Density-functional theory of crystal-melt interfaces.

Abstract

The equilibrium structure and energetics of the crystal-melt interfaces of simple systems are studied using the nonlocal weighted density-functional approximation (WDA) to the Helmholtz free energy. The WDA, previously used to accurately predict bulk phase coexistence at the melting point, is combined with a new flexible, two-parameter parametrization of the crystal-melt interfacial region to predict interfacial properties. The parametrization allows for variations in the width of the interface and in the rate of broadening of the sharp density peaks of the crystal through the interface at fixed width, generating physically appealing profiles similar to those observed in simulation studies. The WDA in tandem with this parametrization thus avoids the use of the perturbation and/or square-gradient expansions previously used to describe both the crystal and the interface. Applying the approach to the model hard-sphere system (diameter \ensuremath{\sigma}), the (100) and (111) fcc-liquid interfaces are found to be four atomic layers in width and nearly isotropic in surface free energy \ensuremath{\gamma}, with \ensuremath{\gamma}(100)=0.66kT/${\ensuremath{\sigma}}^{2}$ and \ensuremath{\gamma}(111)=0.63kT/${\ensuremath{\sigma}}^{2}$. These results and the general interfacial structure are in qualitative agreement with simulation studies on the similar soft-sphere (${r}^{\mathrm{\ensuremath{-}}12}$) potential system. Using a simple hard-sphere perturbation theory, the crystal-liquid phase coexistence and (111) interface of the Lennard-Jones system are also examined. Both the freezing transition and the interfacial properties are dominated by the hard-core interactions, and the predicted value of \ensuremath{\gamma}(111)=0.43\ensuremath{\varepsilon}/${\ensuremath{\sigma}}^{2}$ near the triple point is in reasonable agreement with the recent simulation result of 0.35\ensuremath{\varepsilon}/${\ensuremath{\sigma}}^{2}$. A brief comparison of the present ``liquid'' and the usual self-consistent phonon approaches to the crystal thermodynamics brings out some previously unrecognized similarities.