Vacancy formation and solid solubility in the U–Zr–N system

For the purpose of developing a nuclear fuel with enhanced thermophysical properties and better irradiation performance density functional theory calculations are used to explore UN, ZrN and (U, Zr)N. Negative deviation of ground state energy from the ideal solution model as well as energetically favourable maximal distance between substitutional metal atoms in respective nitrides indicate mutual solubility of UN and ZrN at all temperatures. Nitrogen vacancy formation energies in UN (1.81 eV) and ZrN (1.40 eV) are considerably lower than metal vacancy formation energies. A substitutional Zr atom in UN has little effect on nitrogen vacancy formation energies (∼1.79 eV), while U in ZrN decreases the value by ∼0.1 eV (∼1.30 eV) due to elastic stress and charge density redistribution in the material. The relative distance between a substitutional metal atom and a vacancy in UN has little influence over the radially declining displacement pattern induced by the substitutional atom, while in ZrN the relaxation of atoms is governed by the position of the vacancy. The calculated vacancy formation energies indicate a lower surface energy of ZrN in comparison with UN.