Thermodynamic mixing properties of the UO₂–HfO₂ solid solution: Density functional theory and Monte Carlo simulations

HfO₂ is a neutron absorber and has been mechanically mixed with UO₂ in nuclear fuel in order to control the core power distribution. During nuclear fission, the temperature at the center of the fuel pellet can reach above 1300 K, where hafnium may substitute uranium and form the binary solid solution of UO₂–HfO₂. UO₂ adopts the cubic fluorite structure, but HfO₂ can occur in monoclinic, tetragonal, and cubic structures. The distribution of Hf and U ions in the UO₂–HfO₂ binary and its atomic structure influence the thermal conductivity and melting point of the fuel. However, experimental data on the UO₂–HfO₂ binary are limited. Therefore, the enthalpies of mixing of the UO₂–HfO₂ binary with three different structures were calculated in this study using density functional theory and subsequent Monte Carlo simulations. The free energy of mixing was obtained from thermodynamic integration of the enthalpy of mixing over temperature. From the ΔG of mixing, a phase diagram of the binary was obtained. The calculated UO₂–HfO₂ binary forms extensive solid solution across the entire compositional range, but there are a variety of possible exsolution phenomena associated with the different HfO₂ polymorphs. As the structure of the HfO₂ end member adopts lower symmetry and becomes less similar to cubic UO₂, the miscibility gap of the phase diagram expands, accompanied by an increase in cell volume by 7–10% as the structure transforms from cubic to monoclinic. Close to the UO₂ end member, which is relevant to the nuclear fuel, the isometric uranium-rich solid solutions exsolve as the fuel cools, and there is a tendency to form the monoclinic hafnium-rich phase in the matrix of the isometric, uranium-rich solid solution phase