This variable ionicity may be the reason why LDA fails to describe the relative stability of different polymorphs. 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. 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. We developed a new population analysis scheme in more » which atomic radii are adapted to the actual charge distribution in the material. The GGA values of the bulk modulus of the cotunnite phase were found to be 251 and 259 GPa for ZrO2 and HfO2, respectively. 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). 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. These results provide a comprehensive and accurate thermodynamic model of the monoclinic and tetragonal phases of hafnia on a broad range of temperatures and can serve as input to CALPHAD assessment of multi-component hafnia-based phase = , The predicted heat capacities are in excellent agreement with experiment, and the predicted temperature of the monoclinic to tetragonal phase transition (2173 K) is in good agreement with the experimental value (2078K). As a case study, we develop thermodynamic models of monoclinic and tetragonal HfO2 polymorphs.

A Bayesian model provides interpolated values between these regimes. The approach is based on the quasi-harmonic approximation below the Debye temperature and on ab-initio molecular dynamics calculations above the Debye temperature to predict constant pressure heat capacities (C-p).

We develop and use a coupled quantum mechanical and molecular dynamics approach to create thermodynamic models of hafnia (HfO2) polymorphs from 0 K to 3000 K at ambient pressure. Accurate and precise thermodynamic models of oxide compounds and their phases are important for calculating the phase stability of oxide materials.

Absolute entropy debye