Molecular dynamics investigation on complete Mie-Grüneisen equation of state: Al and Pb as prototypes

Abstract Molecular dynamics (MD) simulations are carried out to comprehensively investigate the Hugoniot curve, isotherms, isentropes, and internal energy, as well as the Mie-Gruneisen equation of state (EOS) for single-crystal Al and Pb via multi-scale shock technology (MSST) in the open source software Large-scale Atomic/Molecular Massively Parallel Simulator, or LAMMPS. The temperatures (TH and TS) along the Hugoniot curve and isentrope, the entropy increment (ΔSH) along the Hugoniot curve, and the Gruneisen coefficient γ are calculated and discussed based on the linear relation of shock wave velocity and particle velocity. Meanwhile, based on the assumptions that γ is only a function of the specific volume V and the specific heat cV = constant, the typical incomplete Mie-Gruneisen EOS is thermodynamically extended to the complete equations of state (EOSs) utilizing the Hugoniot relation as the reference curve at pressures up to 300 GPa. The incomplete and complete Mie-Gruneisen EOSs show a concave surface in the pressure-specific volume-internal energy (P–V-E), pressure-specific volume-shock Hugoniot temperature (P–V-TH), and pressure-specific volume-entropy increment (P–V-ΔSH) spaces.