Sapphire $\left({\mathrm{Al}}_2{\mathrm{O}}_3\right)$, known for its remarkable incompressibility at ambient conditions, plays a pivotal role in both static and dynamic compression research. Accurately characterizing its equation of state (EoS) is essential for these applications. We present a complete Hugoniot of ${\mathrm{Al}}_2{\mathrm{O}}_3$ as locus of experimentally assessed, high-precision, pressure, density and temperature states up to 14 Mbar and 43 kK. The Hugoniot is established with single shock experiments using magnetically launched hyper velocity flyers on the Z Accelerator at Sandia National Laboratories. We explore principal Hugoniot states at very high shock $T$ and $p$ in the solid phase, tracking the solid-liquid boundary and culminating at 2.4-fold compression, where data provides a direct constraint on the liquid phase. Corresponding shock release data probe thermodynamic states complementary to the Hugoniot and place additional constraints on tabular EoS models. Our findings indicate a significant deviation from existing tabular EoS models for ${\mathrm{Al}}_2{\mathrm{O}}_3$ dictating a comprehensive overhaul. We develop two advanced EoSs for ${\mathrm{Al}}_2{\mathrm{O}}_3$ the SESAME 97412 model, featuring an extensive phase diagram that includes three solid phases and the liquid phase, and the updated LEOS 2200m2 model. EoS development is assisted with Quantum Molecular Dynamics simulations. Our experimental data allows for stringent testing of our EoSs. Both models accurately capture the Hugoniot of ${\mathrm{Al}}_2{\mathrm{O}}_3$ up to the highest pressures and temperatures. Rigorous experimental determination of extreme pressures and temperatures, paired with sophisticated models, advances the frontier of EoS development beyond 1 terapascal.

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• Equations of state
• Pressure effects
• Shock waves
• Oxides
• Transition metal oxides
• DFT+DMFT
• Pressure techniques