Prediction of a Reentrant Phase Transition Behavior of Cotunnite in Zirconia and Hafnia at High Pressures

First-principles calculations within the framework of density-functional theory (DFT) are implemented to investigate the high-pressure behavior of ultrahigh high-pressure phases of zirconia (ZrO₂) and hafnia (HfO₂) compounds. We have studied the phase relations among the highest-pressure phases of these dioxides: The previously observed OII (cotunnite) phase, Fe₂P-type phase, and the recently predicted Ni₂In-type phase. Our calculations, using the generalized gradient approximation (GGA), predict unusual phase transition of OII phase with respect to Fe₂P phase. In both dioxides, our enthalpy calculations show that OII phase transforms to Fe₂P phase at 96 GPa (122 GPa) for ZrO₂ (HfO₂), where Fe₂P phase remains stable up to 254 GPa (310 GPa) in ZrO₂ (HfO₂) before it transforms back to OII phase, indicating a reentrant transition behavior of OII phase. Our calculations show that OII → Fe₂P and Fe₂P → OII transitions are associated with a slight change in both volume and enthalpy. Consequently, we have concluded that the transition to Ni₂In phase likely occurs from OII phase rather than Fe₂P phase, and thus we provide an updated high-pressure phase transition sequence for zirconia and hafnia at such extreme pressures. The OII → Ni₂In transition is predicted to occur at 302 and 372 GPa in zirconia and hafnia, respectively. Furthermore, to obtain a deeper insight into the mechanism of the phase transitions in ZrO₂ and HfO₂, the effect of the components of the enthalpy difference across our predicted phase transitions has been thoroughly investigated.