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Zr-based alloys are used primarily as fuel cladding in water-cooled nuclear fission reactors. This is due to their good thermal and mechanical properties and low capture cross section for thermal neutrons. In this work, density functional theory (DFT) simulations were performed to investigate the behaviour of dopant elements in the cladding alloy oxide, with the aim of furthering the understanding of corrosion and hydrogen pick-up in Zr-based alloys. Simulations were performed in both monoclinic and tetragonal ZrO2 on single isolated defects and defect clusters, with the effect of compressive stress on some systems also simulated. Brouwer diagrams were constructed to model the interaction of multiple defect types within a system, in both equilibrium and non-equilibrium overall charge states. The concentration of the dopant elements in the oxide was fixed, and the chemical potential allowed to vary from the reference state, allowing the variation in oxidation state under varying oxygen partial pressure within the oxide to be investigated. Sn was shown to exist as Sn4+ under high oxygen partial pressures in tetragonal ZrO2, however at lower partial pressures a cluster with an oxygen vacancy (VO) and Sn2+ was the dominant defect type. As corrosion progresses, the oxygen partial pressure around a given immobile defect within the oxide layer will increase. Thus, as corrosion progresses the Sn2+:VO cluster will transition to Sn4+, with a consequent reduction in oxygen vacancy concentration. Oxygen vacancies help stabilise the tetragonal phase, and so this transition may cause a transformation from tetragonal to monoclinic to occur. The associated increase in volume (monoclinic phase has a volume ~4% larger) is proposed to be a contributing factor to the early transition observed in Sn-containing alloys. Nb was shown to exist in oxidation states ranging from Nb2+ to Nb5+ in the tetragonal phase, but only as Nb5+ in the monoclinic. In the lower oxidation states, Nb is able to mitigate the space charge which builds up in the oxide layer during corrosion, as a result of the lower oxygen vacancy diffusion rate compared to electrons. By mitigating the space charge, the corrosion kinetics are able to approach parabolic and the HPUF is lowered, both observations are in excellent agreement with experimental work which has shown Zr-Nb alloys to be unique in these properties. At transition, a large proportion of the tetragonal phase present in the oxide layer will transform to monoclinic as compressive stress is relieved. Since Nb was predicted to only exist in the 5+ state in the monoclinic phase, any lower states will oxidise upon phase transformation, releasing electrons into the oxide layer during transition. This oxidation process is proposed as a possible explanation for the sudden drop in HPUF that has been experimentally observed to occur around transition. Sc was shown to exist only as Sc3+ in both tetragonal and monoclinic phases, charge balanced by an increase in the concentration of oxygen vacancies. Since a stable cluster involving Sc3+ and VO would require the close proximity of two Sc3+ defects, it is assumed that at the low doping level in the model alloys produced alongside this work (0.2-0.4 %. wt.) stable clusters are unlikely to form in significant concentrations. Thus, the inclusion of Sc as a dopant increases the concentration of unbound (i.e. mobile) oxygen vacancies in the oxide layer. This is proposed as the reason for the extremely high corrosion rate observed in the Sc-containing model alloys produced and tested alongside this work. It is also assumed that the tetragonal phase fraction in the oxide layer of the Sc-containing alloys is likely to be high due to the increased oxygen vacancy concentration, however experimental testing to verify this prediction has not yet taken place. Sb was shown to exist as Sb5+ at high oxygen partial pressures, transitioning to Sb3+ at lower partial pressures in both the tetragonal and monoclinic phases. The application of a non-equilbrium charge state to the Brouwer diagrams showed that the oxygen partial pressure at which the transition between Sb5+ and Sb3+ occurs is able to smoothly change in order to counteract the applied space charge. This behaviour was observed in both phases, and implies that Sb may be able to act as a space charge compensation mechanism, in a similar fashion to Nb. The Zr-Nb-Sb model alloys produced alongside this work exhibited a lower corrosion rate and HPUF than the Zr-Nb alloys, suggesting that Sb may improve the beneficial effects already observed in Zr-Nb alloys. |
