Thermal Neutron Scattering Law for Beryllium Hydride and Critical Mass Calculations
The thermal neutron scattering law (TSL) for crystalline beryllium hydride (BeH 2 ) is developed from first-principles ab initio lattice dynamics calculations and the impact of neutron thermalization in this material on critical mass is estimated. BeH 2 has a body-centered orthorhombic crystal structure with 12 molecules per unit cell and a theoretical density of 0.755 g/cm 3 . The vibrational (phonon) densities of states for H and Be bound in BeH 2 are determined using VASP density functional theory and PHONON lattice dynamics calculations. The TSLs for H bound in BeH 2 , H(BeH 2 ), and Be bound in BeH 2 , Be(BeH 2 ), are then evaluated in the incoherent approximation from the calculated H and Be partial phonon density of states using FLASSH. Finally, critical mass as a function of 235 U loading density for bare and reflected BeH 2 moderated spheres is predicted from MC21 Monte Carlo neutron transport calculations using ENDF/B-VIII.0 cross sections and the H(BeH 2 ) and Be(BeH 2 ) TSL evaluations. Comparisons are made to water (H 2 O), polyethylene (CH 2 ), and beryllium oxide (BeO) as moderators. These critical mass predictions are a refinement upon the prior work by Rao and Srinivasan that neglected thermal neutron scattering effects. The minimum critical mass of a BeH 2 moderated assembly is estimated to be 0.207 kg 235 U for a 0.20 m thick BeO reflected sphere and 0.178 kg 235 U for a 0.40 m thick BeO reflected sphere.