Tomaschitz,
R. (2021). Extension of finite-strain equations of state to ultra-high
pressure, *Physics Letters *A* ***393**, 127185, DOI: 10.1016/j.physleta.2021.127185

**Abstract **ScienceDirect

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.

description:
Roman Tomaschitz (2021) Extension of finite-strain equations of state to
ultra-high pressure, *Phys. Lett. *A* ***393**, 127185.

**Keywords:**
Ultra-high pressure equation of state (EoS) for solids; Eulerian and Lagrangian
finite-strain expansions; Compression modulus and free energy; Broken power-law
densities; Least-squares regression of the EoS of copper; Birch-Murnaghan EoS

**Highlights**

A four-parameter equation of state (EoS) is proposed for solids, extending finite-strain expansions into the ultra-high pressure regime.

The isothermal EoS, a broken power-law density, is tested with high-pressure data sets of copper, covering pressures up to 60 TPa.

The range of applicability of Eulerian and Lagrangian finite-strain expansions of the EoS is determined.

The third-, fourth- and fifth-order Birch-Murnaghan EoSs are recovered from the Eulerian finite-strain expansion of the EoS.

A closed-form expression of the free energy of copper is obtained, applicable over the full pressure range up to the Thomas-Fermi limit.

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