Calculation of Elastic Constants of UO$_2$ using the Hubbard-Corrected Density-Functional Theory DFT+U

Uranium dioxide which is used as a fuel in light water nuclear reactors, is continually exposed to radiation damage originated from the collision of high-energy particles. Accumulation of the resulting defects gives rise to the evolution in the micro-structure of the fuel which in turn brings about local tensions and strains in the fuel. One of the after effects due to evolution of micro-structure is the swelling of fuel which can damage the fuel cladding and cause environmental contamination by leakage of radioactive particles. Hence, it is vital to continually monitor the evolution of micro-structure and to analyze the changes in mechanical properties of the fuel. The study of elastic constants and analysis of their behavior is very helpful in understanding the mechanical properties of the fuel. In this research, using the Hubbard-corrected first-principles density-functional theory method, we have calculated the elastic constants of the uranium dioxide single crystal and compared the results with existing experimental data. In addition, using the Voigt, Reuss, and Hill models, we have estimated the mechanical properties for the poly-crystalline fresh fuel. The results show a very good agreement between the theory and experiment. Accordingly, we can reliably extend our method of calculations to the complicated system of irradiated fuel pellet, which is in the form of a poly-crystal and hosts various defects.