An improved xenon equation of state for nanobubbles in UO2

Abstract

To understand the thermodynamic behavior of xenon (Xe) bubbles in uranium dioxide (UO2), the pressure of Xe nanobubbles as a function of temperature was systematically investigated using molecular dynamics (MD) simulations at temperatures ranging from 300 to 2100 K. The results show that the maximum pressure decreases with increasing temperature and bubble size. Interestingly, for a critical Xe/Schottky Defect (SD) ratio of 1 to 1.25, within a temperature range from 300 to 1500 K, the increase of pressure attributed to the change of kinetic energy offsets the decrease of pressure due to the change of potential energy with respect to volume, resulting in a roughly constant bubble pressure. The critical Xe/SD ratio slightly decreases with increasing bubble size. As Xe/SD ratios are lower or higher than the critical ratio, the bubble pressure increases or decreases with increasing temperature, respectively. Based on MD simulations of the pressure of unconfined (free) Xe at temperatures of 300, 900, 1500 and 2100 K, a virial equation of state (EOS), which was expanded to the fifth term, is reported for gas, fluid and solid, unconfined Xe at temperatures higher than 300 K. The EOS for free Xe can also be used to assess the pressure of large bubbles in a matrix, since the confinement effect can be negligible. The confinement effect of the UO2 matrix causes an overestimation of Xe density in highly pressurized nanobubbles. Considering the interaction between Xe and the UO2 lattice, the free Xe EOS is modified to calculate the pressure of small intragranular Xe nanobubbles in UO2.