A modified substitutional solution model for describing thermal vacancies

Abstract

Thermal vacancies are critical structural defects in metals, significantly influencing various material properties, such as diffusivity and thermal conductivity. The Compound Energy Formalism (CEF) has been extensively utilized to describe phases with sublattices. However, researchers have yet to reach a consensus on determining the molar Gibbs energies of vacancies, even when employing the substitutional solution model (SSM) as a single-sublattice CEF model. This is due to challenges in assigning physically meaningful values to the molar Gibbs energy of vacancies without encountering issues such as multiple equilibrium vacancy concentrations and phase stability. In this study, we propose a modified SSM (mSSM) to provide a physically consistent description of vacancies. A comprehensive comparison between the SSM and mSSM is presented. The mSSM allows the molar Gibbs energy of vacancies to be assigned physically meaningful values and enables the derivation of a unique analytical solution for the equilibrium vacancy concentration. It is applied to the FCC phase of the Cu-Ni system to accurately predict vacancy formation energies. Notably, parameters previously determined using the SSM can be directly applied in the mSSM, yielding close results at equilibrium. When vacancies are excluded, the mSSM reduces to the SSM. However, it is advisable to reoptimize parameters related to vacancies in the mSSM, such as the positive molar Gibbs energy of vacancies, to obtain physically meaningful results.