Double differential neutron scattering cross sections of materials for ultra high temperature reactors

The five materials with the highest melting point are hafnium, tantalum, niobium and zirconium (ZrC) carbides and graphite (that sublimes). Graphite is the material of choice for very high temperature reactors (VHTR); ultra high temperature reactors (UHTR), like the thermal nuclear propulsion reactor NERVA use a dispersion of ZrC and UC in graphite as the material in the reactor core. Presently there are neither inelastic nor elastic double differential scattering data available that describe the thermalization process in ZrC. We therefore, calculated coherent elastic and incoherent inelastic cross sections for the ZrC crystal which has a face centered cubic (fcc) lattice. The phonon spectrum for the ZrC lattice was calculated with the computer code PHONON using the Hellman-Feynman forces computed with ab-initio methods [Jochyn, P.T., Parlinski, K., 2000. Ab initio lattice dynamics and elastic constants of ZrC. Eur. Phys. J. B 15, 265-268]. This phonon spectrum was then used to compute the S(α, β, T) matrices for the inelastic scattering cross sections for C and Zr in the ZrC lattice using modified versions of the computer codes GASKET, HEXSCAT and NJOY. The results were applied to calculate, with the proper S(α, β, T), criticality and reactivity coefficients of temperate of reactor systems containing ZrC and UC. For comparisons, these parameters were also calculated with approximations of S(α, β, T), i.e. the gas or the graphite scattering kernels. Depending on the degree of thermalization, k eff is underestimated between 0.6% and 1%, and the values and the shape of the reactivity coefficients as a function of temperature change by substantial amounts