A single-volume approach for vacancy formation thermodynamics calculations

Abstract

The vacancy formation Gibbs free energy, enthalpy and entropy in fcc Al, Ag, Pd, Cu, and bcc Mo are determined by first-principles calculations using the quasi-harmonic approximation to account for vibrational contributions. We show that the Gibbs free energy can be determined with sufficient accuracy in a single-volume approach using the fixed equilibrium volume of the defect-free supercell. Although the partial contributions to the Gibbs free energy, namely, the formation enthalpy and entropy exhibit substantial errors when obtained directly in this approach, they can be computed from the Gibbs free energy using the proper thermodynamic relations. Compared to experimental data, the temperature dependence of the vacancy formation Gibbs free energy is accounted for at low temperatures, while it overestimates the measurements at high temperature, which is attributed to the neglect of anharmonic effects.