Relative stability of ${\mathrm{ZrO}}_2$ and ${\mathrm{HfO}}_2$ structural phases

The potentially hard oxides ${\mathrm{ZrO}}_2$ and ${\mathrm{HfO}}_2$ are investigated using ab initio electronic structure calculations and structural properties of the lowest phases compared. In general there are strong similarities between some phases apart from the softer monoclinic baddeyelite phase, which in ${\mathrm{HfO}}_2$ is the lowest energy phase with a bulk modulus almost twice that of ${\mathrm{ZrO}}_2.$ Other differences relate to the formation of the first orthorhombic phase, especially the inter-relation between $\mathrm{Pbc}21\mathrm{}$ and $\mathrm{Pbca}$ structures. The bulk moduli of the high-pressure, cotunnite-type phases are in good agreement with experimental results. The present calculations confirm that these phases are highly incompressible and are thus good candidates for hard materials.