Molecular dynamics study of the point defects in bcc uranium

Thermodynamic properties of bcc uranium with point defects are studied using ab initio molecular dynamics (MD) simulations at 1100 K. The simulations were performed with canonical ensembles of ${\mathrm{U}}_{127}{\mathrm{M}}_{1}$, ${\mathrm{U}}_{128}{\mathrm{M}}_{1}$, and ${\mathrm{U}}_{126}{\mathrm{M}}_{1}{\ensuremath{\square}}_{1}$ for M = $\ensuremath{\square}$, He, Ne, Ar, Kr, Xe, Sr, Zr, I, Cs, and Pu disposed on a bcc lattice lying within a $4\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4$ cubic supercell. This work provides formation energies of substitutional, self, and solute interstitial atom defects as well as binding energies of M-$\ensuremath{\square}$ pair defects. This work demonstrates that our computational scheme based on MD simulations gives reliable formation and binding energies of atomic defects in bcc uranium compared to conventional density functional theory calculations. The equilibrium volume, bulk modulus, and thermal expansion coefficient of pure bcc uranium obtained from our MD simulations compare very well with corresponding experimental results. The vacancy formation energy is predicted to be 0.88 eV. The experimental vacancy formation energy remains uncertain. Experimental study of the formation and binding energies of other point defects as well as the bulk modulus and thermal expansion coefficients of uranium with these defects is also not found in the literature. This work shows that point defects tend to decrease the bulk modulus and increase the thermal expansion coefficient of bcc uranium. The solute formation energies of noble gas atoms show a bearing on their size. A large solute (Xe) has a high formation energy, and vice versa. This size effect is not quite evident for the chemically reactive solutes, namely, Sr, Zr, I, Cs, and Pu. Our MD simulations further show that vacancies are the favorable point defects in bcc uranium rather than both vacancies and self interstitials as predicted by earlier calculations. The formation energies of self interstitial atoms are found to be lower than those of solute interstitial atoms, each calculated in six different basic interstitial dumbbell configurations. That is, bcc U accommodates self interstitials more easily than decay or fission gas interstitials (He, Kr, and Xe). Further, He atoms are found to have comparable formation energies in the substitutional and interstitial locations. The fission product atoms Kr and Xe prefer to occupy vacant substitutional lattice sites rather than interstitial sites. Binding energies of divacancy and solute-vacancy pairs (0.31 vs $\ensuremath{-}0.69$ eV for the Xe-$\ensuremath{\square}$ pair, for instance) from our MD simulation show that nucleation and growth of fission gas bubbles are supported by a thermodynamic driving force, whereas vacancies tend to stay apart. This is in agreement with literature reporting that bcc uranium softens and swells mainly by agglomeration of noble gas bubbles.