Thermoelastic properties of synthetic Mg3Al2Si3O12 pyrope garnet have been measured at high pressure and high temperature by using in situ energy-dispersive X-ray diffraction, using a Kawai-type multi-anvil apparatus. Measurements have been conducted up to 19 GPa and 1,700 K, equivalent to the P–T conditions of the middle part of mantle transition zone. Analyses of the room-temperature P–V data to a third-order Birch–Murnaghan (BM) equation of state (EoS) yields: V0 = 1,500 ± 1 Å3, K0 = 167 ± 6 GPa and \documentclass[12pt]{minimal}
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\begin{document}$$ K_{{_{0} }}^{'} $$\end{document} = 4.6 ± 0.3. When fitting the entire P–V–T data using a high-temperature Birch–Murnaghan (HTBM) EoS at a fixed \documentclass[12pt]{minimal}
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\begin{document}$$ K_{{_{T0} }}^{'} $$\end{document} = 4.6, we obtain V0 = 1,500 ± 2 Å3, KT0 = 167 ± 3 GPa, (∂K/∂T)P = −0.021 ± 0.009 GPa K−1 and α300 = (2.89 ± 0.33) × 10−5 K−1. Fitting the present data to the Mie-Grüneisen-Debye (MGD) EoS with Debye temperature Θ0 = 806 K gives γ0 = 1.19 and 1.15 at fixed q = 1.0 and 1.5, respectively. Comparison of these fittings with two different approaches, we propose to constrain the bulk modulus and its pressure derivative to K0 = 167 GPa and \documentclass[12pt]{minimal}
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\begin{document}$$ K_{{_{0} }}^{'} $$\end{document} = 4.4–4.6, as well as the Grüneisen parameter to γ0 = 1.15–1.19.
