Elasticity of MgO in Giant Planetary Interiors

The structural and elastic properties of MgO were studdied up to terrapascals with first-principle calculations to mimic that of giant planet interiors. The behavior of oxides and silicates at pressures much greater than those in Earth is important for understanding the tidal and thermal evolution of super Earths and rocky cores that may exist at the center of gas and ice giants. Because the melting temperature of oxides and silicates at extreme pressure is very high, rock may exist in solid form deep inside these planetary bodies. Throughout Earth's mantle MgO exists in the form of periclase with the B1 crystal structure, and transforms to the B2 structure near 640 GPa, similar to the pressure at the center of Uranus. We have examined the equation of state and elasticity of B1 and B2 forms of MgO using density functinal theory (DFT) to pressures and temperatures much higher than has previously been done. We compare with existing experimental data, and examine the relationship between an elastic instability in the B1 and B2 phases. We identify high pressure limiting values of the Poisson ratio and the ratio of pressure to bulk modulus, and compare these with results derived from simple model systems (e.g. the one component plasma), and previously proposed extrapolation procedures, including those based on Eulerian and Lagrangian finite strain. We find that B2 develops an instability in the terrapascal region. Finally, we compare these structures to the infinite pressure limit of a uniform electron gas.