As discussed in the previous section, the PBM changed the concept of RDT by recognizing that qualitatively different mechanisms operate in materials when the initial damage is in the form of only FPs and under neutron irradiation, when ther­mally stable glissile SIA clusters are continuously produced in cascades. The successful applications of the PBM have been limited to low irradiation doses (<1dpa) and pure metals (e. g., Cu). Furthermore, it predicts the saturation of void size with increas­ing irradiation dose. Thus, it fails to account for the most important observation under neutron or heavy-ion irradiation: continuous increase in void swelling.

The observed continuous void growth may be explained by the development of spatial correlations between voids and other lattice defects. Such as, precipi­tates and dislocations, that shadow voids from the SIA clusters (see Figures 8-10). It has been argued that this must be the case and the very absence of a void lattice (i. e., a particular case of spatial correla­tion, which is between voids) must be an indication that spatial correlations with other defects prevail.35

To account for this effect, a new parameter, ^c, has been introduced, called the 1 correlation-screening factor, which is equal to unity in the absence of shadowing effects and zero when voids are screened completely from the SIA clusters. The swelling rate is then given by

dS

df

where F is a proportionality coefficient, which is a function of all parameters involved.35 Experimental evidence on the association of large voids with vari­ous precipitates (G, ^, Laves, etc.)120,160-162 and the compression side of edge dislocations163,164 has been available for a long time. More recent evidence can be attributed to Portnykh et al.165 who studied the microstructure of 20% cold-worked 16Cr-15Ni- 2Mo-2Mn austenitic steel irradiated up to ^100 dpa in a BN-600 fast reactor in the temperature range from 410 to 600 °C. TEM studies revealed voids of three types: a-type associated with dislocations, b-type associated with G-phase precipitates and c-type distributed homogeneously. The c-type voids were the smallest and made practically no contribution to swelling, while the a-type voids were the largest. Such spatial correlations must be a common feature under cascade irradiation.

As discussed in Barashev and Golubov,35 the experimental data on void swelling can be fit by eqn

[143] with an appropriate choice of the dependence of on the irradiation dose (see Figure 10). At high doses, the voids must be completely shielded from the SIA clusters: = 0, and the steady-state swelling

rate of ~1% per dpa observed in austenitic steels33 can be interpreted as being equal to about half of the production bias, that is, the fraction of SIAs produced as 1D mobile clusters:

dS 1 g dfNRT ~ 2 Wi

where esurv = (1 — er) « 0.1 is the survival fraction of defects in displacement cascade. The weak depen­dence on steel composition observed is probably because the final defect structure is defined by early stages of cascades, when the energies involved are much higher than the binding energies of defects with solute atoms. The observed correlation of the incubation period prior to swelling with the forma­tion of a dislocation network may be connected with an increase of the volume for the nucleation and growth of voids in which voids are screened from the SIA clusters. Higher dislocation density also cor­responds to a smaller dislocation climb rate, which might be essential for preserving void-dislocation correlations.

Another distinguishing feature of neutron irradia­tion is transmutation of atoms, which transform even pure metals into alloys with increasing irradiation dose. The atmospheres of solute (or transmuted) elements near voids may repel SIA clusters and, hence, assist or even solely explain the unlimited void growth. It was shown (see, e. g., Golubov,166 Golubov etal.,167 and references therein) that RIS can provide an additional mecha­nism of preferential absorption of mobile defects even in the framework of FP3DM, causing a ‘segre­gation’ bias, which must be different for immobile defects (e. g., voids) and mobile defects, such as dis­locations. In the PBM, the interaction of the mobile SIA clusters with different defects may even be more important. Solute atoms may also decrease the mobil­ity of SIA clusters, thereby increasing the recombi­nation rate with migrating vacancies. In the case of very high binding energy of SIA clusters with impu­rity atoms, the ‘Singh—Foreman catastrophe’18 discussed in Section 1.13.6.2.1 may occur.

Thus, two additional features beyond those already in the PBM distinguish the microstructure evolution under neutron compared to electron irradiation at high enough doses: transmutation of atoms and devel­opment of spatial correlations. A fully predictive theory must account for these effects.

The development of a predictive theory requires revisiting all its essential elements: nucleation, growth, movement of voids, and other lattice defects in the presence of spatial correlations, etc. Carefully planned experiments spanning different tempera­tures, defect production rates, etc., must be a central part of these future studies. Development of the RIS theory for accounting for the SIA clusters is necessary for understanding the sensitivity of micro­structure to material composition. Generally, the challenge is to create a theory, where the mean-field approach in its conventional form is abandoned, a task not attempted before.

Acknowledgments

The authors would like to acknowledge the fruitful collaboration and discussions on the physics of radiation damage for many years with Professor Yu. V. Konobeev (IPPE, Russia), Drs. B. N. Singh (Riso National Laboratory, Denmark), H. Trinkaus (Forschungscentrum Julich, Germany), SJ. Zinkle and Yu. N. Osetsky (Oak Ridge National Laboratory, USA), and Professor D. J. Bacon (The University of Liverpool, UK). Various aspects of the author’s research discussed in this chapter were supported by the Division of Material Science and Engineering and the Office of Fusion Energy Sciences, Depart­ment ofEnergy and the Office ofNuclear Regulatory Research, US (SIG and RES) and the UK Engineer­ing and Physical Science Research Council (AVB).