Density functional theory modeling of cation diffusion in tetragonal bulk ZrO_{2}: Effects of humidity and hydrogen defect complexes on cation transport

oleh: Yueh-Lin Lee, Yuhua Duan, Dan C. Sorescu, Dane Morgan, Harry Abernathy, Thomas Kalapos, Gregory Hackett

Format: Article
Diterbitkan: American Physical Society 2021-02-01

Deskripsi

Density functional theory modeling was performed to determine the effect of humidity and H_{2}/O_{2} gas pressure on the defect chemistry, hydrogen solubility and diffusivity, and on cation transport in tetragonal bulk ZrO_{2}, 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, V_{Zr}(−4)], through an H-substituted Zr defect mechanism [via anH substituted Zr defect with −3 charge, H_{Zr}(−3)], and via formation of fully or partially bound Schottky defect complexes (V_{Zr}-V_{O} and V_{O}-V_{Zr}-V_{O}). 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 H_{Zr}(−3) versus that of V_{Zr}(−4) due to the attractive interaction between interstitial hydrogen and the Zr vacancy, leading to a concentration of the H_{Zr}(−3) defect species that is higher than V_{Zr}(−4) specie. The migration barriers of the H_{Zr}(−3) versus V_{Zr}(−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 ZrO_{2} will transit from the V_{Zr}(−4) mechanism at high temperatures to the H_{Zr}(−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 ZrO_{2} is H_{Zr}(−3), and its concentration is 4–6 orders of magnitude higher than that of H interstitial (H_{int}). Nonetheless, the most active hydrogen transport occurs via H_{int}(+1) with migration barriers 0.2–0.4 eV rather than through the stable H_{Zr}(−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 ZrO_{2} 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, V_{Zr} → fully or partially bound Schottky defects, attributed to enhanced entropic stabilization associated with oxygen vacancy formation (in the defect cluster) in equilibrium with O_{2} or H_{2}O 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.