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Let $c(t)$ be the fraction still crystalline. Under the direct-impact amorphization model, damage events occur randomly and independently; an event striking already amorphous material does not create that much additional amorphous volume. Only the crystalline fraction can be newly converted, soThe product of the given event rate density and damage volume has units of inverse time:For $99\%$ radiation-induced amorphization, $c=0.01$, givingUsing $365.25$ days per year, the corresponding calendar date is approximately 3555 CE, measured from disposal preparation in 2050.

A linear estimate $f_a=Rvt$ misses repeated hits to already damaged regions and therefore predicts too rapid an approach to $99\%$. The exponential function model never reaches exactly $100\%$ in finite time. Its assumptions include constant dose rate, fixed effective damage volume, no annealing and no spatial correlation of damage. Actual alpha decay generates recoil damage as well as the alpha particle's track; the stated damage volume must be understood as the effective volume per radioactive decay for the chosen model.

Amorphous is not synonymous with dissolved or failed containment. Radiation damage can change swelling, connected porosity and leach behaviour, so testing must compare structural evolution with element release. Accelerated self-irradiation and parallel dissolution measurements are useful precisely because crystallinity alone is not the performance endpoint.^[ref]