Thermal neutron scattering law calculations using ab initio molecular dynamics

Abstract

In recent years, methods for the calculation of the thermal scattering law (i.e. S(α,β), where α and β are dimensionless momentum and energy transfer variables, respectively) were developed based on ab initio lattice dynamics (AILD) and/or classical molecular dynamics (CMD). While these methods are now mature and efficient, further advancement in the application of such atomistic techniques is possible using ab initio molecular dynamics (AIMD) methods. In this case, temperature effects are inherently included in the calculation, e.g. phonon density of states (DOS), while using ab initio force fields that eliminate the need for parameterized semi-empirical force fields. In this work, AIMD simulations were performed to predict the phonon spectra as a function of temperature for beryllium and graphite, which are representative nuclear reactor moderator and reflector materials. Subsequently, the calculated phonon spectra were utilized to predict S(α,β) using the LEAPR module of the NJOY code. The AIMD models of beryllium and graphite were 5 × 5 × 5 crystal unit cells (250 atoms and 500 atoms respectively). Electronic structure calculations for the prediction of Hellman-Feynman forces were performed using density functional theory with a GGA exchange correlation functional and corresponding core electron pseudopotentials. AIMD simulations of 1000–10,000 time-steps were performed with the canonical ensemble (NVT thermostat) for several temperatures between 300 K and 900 K. The phonon DOS were calculated as the power spectrum of the AIMD predicted velocity autocorrelation functions. The resulting AIMD phonon DOS and corresponding inelastic thermal neutron scattering cross sections at 300 K, where anharmonic effects are expected to be small, were found to be in reasonable agreement with the results generated using traditional AILD. This illustrated the validity of the AIMD approach. However, since the impact of the temperature on the phonon DOS (e.g. broadening of spectral peaks) was observed in AIMD analysis, this technique may be envisioned as the approach for deriving the needed atomistic data for thermal scattering law calculations under realistic temperature and structural conditions for a given material.