Limits to the Validity of Thermal-Pressure Equations of State

Abstract

Thermal-pressure Equations of State (EoS) such as the Mie-Grüneisen-Debye (MGD) model depend on several assumptions, including the quasi-harmonic approximation (QHA) and a simplified phonon density of states. We show how the QHA is violated by materials exhibiting anisotropic thermal pressure. We also show that at pressures lower than those of the isochor of the reference volume, the static pressure may become sufficiently negative to make the compressional part of the EoS invalid. This limit is sensitive to the combined effects of the EoS parameters K’0, q and the Grüneisen parameter γ0. Large values of q, which correspond to a rapid decrease in phonon mode frequencies with increasing volume, can also lead to the bulk modulus becoming zero at high pressures and temperatures that are not particularly extreme for planetary geotherms. The MGD EoS therefore has an extremely limited P and T regime over which it is both valid and has physically-meaningful properties. Outside of this range, additional terms should be included in the thermal pressure that represents the physical properties of the solid. Or, alternatively, ‘isothermal’ EoS in which the temperature variation of the elastic properties is explicitly modeled without reference to a physical model can be used.