Structure–Property Relations in Pb-Supersaturated Metastable Sn-Rich Pb-Sn Alloys

We have performed a theoretical study of three polymorphs of Pb-supersaturated Sn-rich Pb-Sn alloys with the \(\alpha \) $\alpha$ -Sn, \(\beta \) $\beta$ -Sn, and a simple-hexagonal \(\gamma \) $\gamma$ -Sn structure employing quantum-mechanical calculations. We focused on structure–property relations in the case of lattice parameters, thermodynamic stability, elastic properties, and mechanical stability as well as electronic-structure density of states. Compositional trends in structural, thermodynamic, and electronic properties were found nearly linear. Our study also sheds new light on a decades-long controversy surrounding the existence of \(\gamma \) $\gamma$ -phase and \(\beta \) $\beta$ -phase supersaturated Sn-rich Pb-Sn alloys. We suggest that the experimental difficulties when synthesizing them are caused by their high formation energy and mechanical instability of the \(\beta \) $\beta$ -phase.