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 \ce{OH-} and \ce{H^.} are diffusing. In this model an intermediate \ce{UH3} phase sits between the bulk \ce{U} metal and a protective surface \ce{UO2} layer. This surface oxide layer only remains adhered up to a maximum depth $\Delta_{adh}^*$ before spallation occurs leading to significantly increased diffusive transport across the spalled layer. Under these conditions, this mechanistic model is shown to support {\em 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 \ce{UO2}--\ce{UH3} interface propagates into the bulk metal at a constant velocity of
$$
\frac{D_1^{(3)*} C^*}{2\Delta^*_{adh}N^*_2}\,;
$$
$D^{(3)*}_1$ being the diffusion coefficient of \ce{OH-} in \ce{UO2} and $C^*/N^*_2$ the peak relative concentration of \ce{OH-} to \ce{U}. This model predicts that the intermediate hydride layer approaches a constant thickness in the linear regime, with a \ce{UH3}--\ce{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 \ce{OH-} in \ce{UH3} 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 ($\Delta_{adh}^*$ = 50 nm) consistent with recent atom-probe tomography results.