Thermal Pressure in the Thermal Equation of State for Solid and a Proposed Substitute

Abstract

The thermal equation of state (TEOS) for solids is a mathematic model among pressure, temperature and density, and is essential for geophysical, geochemical, and other high pressure–temperature (high P–T) researches. However, in the last few decades, there has been a growing concern about the accuracy of the pressure scales of the calibrants, and efforts have been made to improve it by either introducing a reference standard or building new thermal pressure models. The existing thermal equation of state, P(V, T) = P(V, T0) + Pth(V, T), consists of an isothermal compression and an isochoric heating, while the thermal pressure is the pressure change in the isochoric heating. In this paper, we demonstrate that, for solids in a soft pressure medium in a diamond anvil cell, the thermal pressure can neither be determined from a single heating process, nor from the thermal pressure of its calibrant. To avoid the thermal pressure, we propose to replace the thermal pressure with a well-known thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghan-expansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghan-expansion VPT TEOS model matches the experimental pressure of zero (0) GPa very well, while the pressure prediction from the approximated Anderson PVT TEOS exhibit a big deviation and a wrong trend.

First-principles investigation of the structural stability, electronic, and thermodynamic properties of Ba2NaHaO6 (Ha = Cl, Br, I) periodate double perovskites

“…Thermal pressure represents a pressure change in isochoric heating, a measure of pressure change relative to the temperature at a constant volume. 100 Fig. 5(e) shows that the Ba 2 NaIO 6 structure has a low gradient monotonically increasing behavior of thermal pressure as a function of applied pressure.…”

Pressure-independent thermal expansion and temperature-dependent bulk modulus

“…In paper [3,4], it was demonstrated that thermal expansion coe cient decreases with pressure in an isobaric heating process, which is not consistent with the assumptions in paper [1,2] of pressure independent of thermal expansion.…”