Abstract
We propose an approach for computing the Gibbs free energy difference between phases of a material. The method is based on the determination of the average force acting on interfaces that separate the two phases of interest. This force, which depends on the Gibbs free energy difference between the phases, is computed by applying an external harmonic field that couples to a parameter which specifies the two phases. Validated first for the Lennard-Jones model, we demonstrate the flexibility, efficiency and practical applicability of this approach by computing the melting temperatures of sodium, magnesium, aluminum and silicon at ambient pressure using density functional theory. Excellent agreement with experiment is found for all four elements, except for silicon, for which the melting temperature is, in agreement with previous simulations, seriously underestimated.
Highlights
An accurate location of first-order transition lines at a reasonable computational cost is of paramount importance for a wide spectrum of condensed matter systems, ranging from hard to soft materials and biological matter
Basic principles of equilibrium thermodynamics imply that for a given temperature and pressure the system resides in the phase of lowest Gibbs free energy
From the computational point of view, the task of evaluating a phase diagram represents a significant challenge, as phase transitions occur on long time scales1 such that they cannot be studied using straightforward molecular dynamics or Monte Carlo simulations
Summary
The basic idea of this approach is to compute the average force required to pin the interface of a two-phase system via a harmonic bias potential This external field couples to a suitably defined order parameter Q, which. The application of the bias potential effectively transforms the out-of-equilibrium process of the conventional moving-interface method into a well-defined equilibrium computation, in which the free energy difference G is determined directly. Method (i) fails, since most density functional theory codes yield diverging Coulomb and electronic energies, when two atoms are at the same position in space, whereas approach (ii) is suitable only when reliable model potentials exist Such potentials are, not available for materials with short- and medium-range order in the liquid, such as P, Sb, chalcogenides, and binary systems (oxides, nitrides, zintl alloys), explaining the astoundingly small number of melting-point calculations using ab initio density functional theory.
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