucial role of lattice imperfections

We present nonequilibrium simulations of growth and melting of the atomic FCC (1 0 0) interface. Using Nose–Hoover dynamics we have carefully studied size effects and approximated the dynamics of the solid–liquid interface in a large system as closely as possible. This led to a clear asymmetry of growth and melting rates close to equilibrium. It was possible to explain these findings in terms of the lattice imperfections in crystalline phases in contact with a liquid phase, which automatically developed during growth simulations but were absent in the melting simulations. It was shown that when melting simulations were started with appropriate starting configurations, the asymmetry could be made to disappear.

Crystal growth and interface relaxation rates from fluctuations in an equilibrium simulation of the Lennard-Jones (100) crystal-melt system

The kinetic coefficient of crystallization is calculated according to a previously introduced equilibrium method [Phys. Rev. Lett. 79, 5074 (1997)]. The existence of two regimes of interface relaxation and macroscopic growth, such as they were found in previous nonequilibrium simulations, is fully confirmed by the results of the equilibrium method. Special attention is given to the relation between pressure fluctuations and fluctuations of the amount of crystalline material. Furthermore, we investigate the density and order parameter profiles of the interface and make a clear distinction between the instantaneous structure and the time-averaged profile which is usually presented.

Comments on the use of the Einstein equation for transport diffusion: Application to argon in AlPO4-5

Two methods to calculate corrected collective diffusion coefficients in zeolites are compared. The meaning of the center-of-mass coordinate that occurs in the usual Einstein expression for the corrected diffusivity is discussed. The use of unfolded particle trajectories in the expression is shown to be only valid for periodic systems and only if the entire box is taken as the control volume. A wave vector-dependent Einstein expression is derived, equivalent to the Green–Kubo form that was derived in an earlier study [J. Chem. Phys. 113, 6875 (2000)]. The box size dependence of the diffusivities calculated from the usual Einstein equation is reproduced for small k-values when the new expression is applied to a large box.

Molecular dynamics calculations of melting rates with a novel order parameter: The diatomic Pa3 crystal

A method is presented to design order parameters that can be used as discriminator in two-phase crystal-liquid molecular dynamics simulations. The proposed methodology is an extension to molecular crystal structures of a previously introduced discriminator for the atomic fcc environment [Phys. Rev. Lett. 79, 5074 (1997)] and can be readily applied to any crystal structure with both translational and orientational order. As an example, the discriminator is applied to the molecular Pa3 environment and subsequently used to study crystal melting rates with a diatomic carbon dioxide potential. The systems melting temperature proves to be below the roughening transition which is exemplified by faceted growth. The dynamically corrected melting rates are easily fitted to a rate law for two-dimensional nucleation and growth from which the melting temperature is deduced. The feasibility of the method for the example system holds promise for more extensive microscopic investigations of molecular crystal growth and melting.