First-Principles Study on the Multiphase Equation of State of Tin

Metallic tin is a focal point in high-pressure physics research and a critical material of strategic importance in defense-related technologies. Due to the rich physical phases of tin, it is crucial to study the multiphase equation of state and phase boundaries of tin, whether in basic research or industrial applications. This work systematically investigates the high-temperature and high-pressure multiphase equation of state (EOS), phase boundaries, elastic modulus, sound velocities, and Hugoniot curves of tin using density functional theory (DFT) combined with the mean-field potential (MFP) method. The results not only provide the multiphase EOS of tin under extreme conditions but also demonstrate good agreement with experimental data for the β-γ phase boundary and ambient-pressure sound velocities of β-Sn. Furthermore, this study evaluates the effects of different density functionals (LDA, PBEsol, and SCAN) on the high-pressure EOS. The LDA and PBEsol functionals show superior consistency with experimental Hugoniot curves and ambient-pressure elastic moduli, while the SCAN functional exhibits larger deviations in phase boundary predictions but achieves closer agreement with experimental ambient-pressure sound velocities for β-Sn.