For simplicity, we used the temperature range 260-400 °C for this analysis as the motion of sodium exhibited a unidirectional propagation from the top to the bottom of the continuous oxide layer in this range. In contrast, sodium diffused in various directions within the loosely packed dendritic oxide layer, complicating the measurement of the sodium diffusion length. Measurements of L were performed by drawing a line from the start of the box (x0), i.e., the boundary between continuous oxide and loosely packed oxide, to the maximum vertical extent of the sodium front (xi) (see SI, Experimental Section and Fig. ). We averaged the measurements in four areas (Fig. ) to assess the measurement statistics. We also assume that such unidirectional motion of sodium in the continuous oxide layer was concentration driven (a diffusion process) rather than under the influence of potential. The measured L was then plotted as a function of temperature (Fig. ), showing a nonlinear increase with temperature. Building on Fick's second law of diffusion and a time-dependent diffusivity model, we derived a solid-state diffusion model for sodium within the continuous oxide layer (see SI):