Solution (source code)

= Solution

<void swelling> has a \b[<temperature> window], rather than increasing monotonically with irradiation <temperature>. At sufficiently low <temperature>, <vacancy> migration and cavity growth are slow. At intermediate <temperature>, mobile defects, stable nuclei and unequal sink capture can support rapid cavity growth. At higher <temperature>, increased <vacancy> emission, recombination and changing sink populations can reduce the <vacancy supersaturation> and net <void swelling>. The precise peak depends on alloy, spectrum, dose rate and starting <microstructure>; lower <void swelling> at high <temperature> does not mean that <creep (deformation)> or <helium embrittlement> is harmless there.

Distinguish <void swelling> $S=\Delta V/V_0$ from its slope. With displacement dose $D$, a simple schematic description is
$$
S(D)\simeq0\quad(D<D_0),\qquad
S(D)\simeq k(T)(D-D_0)\quad(D>D_0),
$$
where $D_0$ represents incubation and $k(T)$ an approximately constant post-transient slope over a limited range. Real nucleation and sink evolution make the transition smooth; neither $D_0$ nor $k$ is a universal material constant. At larger dose, microstructural or compositional evolution may change the slope again.

<neutron fluence> is an integrated exposure, $\Phi=\int\phi\,dt$. Under an unchanged spectrum it can track displacement dose, but equal fluence does not necessarily imply equal damage or <helium> production. Even equal dpa can give different <void swelling> at different dose rates because recombination and transport compete in real time. Thus compare specimens at specified <temperature>, spectrum, dose rate and metallurgical condition; do not transfer one <void swelling> curve using fluence alone.