A wide-range equation of state for tin constrained by first-principles phonon calculations

A wide-range equation of state (EOS) for tin is essential for radiation-hydrodynamic modeling of the complex evolution of tin droplets and for predicting the radiative output of extreme-ultraviolet light sources. We develop a computationally efficient wide-range EOS for tin by expressing the Helmholtz free energy as the sum of ionic, electronic, and semiempirical bonding-correction contributions. Material-specific vibrational information from first-principles phonon calculations based on density functional theory is used to determine and calibrate key parameters of the ionic contribution, including the Debye temperature and the Grüneisen parameter. The resulting EOS captures the overall trends of the room-temperature isotherm and principal Hugoniot of tin. It, therefore, provides a practical EOS for rapid evaluation of thermodynamic properties and for related numerical simulations over a wide range of conditions.