Interactions of hydrogen with zirconium alloying elements and oxygen vacancies in monoclinic zirconia

Using Density Functional Theory with hybrid functionals, we calculate the interactions of hydrogen atoms with some point defects in monoclinic zirconia. We consider Nb and Sn substitution for Zr atoms as well as oxygen vacancies, as these are the main defects present in the zirconia layer formed during the corrosion of zirconium claddings in pressurized water reactors. We consider various charges for the complexes formed by hydrogens atoms and the aforementioned defects. The formation and binding energies are thus expressed as functions of the Fermi level in zirconia. We find that there is almost no interaction between H and Sn atoms, while a small but noticeable binding exists between H and Nb atoms. Conversely hydrogen atoms binds strongly to oxygen vacancies which can accommodate up to 2 hydrogen atoms. We observe that there is a range of Fermi levels where the actual stable form of hydrogen is the H2 molecule and not isolated hydrogen ions. We integrate the calculated energies in a thermodynamical model to calculate the concentrations of the various forms of hydrogen. We observe that the driving parameters are the oxygen vacancy to hydrogen ratio and the temperature. There is a change in the main hydrogen species upon decrease of the vacancy concentration from hydrogen trapped in vacancies to interstitial forms of hydrogen. These results provide a possible rationale for the variation of hydrogen diffusion coefficient through the oxide layer observed experimentally in literature.