We present a multi-phase equation of state (EOS) for lead (Pb,
Z=82) addressing a wide range of density and temperature conditions:
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The EOS model is based on a standard decomposition of the Helmholtz free energy as a function of the specific volume and the temperature into the cold term, the ion-thermal term, and the electronic excitation term. The cold term models both the compression and the expansion states, the ion-thermal term introduces the Debye approximation and the melting entropy, and the electronic excitation term employs the Thomas–Fermi–Kirzhnits (TFK) model. The thermodynamic properties of the warm-dense lead are calculated using the extended first-principles molecular dynamics (ext-FPMD) method, up to five times compressed ambient density and 0.4 MK in temperature. Predictions are made from our EOS model for the principle Hugoniot, the room-temperature isotherm, the melting curve, and the thermodynamic properties in the warm-dense region. A systematic comparison is drawn to the experimental data, the SESAME-3200 table, and the ext-FPMD calculations. Our EOS model not only agrees with the various experimental data, but also coincides with the ext-FPMD calculations, establishing some superiority over the SESAME-3200 table in the warm-dense region. The datasets presented in this paper, including the tabular EOS consisting of internal energy and pressure at the different densities and temperatures, are openly available at https://www.doi.org/10.57760/sciencedb.j00213.00166(https://www.scidb.cn/s/3mAjeq).
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