Hugoniot States and Mie–Grüneisen Equation of State of Iron Estimated Using Molecular Dynamics

The objective of this study was to develop a micromechanical approach for determining the Mie–Gruneisen EOS parameters of iron under the Hugoniot states. The multiscale shock technique (MSST) coupled with molecular dynamics (MD) simulations was employed to describe the shocked Hugoniot relation of single-crystal (SC) and nanocrystalline (NC) iron under high pressures. The Mie–Gruneisen equation of state (EOS) parameters, the cold pressure (Pc), the cold energy (Ec), the Gruneisen coefficient (γ), and the melting temperature (Tm) are discussed. The error between SC and NC iron results was found to be less than 1.5%. Interestingly, the differences in Hugoniot state (PH) and the internal energy between SC and NC iron were insignificant, which shows that the effect of grain size (GS) under high pressures was not significant. The Pc and Ec of SC and NC iron calculated based on the Morse potential were almost the same with those calculated based on the Born–Mayer potential; however, those calculated based on the Born–Mayer potential were a little larger at high pressures. In addition, several empirical and theoretical models were compared for the calculation of γ and Tm. The Mie–Gruneisen EOSs were shown on the 3D contour space; the pressure obtained with the Hugoniot curves as the reference was larger than that obtained with the cold curves as the reference.