Evaluation of Thermal Neutron Scattering Cross Section of Uranium Silicide with Ab Initio Lattice Dynamics
Uranium silicide (U 3 Si 2 ) is a candidate material for the high-density nuclear fuel in commercial light water reactors [1], [2]. Its higher uranium density, 11.3 g-U/cm3, compared to that of uranium dioxide (UO 2 ), 9.7 g-U/cm3, can improve the performance of a nuclear reactor while using low enriched uranium (LEU) and diversify the choice of cladding materials [1]–[3]. It also has a higher thermal conductivity than UO 2 , which can reduce the thermal stress on the material caused by a temperature gradient across the fuel pellet and provide a larger margin for some postulated accidents [1], [2], [4]. Furthermore, compared to U3Si, another high-density fuel candidate, it has better resistance to in-pile swelling due to less irradiation-induced rapid amorphization [1], [3]. Corresponding to its importance in nuclear engineering, many previous studies have reported the properties of U3Si2. Experiments showed that U 3 Si 2 is a paramagnetic (PM) metal, where a slight linear increase in magnetic susceptibility was measured with increasing temperature [5], [6]. In addition, thermodynamic quantities such as thermal expansion coefficient, heat capacity, and thermal conductivity were experimentally determined over a wide temperature range [1], [7], [8]. In several computational studies, ab initio atomistic simulations based on density functional theory (DFT) were performed to calculate various properties including elastic constants, electronic density of states (DOS), and phonon dispersion curves [9]–[12]. Nevertheless, thermal neutron scattering cross sections, which are critical to the prediction of the parameters in reactor physics that are ultimately related to reactor criticality, have not yet been evaluated for U3Si2. The scattering cross section can be calculated from the phonon DOS, or the energy spectrum of lattice vibrations, of the crystalline system [13], [14]. However, there is also no experimental data available for the phonon DOS of U 3 Si 2 . While some computational studies reported the phonon DOS and/or dispersion curves from ab initio simulations [9]–[12], the accuracy cannot be guaranteed because it is unclear whether the spin-polarization behavior of PM U 3 Si 2 was properly described. In the present study, the thermal neutron scattering cross section for U 3 Si 2 is evaluated for the first time by calculating the phonon DOS for U3Si2 from ab initio lattice dynamics (AILD) simulations based on DFT. First, U 3 Si 2 is modeled based on the experimental structure, and AILD simulations are performed on the modeled U3Si2 to optimize the structure. Next, AILD simulations are performed for supercells with atomic displacement to calculate Hellmann-Feynman forces. Based on the calculated forces, partial phonon DOSs for U and Si are obtained, and the thermal neutron scattering law (TSL) for U 3 Si 2 is finally evaluated. To verify the accuracy of the calculations in the present study, the calculation results are compared with experimental data on the structure and heat capacity of U3Si2 [1], [7], [8], [15].