Impact of homogeneous strain on uranium vacancy diffusion in uranium dioxide

Abstract

We present a detailed mechanism of, and the effect of homogeneous strains on, the migration of uranium vacancies in UO2. Vacancy migration pathways and barriers are identified using density functional theory (DFT) and the effect of uniform strain fields are accounted for using the dipole tensor approach. We report complex migration pathways and non-cubic symmetry associated with the uranium vacancy in UO2 and show that these complexities need to be carefully accounted for to predict the correct diffusion behavior of uranium vacancies. We show that under homogeneous strain fields, only the dipole tensor of the saddle with respect to the minimum is required to correctly predict the change in the energy barrier between the strained and the unstrained case. Diffusivities are computed using kinetic Monte Carlo (KMC) simulations for both neutral and fully charged state of uranium single and di-vacancies. We calculate the effect of strain on migration barriers in the temperature range 800 -1800 K for both vacancy types. Homogeneous strains as small as 2% have a considerable effect on diffusivity of both single and di-vacancies of uranium, with the effect of strain being more pronounced for single vacancies than di-vacancies. In contrast, the response of a given defect to strain is less sensitive to changes in the charge state of the defect. Further, strain leads to anisotropies in the mobility of the vacancy and the degree of anisotropy is very sensitive to the nature of the applied strain field for strain of equal magnitude. Our results suggest that the influence of strain on vacancy diffusivity will be significantly greater when single vacancies dominate the defect structure, such as sintering, while the effects will be much less substantial under irradiation conditions where di-vacancies dominate.

Effect of additives on self-diffusion and creep of UO 2

“…At low stresses, the strain rate varies linearly with the applied stress (Harper-Dorn creep), whereas at higher stresses, a power law dependence on applied stress has been observed [16]. In the literature, as has been stated in [12], there is no concord in regard to the dominant mechanism of thermal creep in UO 2 . Doping UO 2 brings about additional complications to its creep behavior, depending on the type and concentration of the dopant.…”

“…For the effect of homogeneous strain (stress) on the migration energy of vacancies, see e.g. the analyses in [12,70,71]. So this effect could yet be another source of uncertainty in the analysis of self-diffusion controlled creep.…”

“…As noted in [22], it is in the lower stress regions, typified by a linear stress dependence of creep rate, that the most prominent creep modes occur during normal reactor operating conditions. Sawbridge et al [22] used the Nabarro-Herring creep formula with lattice diffusivity like (12) to evaluate their experimental data. However, they do not provide numerical values for the formation energies of the defects nor specify the lattice diffusivity of uranium vacancies.…”

“…These have been reviewed in the literature; see e.g. [10,11] and the recent paper by Goyal et al [12]. In brief, one may classify the creep mechanisms into lattice diffusion controlled (Nabarro-Herring), grain boundary diffusion (Coble) and dislocation induced creep.…”

Uranium vacancy mobility at the Σ5 symmetric tilt and Σ5 twist grain boundaries in UO2

“…Thus, to understand how the distribution of fission gases evolves in the fuel, we must understand the underlying transport mechanisms, tied to the concentrations and mobilities of defects within the material, and how these gases interact with microstructural features that might act as sinks. The mobility of cation defects and fission products in bulk urania (UO 2 ) has received significant attention in the literature [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] as has the segregation of various fission products to microstructural features such as bubbles, dislocations and grain boundaries [20][21][22][23]. However, once a fission product has reached a sink, such as a grain boundary, its mobility may be different there than in the grain interior and predicting how, for example, bubbles nucleate within grain boundaries necessitates an understanding of how fission gases diffuse within boundaries.…”