  Using density functional theory (DFT) calculations, we have systematically
investigated the thermodynamic properties and structural stabilities of thorium
dioxide (ThO$_2$). Based on the calculated phonon dispersion curves, we
calculate the thermal expansion coefficient, bulk modulus, and heat capacities
at different temperatures for ThO$_2$ under the quasi-harmonic approximation.
All the results are in good agreement with corresponding experiments proving
the validity of our methods. Our theoretical studies can help people more
clearly understand the thermodynamic behaviors of ThO$_2$ at different
temperatures. In addition, we have also studied possible defect formations and
diffusion behaviors of helium in ThO$_2$, to discuss its structural stability.
It is found that in intrinsic ThO$_2$ without any Fermi energy shifts, the
interstitial Th$_i^{4+}$ defect other than oxygen or thorium vacancies,
interstitial oxygen, and any kinds of Frenkel pairs, is most probable to form
with an energy release of 1.74 eV. However, after upshifting the Fermi energy,
the formation of the other defects also becomes possible. For helium diffusion,
we find that only through the thorium vacancy can it happen with the small
energy barrier of 0.52 eV. Otherwise, helium atoms can hardly incorporate or
diffuse in ThO$_2$. Our results indicate that people should prevent upshifts of
the Fermi energy of ThO$_2$ to avoid the formation of thorium vacancies and so
as to prevent helium caused damages.
