High-densityZrO2andHfO2:Crystalline structures and equations of state

Abstract

On the basis of Raman spectra and x-ray-diffraction patterns, we show that both dense zirconium and hafnium dioxides adopt the same structural phases, in similar pressure ranges. Furthermore both dioxides may be quenched at room conditions from high pressure to give polycrystalline solids which present optical transparency. From energy dispersive and angle dispersive x-ray diffraction using synchrotron radiation, the structure of the quenched phase is confirmed to be of the nine-coordinated ${\mathrm{PbCl}}_2$-type structure (cotunnite), space group $\mathrm{Pnma}\mathrm{}(Z=4\mathrm{}),$ as proposed earlier. Equations of state of all phases encountered in the pressure range investigated are also given. It is shown that the volume-pressure relationship for the quenched phase at room temperature is not well modeled by a usual equation of state based on the finite strain theory, as the room conditions bulk moduli are very high and the first derivative of the bulk moduli are small for both oxides. Nevertheless values for the bulk modulus of the high-density solids recovered at room conditions from at high pressure in the cotunnite phase, 444±15 GPa and 340±10 GPa, for ${\mathrm{ZrO}}_2$ and ${\mathrm{HfO}}_2,$ respectively, indicate a very low compressibility for both dioxides. If the correlation between hardness and high bulk modulus in materials is admitted, then high density cotunnite ${\mathrm{ZrO}}_2$ and ${\mathrm{HfO}}_2$ can be considered as candidates for potentially ultrahard materials.