Ruslan L. Davidchack

Direct calculation of the hard-sphere crystal/melt interfacial free energy

We present a direct calculation by molecular-dynamics computer simulation of the crystal/melt interfacial free energy gamma for a system of hard spheres of diameter sigma. The calculation is performed by thermodynamic integration along a reversible path defined by cleaving, using specially constructed movable hard-sphere walls, separate bulk crystal, and fluid systems, which are then merged to form an interface. We find the interfacial free energy to be slightly anisotropic with gamma = 0.62+/-0.01, 0.64+/-0.01, and 0. 58+/-0.01k(B)T/sigma(2) for the (100), (110), and (111) fcc crystal/fluid interfaces, respectively. These values are consistent with earlier density functional calculations and recent experiments.

Direct calculation of the crystal–melt interfacial free energies for continuous potentials: Application to the Lennard-Jones system

Extending to continuous potentials a cleaving wall molecular dynamics simulation method recently developed for the hard-sphere system [Phys. Rev. Lett. 85, 4751 (2000)], we calculate the crystal–melt interfacial free energies, γ, for a Lennard-Jones system as functions of both crystal orientation and temperature. At the triple point, T*=0.617, the results are consistent with an earlier cleaving potential calculation by Broughton and Gilmer [J. Chem. Phys. 84, 5759 (1986)], however, the greater precision of the current calculation allows us to accurately determine the anisotropy of γ. From our data we find that, at all temperatures studied, γ111<γ110<γ100. A comparison is made to the results from our previous hard-sphere calculation and to recent results for Ni by Asta, Hoyt, and Karma [Phys. Rev. B 66 100101(R) (2002)].

Simulation of the hard-sphere crystal-melt interface

In this work, we examine in detail the structure and dynamics of the face-centered cubic (100) and (111) crystal–melt interfaces for systems consisting of approximately 104 hard spheres using molecular dynamics simulation. A detailed analysis of the data is performed to calculate density, pressure, and stress profiles (on both fine and coarse scales), as well as profiles for the diffusion and orientational ordering. The strong dependence of the coarse-grained profiles on the averaging procedure is discussed. Calculations of 2-D density contours in the planes perpendicular to the interface show that the transition from crystal to fluid occurs over a relatively narrow region (over only 2–3 crystal planes) and that these interfacial planes consist of coexisting crystal- and fluidlike domains that are quite mobile on the time scale of the simulation. We also observe the creation and propagation of vacancies into the bulk crystal.

The anisotropic hard-sphere crystal-melt interfacial free energy from fluctuations

We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/-0.02k(B)Tsigma(-2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inverse-power potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].

Determination of the solid-liquid interfacial free energy along a coexistence line by Gibbs-Cahn integration

We calculate the solid-liquid interfacial free energy gamma(sl) for the Lennard-Jones (LJ) system at several points along the pressure-temperature coexistence curve using molecular-dynamics simulation and Gibbs-Cahn integration. This method uses the excess interfacial energy (e) and stress (tau) along the coexistence curve to determine a differential equation for gamma(sl) as a function of temperature. Given the values of gamma(sl) for the (100), (110), and (111) LJ interfaces at the triple-point temperature (T( *)=kT/varepsilon=0.618), previously obtained using the cleaving method by Davidchack and Laird [J. Chem. Phys. 118, 7657 (2003)], this differential equation can be integrated to obtain gamma(sl) for these interfaces at higher coexistence temperatures. Our values for gamma(sl) calculated in this way at T( *)=1.0 and 1.5 are in good agreement with those determined previously by cleaving, but were obtained with significantly less computational effort than required by either the cleaving method or the capillary fluctuation method of Hoyt, Asta, and Karma [Phys. Rev. Lett. 86, 5530 (2001)]. In addition, the orientational anisotropy in the excess interface energy, stress and entropy, calculated using the conventional Gibbs dividing surface, are seen to be significantly larger than the relatively small anisotropies in gamma(sl) itself.

Hard spheres revisited: Accurate calculation of the solid–liquid interfacial free energy

We revise the earlier [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)] direct calculation of the hard sphere solid-liquid interfacial free energy by the cleaving walls method. The revisions of the method include modified interactions with the cleaving walls and the use of a nonequilibrium work measurements approach, which allows for a more robust control of the accuracy of the obtained results. We find that the new values are lower compared to the original ones, which is consistent with the more recent indirect estimates based on extrapolation from the soft-sphere results [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)], as well as those obtained using the capillary fluctuations method [R. L. Davidchack, J. R. Morris, and B. B. Laird, J. Chem. Phys. 125, 094710 (2006)].

Towards complete detection of unstable periodic orbits in chaotic systems

Abstract We present a rigorous analysis and numerical evidence indicating that a recently developed methodology for detecting unstable periodic orbits is capable of yielding all orbits up to periods limited only by the computer precision. In particular, we argue that an efficient convergence to every periodic orbit can be achieved and the basin of attraction can be made finite and accessible for typical or particularly chosen initial conditions.

Langevin thermostat for rigid body dynamics

We present a new method for isothermal rigid body simulations using the quaternion representation and Langevin dynamics. It can be combined with the traditional Langevin or gradient (Brownian) dynamics for the translational degrees of freedom to correctly sample the canonical distribution in a simulation of rigid molecules. We propose simple, quasisymplectic second-order numerical integrators and test their performance on the TIP4P model of water. We also investigate the optimal choice of thermostat parameters.

Calculation of the interfacial free energy of a fluid at a static wall by Gibbs–Cahn integration

The interface between a fluid and a static wall is a useful model for a chemically heterogeneous solid-liquid interface. In this work, we outline the calculation of the wall-fluid interfacial free energy (gamma(wf)) for such systems using molecular simulation combined with adsorption equations based on Cahns extension of the surface thermodynamics of Gibbs. As an example, we integrate such an adsorption equation to obtain gamma(wf) as a function of pressure for a hard-sphere fluid at a hard wall. The results so obtained are shown to be in excellent agreement in both magnitude and precision with previous calculations of this quantity, but are obtained with significantly lower computational effort.

Ice Ih–Water Interfacial Free Energy of Simple Water Models with Full Electrostatic Interactions

We employ the cleaving approach to calculate directly the ice Ih-water interfacial free energy for the simple models of water, TIP4P, TIP4P-Ew, and TIP5P-E, with full electrostatic interactions evaluated via the Ewald sums. The results are in good agreement with experimental values, but lower than previously obtained for TIP4P-Ew and TIP5P-E by indirect methods. We calculate the interfacial free energies for basal, prism, and {112̅0} interfaces and find that the anisotropy of the TIP5P-E model is different from that of the TIP4P models. The effect of including full electrostatic interactions is determined to be smaller than 10% compared to the water models with damped Coulomb interactions, which indicates that the value of the ice-water interfacial free energy is determined predominantly by the short-range packing interaction between water molecules. We also observe a strong linear correlation between the interfacial free energy and the melting temperature of different water models.