Low-temperature Polymorphs of ZrO2 and HfO2. A Density Functional Theory Study
We present density functional calculations of the total energies and equations of state of the monoclinic, tetragonal, cubic, orthorhombic-I (Pbca) and orthorhombic-II (cotunnite)-structure phases of zirconia and hafnia in the local density (LDA) and generalized-gradient (GGA) approximations. The accuracy of the LDA approximation is not sufficient and GGA corrections are critical 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 were found to be 251 and 259 GPa for ZrO2 and HfO2, respectively. We developed a new 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, which is a drastic manifestation of the relativistic lanthanide contraction. The population analysis results demonstrate that ionicity: (i) increases from the monoclinic to the cotunnite phase, and (ii) is larger for HfO2 than for ZrO2. This variable ionicity may be the reason why LDA fails to describe the relative stability of different polymorphs. The bandgap and heat of formation are also larger for monoclinic HfO2 than for ZrO2 by 0.6 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.
- Research Organization:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States). Environmental Molecular Sciences Lab. (EMSL)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC05-76RL01830
- OSTI ID:
- 859954
- Report Number(s):
- PNNL-SA-39972; 3568; KC0302010; TRN: US0504801
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, 72(14):144107, Vol. 72, Issue 14
- Country of Publication:
- United States
- Language:
- English
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