Influence of Quantum Oscillations in the Thermal Scattering Law of Zirconium Carbide on Neutron Thermalization and Criticality

Zirconium carbide (ZrC) is a candidate material for advanced high temperature reactors, including space nuclear thermal propulsion applications. Thermal scattering laws (TSLs) are generated in the incoherent approximation for carbon bound in ZrC [C(ZrC)] and zirconium bound in ZrC [Zr(ZrC)], using ab initio lattice dynamics methods. Disordered alloy theory is introduced to improve treatment of isotopic composition within the elastic scattering cross section. Localized higher-energy vibrational modes and the presence of a phonon band gap in C(ZrC) cause quantized oscillation in the TSL atypical of nonhydrogenous solids. These oscillations yield a significant likelihood of large energy downscattering and upscattering interactions such that the quanta of energy transfer affecting neutron thermalization is substantially greater than classically expected. MC21 critical mass calculations of ZrC mixtures with high-enriched uranium demonstrate an impact of TSLs when compared to a free-gas treatment for thermal neutron–driven ²³⁵U loadings. The critical mass of homogenous mixed moderator systems of ZrC and reactor-grade graphite are also sensitive to the ZrC TSL. Moreover, the effect of quantized energy exchange on the neutron spectra is found to influence the temperature feedback coefficient.