Density functional theory modeling of cation diffusion in tetragonal bulk Zr O2: Effects of humidity and hydrogen defect complexes on cation transport

Abstract

Density functional theory modeling was performed to determine the effect of humidity and H2/O2 gas pressure on the defect chemistry, hydrogen solubility and diffusivity, and on cation transport in tetragonal bulk ZrO2, for the temperature range 400-1200°C. The main goal of this study is to identify the stable defect complexes and hydrogen-related defect species relevant to bulk cation transport kinetics at various gas pressure, humidity, and temperature conditions, including cation diffusion via a Zr vacancy mechanism [with -4 charge, VZr(-4)], through an H-substituted Zr defect mechanism [via anH substituted Zr defect with -3 charge, HZr(-3)], and via formation of fully or partially bound Schottky defect complexes (VZr-VO and VO-VZr-VO). At low temperatures (T<500°C) and humidity condition of 3%, the modeling results show a 0.5-0.7-eV reduction in the apparent formation free energy of HZr(-3) versus that of VZr(-4) due to the attractive interaction between interstitial hydrogen and the Zr vacancy, leading to a concentration of the HZr(-3) defect species that is higher than VZr(-4) specie. The migration barriers of the HZr(-3) versus VZr(-4) are found to be comparable, i.e., 2.7 eV versus 2.4 eV for the out-of-ab-plane migration and 3.1 eV versus 3.0 eV for the in-ab-plane migration, respectively. The calculated diffusion coefficients reveal that cation diffusion in tetragonal bulk ZrO2 will transit from the VZr(-4) mechanism at high temperatures to the HZr(-3) mechanism upon lowering the operating temperature and/or increasing the humidity content. The defect thermodynamic modeling results indicate that most of the stable hydrogen defect species in tetragonal bulk ZrO2 is HZr(-3), and its concentration is 4-6 orders of magnitude higher than that of H interstitial (Hint). Nonetheless, the most active hydrogen transport occurs via Hint(+1) with migration barriers 0.2-0.4 eV rather than through the stable HZr(-3) defect which has a larger migration barrier of 1.6 eV. At temperatures higher than 1173 K, the protonic transport rate in bulk tetragonal ZrO2 is predicted to be several orders of magnitude higher than the bulk cation transport rate. Above 1573 K, the modeling results further predict another transition in the bulk cation transport mechanisms, VZr → fully or partially bound Schottky defects, attributed to enhanced entropic stabilization associated with oxygen vacancy formation (in the defect cluster) in equilibrium with O2 or H2O gas phase at the respective temperature. Overall, the results obtained highlight the importance of the coupling of the bulk cation transport kinetics with the dissolved H defect species at lower temperature and respectively, with the cation-anion vacancy clusters at higher temperature, and predict several temperature dependent mechanistic transitions for the cation transport in tetragonal bulk zirconia.