Azat O. Tipeev

Crystal nucleation rate isotherms in Lennard-Jones liquids

We present the results of molecular dynamics simulations of the crystal nucleation rate in a supercooled Lennard-Jones liquid. The nucleation rate as a function of the pressure has been calculated by the method of determining the expectation time for liquid crystallization at temperatures higher than that of the triple point (T(*) = 0.865), close to the temperature of the terminal critical point of the metastable extension of the melting curve (T(*) = 0.55) and below this temperature (T(*) = 0.4). In computer experiments the nucleation rate varied from 10(32) to 10(35) s(-1) m(-3). The dimensions of critical nuclei and the pressure inside them, the surface free energy at a critical crystal nucleus-liquid interface, the height of the nucleation barrier, and the Zeldovich factor have been determined from the results of molecular dynamics simulations and their comparison with classical homogeneous nucleation theory. It is shown that the surface free energy at a curved crystal-liquid interface, as distinct from a flat interface, has also been determined at temperatures lower than the temperature of the terminal critical point of the melting curve and is a monotonically increasing function of the temperature.

Crystal nucleation and the solid–liquid interfacial free energy

We present the results of molecular dynamics simulation of crystal nucleation in a supercooled Lennard-Jones liquid. Temperature and baric dependences of the nucleation rate, the Zeldovich factor, nucleus size diffusion coefficient, the radius, and the pressure in a critical crystal nucleus are defined in computer simulation. The data obtained have been used in the framework of classical nucleation theory to calculate the effective surface energy of crystal nuclei γ(e). It is shown that the value of γ(e) at T = const exceeds the value of the interfacial free energy at a flat crystal-liquid interface γ(∞) and γ(e) < γ(∞) at p = const.

Temperature dependence of the crystal-liquid interfacial free energy and the endpoint of the melting line

The crystal-liquid interfacial free energy γ has been calculated as a function of the crystal orientation in a molecular dynamics experiment in a system of Lennard-Jones (LJ) particles with a cutoff radius of the potential rc(*)=rc/σ=6.78 at a triple-point temperature Tt(*)=kBTt/ε=0.692 and temperatures above (in the region of the stable coexistence of liquid and solid phases) and below (metastable continuation of the coexistence curve of liquid and solid phases) the temperature Tt(*). At T(*)=Tt(*), for determining γ use was made of the method of cleaving potential. The temperature dependence of γ on the crystal-liquid coexistence curve has been determined by the Gibbs-Cahn thermodynamic integration method. In the region of stable phase coexistence (T(*)>Tt(*)) good agreement with the data of Davidchack and Laird [J. Chem. Phys. 118, 7651 (2003)] has been obtained with respect to the character of the temperature dependence of γ and the orientation anisotropy. In the region of metastable phase coexistence (T(*)<Tt(*)) at the approach to the endpoint of the melting line (TK(*)=0.529) (the existence of which was established first by Baidakov and Protsenko [Phys. Rev. Lett. 95, 015701 (2005)]) the interfacial free energy decreases, approaching at T(*)=TK(*) the orientation-averaged value γ0K(*)=γ0Kσ(2/ε)=0.365. The paper discusses the behavior of the excess interfacial energy, excess interfacial entropy and excess interfacial stress on the metastable extension of the melting line and close to T(*)=TK(*).

Nucleation of liquid droplets and voids in a stretched Lennard-Jones fcc crystal

The method of molecular dynamics simulation has been used to investigate the phase decay of a metastable Lennard-Jones face-centered cubic crystal at positive and negative pressures. It is shown that at high degrees of metastability, crystal decay proceeds through the spontaneous formation and growth of new-phase nuclei. It has been found that there exists a certain boundary temperature. Below this temperature, the crystal phase disintegrates as the result of formation of voids, and above, as a result of formation of liquid droplets. The boundary temperature corresponds to the temperature of cessation of a crystal-liquid phase equilibrium when the melting line comes in contact with the spinodal of the stretched liquid. The results of the simulations are interpreted in the framework of classical nucleation theory. The thermodynamics of phase transitions in solids has been examined with allowance for the elastic energy of stresses arising owing to the difference in the densities of the initial and the forming phases. As a result of the action of elastic forces, at negative pressures, the boundary of the limiting superheating (stretching) of a crystal approaches the spinodal, on which the isothermal bulk modulus of dilatation becomes equal to zero. At the boundary of the limiting superheating (stretching), the shape of liquid droplets and voids is close to the spherical one.

Surface free energy of the crystal-liquid interface on the metastable extension of the melting curve

The surface free energy γ, excess surface energy e, and excess surface stress τ at the crystal-liquid interface of a Lennard-Jones system have been determined by molecular dynamics simulation. The calculations have been performed for temperatures both above and below the triple-point temperature for the region where each of the coexisting phases is metastable and is at a negative pressure. The asymptotic behavior of γ, e, and τ has been analyzed near the endpoint of the melting curve, which is a point of the contact of the metastable extension of the melting curve and the spinodal of the stretched liquid [V.G. Baidakov and S.P. Protsenko, Phys. Rev. Lett. 95, 015701 (2005)]. It has been found that γ, e, and τ at this point are finite and the excess surface entropy is zero.

Evaluation of metastable region boundaries for liquid and solid states in MD simulations

An automatic method based on MD simulations was developed for detecting and tracing the boundaries of metastable states of superheated crystal and supercooled liquid. The main criterion of the detection of early nucleation of new phase is the self-diffusion coefficient temperature dependence. The scanning for nucleation events is performed at continuous temperature change. The set of independent nucleation events at a given pressure allows evaluation of temperature dependence of specific nucleation frequency. The collection of a large number of these calculations allows accurate approximation of pressure and temperature dependence of the specific nucleation frequency in both directions between phases. This dependence allows estimating the behavior of the free energy in the region between superheating and supercooling curves. In addition, dependence of nucleation frequency on pressure and temperature provides an opportunity to integrate the probability of nucleation under dynamic loading and subsequent release and thus to determine the likelihood of the crystallization and melting. The technique was applied to tin. MD simulation was carried out with the help of the EAM interatomic potential, well reproducing the properties of BCC phase.