Theoretical Evaluation of Oxidation Rate of Zr
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Theoretical Evaluation of Oxidation Rate of Zr Yasunori Yamamoto1, Kazunori Morishita2, Hirotomo Iwakiri3 and Yasunori Kaneta4 Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011, Japan. 2 Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011, Japan. 3 Faculty of Education, University of the Ryukyus, Nakagami-gun, Okinawa 903-0212, Japan. 4 Akita National College of Technology, Akita, Akita 011-8511, Japan. 1
ABSTRACT First principle calculations were performed to evaluate stress effect on the diffusion process of oxygen vacancy in ZrO2 film, and oxidation rate of Zr was evaluated by solving simple diffusion equations. Our calculation results have indicated that both the vacancy formation and migration energies of ZrO2 increase with increasing compressive applied stress. The energy increase causes a decrease in the diffusion coefficient of oxygen vacancy in ZrO2, leading to a decrease in oxidation rate of Zr. The stress effect on diffusion process may explain the experimental fact that Zr is oxidized in proportion to the cubic root of time.
INTRODUCTION In nuclear light water reactors, Zr alloys are used as component material of fuel cladding due to their small thermal neutron cross-section and good corrosion resistance. One of the main issues to be solved for establishment of the reliability of fuel cladding is Zr-water oxidation reaction, which may cause emblittlement of Zr alloy, a reduction in thermal conductivity, and so on. At the accident at the Fukushima Daiichi nuclear power plant, hydrogen explosion occurred where hydrogen gas produced by the Zr-water oxidation reaction may play an important role. Therefore, the oxidation of fuel cladding should be controlled as low as possible not only under normal operation but also in an accident. However, the precise mechanism of oxidation process of Zr alloys is not yet understood well. The oxidation process is so-called the multiscale phenomenon, which is caused by atomistic scale processes such as oxygen diffusion process in a Zr oxide film. The diffusion process is considered to be a key to the oxidation rate, where the film may act as a barrier against the diffusion. It has been reported by experiments that the early stage of oxidation proceeds in proportion to the cubic root of time [1], which cannot be explained by normal diffusioncontrolled process. Therefore, it is considered that there may be some factors that decrease the diffusion rate of oxygen in Zr oxide film. In this study, we focused on the stress effect on diffusion process, which is caused at the oxide/metal interface due to a difference of equilibrium volumes between the oxide and the metal. In experiments [2,3], 1 GPa of compressive stress is applied on Zr oxide film at maximum. Since oxygen atom is supposed to diffuse in Zr oxide film by the vacancy mechanism, the formation and migration energies of an oxygen vacancy is important to understand the oxidation process. In this study, these energies were calculated by first principle calculations as a function of a
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