Impact of temperature- and phase-dependent zirconium hydride phonons on criticality

Zirconium hydride is a solid moderator material that has a high (albeit variable) hydrogen content. Proper modeling of the thermal neutron population in zirconium hydride requires that the thermal neutron scattering law be used, which incorporates the material structure into the cross section. In the incoherent approximation, this scattering law may be calculated using a material’s phonon distribution and other material parameters. Historically, the partial phonon distributions for zirconium hydride (ZrH${}_x$) have often been assumed to be independent of hydrogen content, crystalline phase, and temperature. The present work aims to relax this approximation by generating phonon distributions using molecular dynamics while varying (1) the hydrogen content, (2) crystalline phase, and (3) material temperature. Through this work, hydrogen content and crystalline phase have shown to have mild impacts on the vibrational structure, while temperature appears to hold strong influence over the vibrational properties of the materials considered. Temperature-dependent H(ZrH${}_x$) phonon distributions for $\delta$-ZrH_1.67, $ϵ$-ZrH_1.82, and $ϵ$-ZrH₂ were tested on models of a TRIGA reactor and a SNAP reactor, showing how material-specific vibrational models can noticeably influence $k_{\mathrm{eff}}$, flux distributions, and reactivity coefficients.