Successful applications of the PBM have been limited to low irradiation doses (< 1 dpa) and pure metals (e. g., copper). There are two apparent problems preventing the general application of the model at higher doses.

1.13.6.3.1 Swelling saturation at random void arrangement

The PBM predicts a saturation of void size.30 This originates from the mixture of 1D and 3D diffusion- reaction kinetics under cascade damage conditions, the assumption lying at the heart of the model. More specifically, it stems from the fact that the interaction cross-section with a void is proportional to the void radius, R, for 3D migrating vacancies and to R2 for 1D diffusing SIA clusters. As a result, above some critical radius, the latter becomes higher than the former and the net vacancy flux to such voids is negative. In contrast, experiments demonstrate indefinite void growth in the majority of materials and conditions.31- 34 An attempt to resolve this contradiction was under­taken by including thermally activated rotations of the SIA-cluster Burgers vector23,25,27; but it has been shown by Barashev et a/.25 that this is not a solution. Thus, the PBM fails to account for this important and common observation, that is, the indefinite void growth under cascade irradiation. A way ofresolving this issue is discussed in Section 1.13.7.

1.13.6.3.2 Absence of void growth in void lattice

Another problem of the PBM is that it fails to explain swelling saturation at rather low swelling levels (approximately several percent) observed in void lat­tices. In fact, it even predicts an increase in the swelling rate when a random void arrangement is changed to that of a lattice.25 This is because the free channels between voids along close-packed directions, which are formed during void ordering, provide escape routes for 1D migrating SIA clusters to disloca­tions and GBs, thereby allowing 3D migrating vacan­cies to be stored in voids. A possible explanation of the problem is discussed in a forthcoming paper by Golubov eta/.37