Computing the absolute Gibbs free energy in atomistic simulations: Applications to defects in solids

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, so the potential energy of a system is often used as a proxy. In this paper, we use a combination of thermodynamic integration methods to accurately evaluate the Gibbs free energies associated with defects in crystals, including the vacancy formation energy in bcc iron, and the stacking fault energy in fcc nickel, iron, and cobalt. We quantify the importance of entropic and anharmonic effects in determining the free energies of defects at high temperatures, and show that the potential energy approximation as well as the harmonic approximation may produce inaccurate or even qualitatively wrong results. Our calculations manifest the necessity to employ accurate free energy methods such as thermodynamic integration to estimate the stability of crystallographic defects at high temperatures.