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.