Generation of phonon density of states and thermal scattering law using ab initio molecular dynamics

The operation and safety of thermal nuclear reactors is dependent on the ability to accurately predict the thermal neutron spectrum; a distribution which is correlated to the inelastic thermal neutron scattering cross-section of the neutron moderator. The inelastic thermal neutron scattering law, S(α,β), of a moderator is a fundamental property of the material describing the permitted vibrational excitations of the atoms, i.e. phonons, and may be calculated using atomistic methods. The current state-of-the-art ab initio lattice dynamics (AILD) methods have been used to calculate phonon density of states (DOS) at 0 K for use in the generation of S(α,β) under reactor conditions. Modern computational power, however, has made accessible ab initio molecular dynamics (AIMD) methods. The AIMD technique captures temperature effects and permits the calculation of the phonon DOS from first principles. This is in contrast to AILD, where temperature effects are lacking, and classical molecular dynamics methods that use semi-empirical force fields. The aim of this work is to demonstrate the use of AIMD in the generation of the phonon DOS for beryllium as an exemplar moderating material. The phonon DOS was computed from AIMD simulations at 300 K and compared to AILD. Subsequently, S(α,β) and the inelastic scattering cross-section were generated using the NJOY package for both methods. The predicted phonon DOS and inelastic scattering cross-section for the AIMD method were found to be consistent with those predicted using AILD.