The interaction of cavities with mobile interstitial clusters is believed t
o be responsible for the saturation of swelling in irradiated materials. We
show that the saturation limit depends on the microstructure of the materi
al, and that the origin of the effect is associated with the violation of t
he low-density approximation in the case of scattering of one-dimensionally
moving interstitial clusters by grain boundaries. For large grains, swelli
ng is enhanced near the boundaries, while for small grains swelling is maxi
mum in the grain interior. The maximum size of cavities corresponding to th
e saturation of swelling is found to be many times the mean-field estimate.