Adjusted Graphite Thermal Scattering Data Applied to Fluoride-Salt-Cooled Reactors
Thermal scattering data is a key component of fission reactor simulation. While most materials can be reasonably modeled with a free gas approximation, the moderators in thermal systems require a more rigorous treatment to sufficiently capture their specific neutron interaction physics. Graphite does not typically feature as a principle moderator in power reactors in service today, but remains an attractive prospect for a number of new reactor concepts currently in development. In comparison to light water, a material nearly ubiquitous in thermal reactors, graphite offers a better neutron economy by way of a small absorption cross section, high thermodynamic stability and can be incorporated into the structure of the core itself. Graphite in its purest form is a crystalline material composed of stacked layers of graphene, a hexagonal planar lattice of carbon atoms. In-plane, each carbon atom is covalently bonded to 3 neighbouring carbon atoms, creating a strong bond, while between planes only a weak van der Waals force exists. Pure graphite has a density of 2.26 g/cm{sup 3}. However, reactor-grade contains a significant amount of carbon binder, leading to a porous bulk medium with randomly oriented micro crystals. Densities of 1.5 - 1.9 g/cm{sup 3} are typical for reactor-grade graphite, corresponding to porosities on the order of 10-30%. This deviation from pure crystalline graphite should be accounted for in the thermal scattering data. When an incident neutron is in or near the thermal region, its de Broglie wavelength is the same order as the molecular bond lengths, leading to elastic scattering. At similar energies, the dynamics of the moderator lattice (in the case of solid moderators) can cause inelastic scattering. For these moderators, special cross sections should be calculated and used in reactor simulations. To generate this thermal scattering data, parameters pertaining to the properties and structure of the material in question are fed into a nuclear data processing code, such as NJOY. Within NJOY is a module called LEAPR which is used to generate the thermal scattering law S(α,β), which is in turn is fed into another module THERMR which is used to generate thermal cross sections that factor in the molecular-scale scattering phenomena. The core of the thermal scattering law is the phonon spectrum ρ(β) which describes the modes of excitation of the material lattice. An investigation into the phonon frequency spectrum was conducted at North Carolina State University (NCSU) for reactor-grade graphite which accounts for porosity. This phonon spectrum was calculated using the ab initio density functional theory (DFT) code VASP. The inelastic cross section calculated using this spectrum was found to have good agreement with relevant experimental data. The resulting spectra differed from the benchmark spectrum produced by Young and Koppel, the same data used in current nuclear data evaluations. The latter uses the lattice dynamics of perfect crystalline graphite with four force constants fitted to the model from thermodynamics data from reactor-grade (porous) graphite, which yields a reasonable approximation to the phonon spectrum of reactor-grade graphite.