Thermodynamic activity of solute in multicomponent alloy from first-principles: Excess Mg in Mg-3(Sb1-xBix)(2) as an example

Assessment of the thermodynamic activity and solid solubility for solute element in multi-component alloy is critical in thermodynamics, but an effective first-principles estimation of the parameter has been an unsolved issue for many years. By taking the excess Mg in Mg-3(Sb1-xBix)(2) alloy as an example, Mg atoms could occupy the regular lattice sites and the interstitial sites as well, which makes the estimation of thermodynamic activity of Mg solute not easy. In this work, we develop a model to estimate the activity and solid solubility of Mg in alloys such as Mg-3(Sb1-xBix)(2) by considering the formation energy contribution from both Mg interstitials and Mg vacancies, and the associated entropies to final Gibbs energy. Accurate assessment of the parameter by using first-principles thermodynamics approach is also realized. The estimated activity of Mg in Mg3Bi2 and Mg3Sb2 reproduce well the available experimental results. The solubility limits of Mg and equilibrium concentrations of Mg interstitials and Mg vacancies in Mg-3(Sb1-xBix)(2) are also estimated. The results could be used to understand Mg-Mg3Sb2-Mg3Bi2 phase diagram as well as the Mg effect on thermoelectric performance of Mg-3(Sb1-xBix)(2) alloy.