The Influence of Lattice Strain on Single Vacancy and Krypton Atom Diffusion in Uranium Dioxide
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The Influence of Lattice Strain on Single Vacancy and Krypton Atom Diffusion in Uranium Dioxide Torey Semi1 and Timothy J. Bartel2 and Mark T. Lusk1 1 Colorado School of Mines, 1523 Illinois, Golden, CO 80401, U.S.A. 2 Sandia National Laboratories, 1515 Eubank SE, Albuquerque, NM, 87123, U.S.A. ABSTRACT Nuclear fuel pins exhibit distortions in the UO2 lattice in response to temperature gradients, defects and the introduction of fission product (FP) gases. These distortions can have a significant influence on the activation barriers associated with fission product gas diffusion. A predictive understanding of this relationship is particularly relevant to anticipating the evolution of fission product gases during rapid temperature transients. Density Functional Theory (DFT) has the capacity to provide a relationship between lattice distortion and FP gas diffusivity by generating estimates of dilation dependent activation energies. As a first step in this direction, the relation between lattice dilation and activation energy for isolated vacancies within an otherwise pristine block of alpha-quartz is quantified, where precise experimental data is readily available. The results lend confidence to the basic approach which is based on a one-shot transition state method, developed to lessen the computational resources required by the full transition state method. This technique is first applied to α-quartz for O vacancy hopping and diamond-Si for Si vacancy hopping. The method is subsequently extended to consider isolated uranium vacancies in UO2. This in turn is further generalized to estimate the activation volume for Kr atoms in UO2. Thus two different types of defects are considered; those of species native to the material and, in the case of UO2, FP gases introduced through the fission process. INTRODUCTION Nuclear energy is a vital component of the solution to global reliance on carbon-based fuels. Uranium dioxide (UO2) is the predominant source of fuel in nuclear reactors of the near future. As burnup proceeds, the UO2 lattice is subject to temperature gradients, defects and the production, presence and motion of fission product gases. To gain an appreciation of the response of UO2 to this environment, and to ensure the efficacy and safety of the nuclear fuel pin, intimate knowledge of the behavior of UO2 at the electronic structure level is fundamental. Specifically, the motion of U vacancies and Kr atoms in UO2 under strain is the focus of this investigation. UO2 is a difficult material to model accurately. Its mass is such that relativistic effects need to be included, and its partially-filled f-electron band is responsible for its insulating antiferromagnetic ground state, which is not correctly reproduced using LDA and GGA functionals. Adding a Coulomb on-site interaction (a '+U') to the GGA functional improves these results considerably, but adds to the complexity of the calculation. It is possible that the effect of the f-electrons is of
an order that these effects are negligible when studying energetics1,2,
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