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,
 Award ID(s):
 2119308
 NSFPAR ID:
 10447049
 Date Published:
 Journal Name:
 Philosophical transactions A
 Volume:
 381
 ISSN:
 20587457
 Page Range / eLocation ID:
 20220331
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract P (V ,T ) =P (V ,T _{0}) +P _{th}(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 wellknown thermal expansion model, and integrate it with the isothermal compression model to yields a Birch–Murnaghanexpansion TEOS model, called VPT TEOS. The predicted pressure of MgO and Au at ambient pressure from Birch–Murnaghanexpansion 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. 
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