Multiphase equation of state for lead: adjustment by the maximum likelihood estimation approach and variations in the liquid

In this study, we propose a new multiphase EoS for lead consisting of one solid phase and one liquid phase.

To this purpose, we built a calibration database containing static high-pressure, shock, ambient and ab initio data with uncertainties. To adjust parameters in each phase, we used the POOH code [1] developed by CEA and based on maximum likelihood estimation (MLE).

Solid EoS is classical whereas the fluid phase modelisation is more tricky. The inconsistency observed between different liquid Cp​ values obtained with various measurement techniques led us to perform ab initio calculations to assess the theoretical data at 1 bar for the liquid (Cp​, dilatation, enthalpy). Ab initio uncertainties account for statistical errors and computational choices (XC, SOC, PAW). These ab initio results were integred into the calibration database. We also explored different liquid models (solid-gas interpolation and Correa model). Thanks to the MLE approach, different EoS have been proposed, which highlights the robustness and the versatility of our approach. We show the quality of the restitution of the database for each variation of EoS.

[1] G. Robert, V. Dubois, and P. Legrand, "Using maximum likelihood estimation approach to adjust parameters of multiphase equations of state: Molybdenum as an example", Journal of Applied Physics 131, 105901 (2022) https://doi.org/10.1063/5.0081299