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Description
Metal hydrides have a variety of mechanical, thermal, and neutronic properties that are ideal for applications to nuclear technologies. As a result, zirconium hydride has been used in the fuel of TRIGA reactors for over half a century. More recently, calcium hydride (CaH${}_{2}$), a saline hydride, has been investigated and shows promise for use as a moderator in microreactors. As of yet, there is not a Thermal Scattering Law (TSL) evaluation for CaH${}_{2}$ in the ENDF database. In addition, the evaluation that exists in the European counterpart, JEFF, contains physical inaccuracies in the Ca portion of the cross section due to limitations in the thermal neutron scattering code used for the evaluation. The purpose of this work is to evaluate the thermal neutron scattering cross sections of CaH${}_{2\ }$from first principles, using accurate physical models, for publication and use in reactor design.
The probability of a thermal neutron to scatter from incident energy E into energy E${}^{'}$ through solid angle $\mathrm{\Omega }$ is described by the double differential scattering cross section and, therefore, the TSL. In the case of CaH${}_{2}$, the incoherent, harmonic, and cubic approximations are implemented in the calculation of the TSL, which is performed using a phonon expansion where all second- and higher-order terms represent inelastic scattering via the exchange of phonons. The phonon density of states (DOS), also known as the vibrational DOS, is a key input in this calculation under the cubic approximation. Using ab initio lattice dynamics (AILD), density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP) with a GGE-PBE pseudopotential. The structure optimization led to lattice constant and atom positions that differ by less than 1% from experiment and determined that a plane wave cutoff energy of 675 eV and a 9x9x9 Monkhorst-Pack k-point mesh were sufficient. The obtained Hellman-Feynman forces were used in the PHONON code to calculate the phonon dispersion curves and DOS using the dynamical matrix method. Finally, the cross sections were calculated, under the incoherent approximation, using the Full Law Analysis Scattering System Hub, $FLASSH$, a code developed by the Low Energy Interaction Physics (LEIP) group at North Carolina State University.
Consequently, this work produced a phonon DOS that closely matches experiment and thermal neutron scattering cross sections for the three CaH${}_{2}$ nonequivalent sites (Ca, H${}_{1}$, H${}_{2}$) that demonstrate the expected physical behavior. In addition to the incoherent inelastic cross sections, the Ca evaluation contains a coherent elastic component that accounts for interference effects from the entire CaH${}_{2}$ lattice, while the H${}_{1}$ and H${}_{2\ }$evaluations contain incoherent elastic contributions. Additionally, the hydrogen inelastic cross sections demonstrate oscillatory behavior that was predicted by Fermi in 1936.${}^{\ }$The cross sections calculated in this work are being finalized for entry into the ENDF database.