Hydride prediction during late-stage oxidation of uranium in a water vapour environment

We present a reaction-advection-diffusion (RAD) model for (low temperature) uranium oxidation in a water-vapour environment, where both ${\mathrm{OH}}^{-}$ and $H^{•}$ are diffusing. In this model an intermediate ${\mathrm{UH}}_3$ phase sits between the bulk $U$ metal and a protective surface ${\mathrm{UO}}_2$ layer. This surface oxide layer only remains adhered up to a maximum depth ${\Delta }_{\mathrm{adh}}^{\ast }$ before spallation occurs leading to significantly increased diffusive transport across the spalled layer. Under these conditions, this mechanistic model is shown to support both a parabolic ($\propto \sqrt{t}$) oxide growth up to the point of spallation, before smoothly transitioning to a linear ($\propto t$) oxidation solution at later times. In the late-stage linear regime, a ${\mathrm{UO}}_2-{\mathrm{UH}}_3$ interface propagates into the bulk metal at a constant velocity of$\frac{D_1^{\left(3\right)\ast }{C}^{\ast }}{2{\Delta }_{\mathrm{adh}}^{\ast }{N}_2^{\ast }};$

$D_1^{\left(3\right)\ast }$ being the diffusion coefficient of ${\mathrm{OH}}^{-}$ in ${\mathrm{UO}}_2$ and $C^{\ast }/N_2^{\ast }$ the peak relative concentration of ${\mathrm{OH}}^{-}$ to $U$. This model predicts that the intermediate hydride layer approaches a constant thickness in the linear regime, with a ${\mathrm{UH}}_3-U$ interface propagating into the bulk metal at the same velocity. The length scale of this emergent hydride layer is shown to be most sensitive to the diffusivity of ${\mathrm{OH}}^{-}$ in ${\mathrm{UH}}_3$ and the corresponding reaction rate constant. Plausible parameter values are shown to lead to hydride layers $<10$ nm for room temperature oxidation in a vapour pressure of 20 Torr (${\Delta }_{\mathrm{adh}}^{\ast }=50$ nm) consistent with recent atom-probe tomography results.