|Abstract:||Zirconium-based fuel cladding used in nuclear reactors is susceptible to significant hydrogen uptake during normal operating conditions. This results in the formation of zirconium hydride. The nucleation of a brittle hydride phase results in a degradation of cladding mechanical properties in the long term as plate-like hydrides provide pathways for the propagation of cracks in the cladding. These hydride structures can be modified to reduce the possibility of cracking by alloying yttrium into the zirconium. Yttrium acts as a hydrogen getter, and provides dispersed nucleation sites and nodular hydrides. Using yttrium has two drawbacks: increased hydrogen uptake and increased oxidation kinetics. Hydrogen uptake in zirconium-based cladding under simulated reactor water chemistry has been observed to be dependent upon the alloying elements commonly used in cladding material. An inverse relationship between power-law exponent of the weight gain and the hydrogen uptake has been observed. The space-charge-theory of oxidation has been used to explain the link between the kinetics and hydrogen uptake. Allowing for local charge imbalance to occur in the oxide creates an electric field. At thicker oxides, once the electric field becomes large enough, it will limit the electron flux resulting in a smaller power-law exponent. Alloying elements dope the oxide, either increasing or decreasing the net space charge in the oxide, and therefore changing the oxidation kinetics. Hydrogen serves as an additional charged species which can compensate for a limited electron flux, and at smaller values for the power-law exponent, greater hydrogen uptake occurs to compensate for this limited flux. This doctoral research investigates how increased hydrogen uptake due to yttrium, as well as yttrium doping of the oxide, affects the high temperatures steam oxidation kinetics of zirconium through systematic experimental work coupled with a computational study of oxygen, electron, and hydrogen diffusion.
Experiments focused on the oxidation of 0.01-1 wt% yttrium in pure zirconium samples and the characterization of the resultant oxides and hydrides. A thermogravimetric analysis instrument was used to collect active weight gain during oxidation in both steam and oxygen/argon environments at temperatures ranging from 500C to 1100C. Synchrotron diffraction of the steam-exposed samples provided information about the hydrogen uptake through the intensity of the zirconium hydride phase, as well as identification of oxides formed. Powder diffraction samples were fabricated from oxidized samples to provide a stress free environment to study the effect of yttrium concentration on the oxides. Additional cross-sectional optical microscopy was performed to confirm the zirconium hydride phase evolution as a function of yttrium concentration. It was observed that without hydrogen, the addition of yttrium decreased the power-law exponent, n, from 0.39 to 0.31 at 500C due to an increase in the space charge. The rate constant, k, increased from 0.16(g/(m^2*t^n)) to 0.51(g/(m^2*t^n)) due to the generation of oxygen vacancies. In steam, significant hydrogen uptake occurred at 500C and 700C. Both the amount of hydrogen absorbed, and the oxidation power-law exponent increased (0.39 to 0.44) with increasing yttrium. These results are a departure from what has been previously observed. The powder diffraction data indicated that the amount of yttrium doping of the zirconia was directly related to both the temperature and concentration of yttrium in solid solution in the starting zirconium.
To better understand the oxidation kinetics fit from the weight gain data, the Poisson-Nernst-Planck (PNP) system of differential equations was solved using Multiphysics Object Oriented Simulation Environment (MOOSE); the PNP system describes a space charge controlled oxidation model. These computations were performed by solving the steady state solution for increasing oxide thicknesses. It was found that the oxygen vacancy flux as a function of oxide thickness followed a power-law function allowing for the oxidation kinetics to be calculated from the oxide thickness-dependent flux equations. The resulting model was initially tested on an oxide with only electron/oxygen vacancy diffusion to compare with previous work, and then hydrogen was added as an additional charged species. The effect of changing the hydrogen diffusivity or hydrogen concentration at the steam/oxide interface was modeled. It was found that changing the diffusivity and concentration did not have a large effect on the oxidation kinetics; the hydrogen flux initially increased, however, the space charge effect countered the effects of the perturbations. Implementing a simple, flat chemical potential to simulate hydrogen gettering resulted in an increase in both the power-law exponent, n, from 0.4 to 0.47, and in the hydrogen uptake. Driving hydrogen into the system created a new current, necessitating increased hydrogen and oxygen vacancy fluxes to compensate. This resulted in an increase in the oxygen diffusion into the oxide and an increase in n. By increasing this chemical potential, which simulated an increase in the yttrium concentration, both the hydrogen uptake and power-law exponent increased. An additional result from the modeling was the observation that the value of the rate constant, k, changed inversely with that of the power-law exponent n.
Several important conclusions can be drawn from this work. First, using yttrium as an alloying element will increase the steam oxidation rate of zirconium at intermediate temperatures (500C to 900C), and result in an increased hydrogen uptake. Fortunately, the effects of yttrium on the oxidation kinetics at high temperatures which would be experienced in accidents are either nonexistent or beneficial. Second, hydrogen uptake driven-oxidation instead of oxidation-driven hydrogen uptake was observed. This serves as additional confirmation of the space charge oxidation model can be used to describe the oxidation kinetics of zirconium.