Extension of finite-strain equations of state to ultra-high pressure

Abstract

Eulerian and Lagrangian finite-strain expansions are extended into the ultra-high pressure range by way of an isothermal closed-form EoS, a broken power-law density depending on four parameters determined by least-squares regression. The EoS is put to test with high-pressure data sets of copper up to 60 TPa and can be used to extrapolate data sets obtained in the GPa range to ultra-high densities approaching the Thomas-Fermi free-electron regime. In the low and intermediate pressure range up to a few hundred GPa, the EoS admits finite-strain ascending series expansions, which coincide with the third-, fourth- and fifth-order Birch-Murnaghan and Lagrangian EoSs, subject to the finite-strain expansion parameter used. The pressure evolution of the compression modulus of copper is obtained from the regressed EoS. A closed-form expression of the free energy over the full pressure range up to the Thomas-Fermi limit is derived and compared with finite-strain theory.