Computing the Absolute Gibbs Free Energy in Atomistic Simulations: Applications to Defects in Solids

TL;DR

This paper presents a thermodynamic integration method to accurately compute the absolute Gibbs free energy in atomistic simulations, accounting for entropic and anharmonic effects, with applications to defects in solids.

Contribution

It introduces a novel approach combining thermodynamic routes to directly calculate free energies of solids from a harmonic reference, improving defect energy estimates.

Findings

Overestimation of vacancy free energy by 60% using potential energy alone.

Stacking-fault energy overestimated by nearly 300% without proper free energy calculation.

Method enables direct comparison of free energies between different solid structures.

Abstract

The Gibbs free energy is the fundamental thermodynamic potential underlying the relative stability of different states of matter under constant-pressure conditions. However, computing this quantity from atomic-scale simulations is far from trivial. As a consequence, all too often the potential energy of the system is used as a proxy, overlooking entropic and anharmonic effects. Here we discuss a combination of different thermodynamic integration routes to obtain the absolute Gibbs free energy of a solid system starting from a harmonic reference state. This approach enables the direct comparison between the free energy of different structures, circumventing the need to sample the transition paths between them. We showcase this thermodynamic integration scheme by computing the Gibbs free energy associated with a vacancy in BCC iron, and the intrinsic stacking fault free energy of nickel. These examples highlight the pitfalls of estimating the free energy of crystallographic defects only using the minimum potential energy, which overestimates the vacancy free energy by 60% and the stacking-fault energy by almost 300% at temperatures close to the melting point.