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h i g h l i g h t s" We perform MD simulation of oxygen diffusion in UO2 (up to 50 000 ions and 1 ls time)." We reached 1400 K and 10 À12 cm 2 /sec, which allowed direct comparison to experiments." S-shaped T-dependence of activation energy and k-peak of its derivative were obtained. " Continual superionic phase transition (rather than first or second order) was proved. t r a c tOur series of articles is devoted to high-precision molecular dynamics simulation of mixed actinide-oxide (MOX) fuel in the approximation of rigid ions and pair interactions (RIPI) using high-performance graphics processors (GPU). In this article we study self-diffusion mechanisms of oxygen anions in uranium dioxide (UO 2 ) with the 10 recent and widely used sets of interatomic pair potentials (SPP) under periodic (PBC) and isolated (IBC) boundary conditions. Wide range of measured diffusion coefficients (from 10 À3 cm 2 /s at melting point down to 10 À12 cm 2 /s at 1400 K) made possible a direct comparison (without extrapolation) of the simulation results with the experimental data, which have been known only at low temperatures (T < 1500 K). A highly detailed (with the temperature step of 1 K) calculation of the diffusion coefficient allowed us to plot temperature dependences of the diffusion activation energy and its derivative, both of which show a wide ($1000 K) superionic transition region confirming the broad k-peaks of heat capacity obtained by us earlier. It is shown that regardless of SPP the anion self-diffusion in model crystals without surface or artificially embedded defects goes on via exchange mechanism, rather than interstitial or vacancy mechanisms suggested by the previous works. The activation energy of exchange diffusion turned out to coincide with the anti-Frenkel defect formation energy calculated by the lattice statics.

In this article we investigated surface of nanocrystals (NC) of uranium dioxide (UO2) using molecular dynamics (MD) under isolated (non-periodic) boundary conditions with the approximation of pair potentials and rigid ions. It is shown that a cubic shape of the model NCs is metastable and the stable equilibrium is reached in the process of structural relaxation to the octahedral shape over a time of 1000 ns (200 million MD steps), which increases with the size of NC. We measured the size dependences of the lattice parameter and the surface energy density for NC of cubic and octahedral shape with volume up to 1000 nm3 (50000 particles) at temperatures of 2200K and 2300K. For the surfaces {100} and {111} we obtained the energy density {\sigma}100=1.602\pm0.016 J/m^2, {\sigma}111=1.137\pm0.032 J/m^2 and surface tension constant {\gamma}111=0.875\pm0.008 J/m^2. The resulting ratio of {\sigma}100/{\sigma}111=1.408\pm0.042 within the error coincides with the experimental value of 1.42\pm0.05 measured for microscopic cavities in monocrystals of UO2.Comment: 11 pages, 8 figures, 5 table

Melting of uranium dioxide (UO 2 ) nanocrystals has been studied by molecular dynamics (MD) simulation. Ten recent and widely used sets of pair potentials were assessed in the rigid ion approximation. Both isolated (in vacuum) and periodic boundary conditions (PBC) were explored. Using barostat under PBC the pressure dependences of melting point were obtained. These curves intersected zero near -20 GPa, saturated near 25 GPa and increased nonlinearly in between. Using simulation of surface under isolated boundary conditions (IBC) recommended melting temperature and density jump were successfully reproduced. However, the heat of fusion is still underestimated. These melting characteristics were calculated for nanocrystals of cubic shape in the range of 768-49 152 particles (volume range of 10-1000 nm 3 ). The obtained reciprocal size dependences decreased nonlinearly. Linear and parabolic extrapolations to macroscopic values are considered. The parabolic one is found to be better suited for analysis of the data on temperature and heat of melting.

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a b s t r a c tThis article is devoted to investigation of cation self-diffusion mechanisms, taking place in UO 2 , UO 2+x , and UO 2Àx crystals simulated under periodic (PBC) and isolated (IBC) boundary conditions using the method of molecular dynamics in the approximation of rigid ions and pair interactions. It is shown that under PBC the cations diffuse via an exchange mechanism (with the formation of Frenkel defects) with activation energy of 15-22 eV, while under IBC there is competition between the exchange and vacancy (via Schottky defects) diffusion mechanisms, which give the effective activation energy of 11-13 eV near the melting temperature of the simulated UO 2.00 nanocrystals. Vacancy diffusion with lower activation energy of 6-7 eV was dominant in the non-stoichiometric crystals UO 2.10 , UO 2.15 and UO 1.85 . Observations showed that a cation vacancy is accompanied by different number of anion vacancies depending on the deviation from stoichiometry: no vacancies in UO 2.15 , single vacancy in UO 2.00 and four vacancies in UO 1.85 . The corresponding law of mass action formulas derived within the Lidiard-Matzke model allowed explaining the obtained activation energies and predicting a change in the activation energy within the temperature range of the superionic phase transition. The diffusion of cations on the surface of nanocrystals had activation energy of 3.1-3.6 eV.

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