Large volume change across OI --$>$ OII phase transition in transition-metal dioxides TiO$_{2}$, ZrO$_{2}$, and HfO$_{2}$ as determined by experiment and theory

The nature of bonding in transition-metal dioxides TiO$_{2}$, ZrO$_{2}$, and HfO$_{2}$ is of interest as they are potential superhard materials with many industrial applications. Using high-resolution synchrotron x-ray powder diffraction for TiO$_{2}$ and ZrO$_{2}$, and complementary \textit{ab-initio} computations of these dioxides, we have determined the equation of state of the orthorhombic I (OI) and orthorhombic II (OII) phases. Our measurements are in agreement with the computationally predicted phase sequence of these oxides. The measured volume change across OI --$>$ OII transition is 8.3{\%} for TiO$_{2}$ and 10{\%} for ZrO$_{2}$ in good agreement with our density-functional theory (DFT) calculations that predict a large volume change for all of these dioxides across the OI --$>$ OII phase transition. For TiO$_{2}$, this volume collapse is significantly higher than previously measured (2.6{\%}), but consistent with the volume decreases observed in both ZrO$_{2}$ and HfO$_{2}$ across this transition. Furthermore, the OII phase was observed to be the most stable phase of TiO$_{2}$ and ZrO$_{2}$ at high pressure (56 GPa) after heating to high temperatures (above $\sim $1800 K) and no post-OII phase was observed under these conditions.