P-V-T Equation of State for Periclase

Collecting the complete data set of previous experiments on periclase, covering a pressure and temperature range of 0-141.8 GPa and 100-3031 K respectively, the first comprehensive P-V-T description of MgO is presented comprising all previous experiments. The P-V-T EoS of Birch-Murnaghan, Rydberg-Vinet and Garai are determined by unrestricted fitting. The three EoSs are consistent and a unique set of parameters is able to cover the entire pressure and temperature range. The RMS misfits for the pressure are 0.371 GPa, 0.381 GPa and 0.396 GPa for the Garai, Birch-Murnaghan and Rydberg-Vinet EoSs. The RMS misfits for the volume and the temperature are 0.018 cm3 and 60.3 K for the EoS of Garai.

💡 Research Summary

The authors present the first comprehensive pressure‑volume‑temperature (P‑V‑T) equation of state (EoS) for periclase (MgO) that incorporates all previously published experimental data spanning 0–141.8 GPa and 100–3031 K. By gathering 406 independent measurements performed under hydrostatic or semi‑hydrostatic conditions, they ensure a robust dataset free from systematic deviatoric stress effects. Three widely used isothermal EoSs—third‑order Birch‑Murnaghan (B‑M), Rydberg‑Vinet (R‑V), and a semi‑empirical eight‑parameter formulation introduced by Garai—are extended to full P‑V‑T form. The extension relies on defining absolute reference quantities (initial volume V₀, bulk modulus K₀, and thermal‑expansion coefficient α₀) and incorporating the Anderson‑Grüneisen parameter δ to describe temperature dependence of the bulk modulus. Linear approximations for thermal expansion are applied above the Debye temperature, which is justified for the temperature range of interest.

Parameter optimization is performed via unrestricted nonlinear least‑squares fitting, and model performance is evaluated using both root‑mean‑square (RMS) misfits and the Akaike Information Criterion (AIC). The Garai EoS yields the smallest RMS pressure error (0.371 GPa) and the lowest AIC (‑804.5), indicating the best balance of fit quality and model complexity. The B‑M and R‑V formulations produce comparable RMS errors (0.381 GPa and 0.396 GPa, respectively) and slightly higher AIC values. For volume and temperature, the Garai model achieves RMS deviations of 0.018 cm³ and 60.3 K, respectively, which are within experimental uncertainties.

Using the fitted parameters, the authors calculate derived thermodynamic quantities such as the volume coefficient of thermal expansion, bulk modulus, and constant‑pressure heat capacity. The calculated thermal expansion matches ambient‑condition measurements, while the bulk modulus shows modest discrepancies that can be reduced by fixing K₀ to an independently measured value (6.161 GPa at 298 K). Heat‑capacity predictions based on the Debye model combined with the fitted expansion and bulk‑modulus data agree well with low‑pressure calorimetric data, further validating the parameter set.

The three EoSs predict pressures at 300 K and 3000 K that differ by at most 2.8–3.5 GPa across the entire pressure range, with near‑identical behavior up to ~120 GPa. Above this, minor divergence appears but remains within acceptable limits for geophysical applications. The Garai formulation’s ability to compute volume and temperature directly without iterative inversion is highlighted as a practical advantage.

In conclusion, the study demonstrates that a single set of thermodynamic parameters can accurately describe MgO’s P‑V‑T behavior over an unprecedented range of conditions. The results provide a reliable reference for high‑pressure calibration, mantle modeling, and planetary interior studies, and they establish the Garai EoS as a convenient tool for rapid calculations in both experimental and theoretical contexts.