  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.
