Abstract:
Aluminum oxide (Al$_2$O$_3$) is an important ceramic material with remarkable
compressive strength and hardness. Al$_2$O$_3$ is a major component of Earth's mantle which
makes a significant contribution to high-pressure physics. The construction of a shock
adiabatic curve in a wide range of pressures and the determination of the location of phase
transitions under shock-wave loading are associated with the derivation of the equation of
state. The shock-wave loading of Al$_2$O$_3$ is numerically simulated using a thermodynamic
equilibrium model. The equations of state for the two phases of the material are constructed. The missing parameters are obtained based on the correspondence with the experimental data. The dependences of the heat capacity and entropy on the temperature
of both phases are plotted, and shock adiabatic curves in the pressure range from 1 GPa
to 1.2 TPa are constructed. The high-pressure phase transition is taken into account in calculations. The obtained results are verified and validated using available data from other
authors. The presented results provide a basis for considering the theoretical equation
of state under extreme conditions, where, nowadays, the model calculations demonstrate
significant diversity.
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