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

• Published in: Physics letters. A Vol. 393; p. 127185
• Main Author: Tomaschitz, Roman
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 26.03.2021
• Subjects: Birch-Murnaghan EoS; Broken power-law densities; Compression modulus and free energy; Eulerian and Lagrangian finite-strain expansions; Least-squares regression of the EoS of copper; Ultra-high pressure equation of state (EoS) for solids; Broken power-law densities; Compression modulus and free energy; Least-squares regression of the EoS of copper; Birch-Murnaghan EoS; Eulerian and Lagrangian finite-strain expansions; Ultra-high pressure equation of state (EoS) for solids
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2021.127185

•A four-parameter equation of state (EoS) is proposed for solids, applicable in the ultra-high pressure regime.•The isothermal EoS, a broken power-law density, is tested with high-pressure data sets of copper extending 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 is obtained, covering densities up to the Thomas-Fermi free-electron limit. 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.