Low-temperature polymorphs of ZrO2 and HfO2:: A density-functional theory study -: art. no. 144107

The total energy and equation of state of the monoclinic, tetragonal, cubic, orthorhombic-I (Pbca) and orthorhombic-II (cotunnite) phases of zirconia and hafnia are determined using density functional theory (DFT) in the local density (LDA) and generalized-gradient (GGA) approximations. It is found that GGA corrections are needed to obtain low-temperature phase transitions under pressure that are consistent with experiment, i.e., (monoclinic -> orthorhombic-I -> cotunnite). The GGA values of the bulk modulus of the cotunnite phase are found to be 251 and 259 GPa for ZrO2 and HfO2 respectively, highlighting the similarity of these two compounds. We introduce a population analysis scheme in which atomic radii are adapted to the actual charge distribution in the material. The results indicate that the effective atomic radius of Hf is smaller than that of Zr, a drastic manifestation of the relativistic lanthanide contraction. The population analysis demonstrates that ionicity: (i) decreases from the monoclinic to the cotunnite phase, and (ii) is larger for HfO2 than for ZrO2. The bandgap and heat of formation are also larger for monoclinic HfO2 than for ZrO2 by 0.60 eV and 0.60 eV/ formula unit, respectively. The tetragonal phase, which often exists as a metastable phase at ambient conditions, has a bandgap larger than the monoclinic phase by 0.35 and 0.65 eV for ZrO2 and HfO2, respectively.