The actual number of defects that survive the dis­placement cascade and their spatial distribution in solids will determine the effect on the irradiated microstructure. Figure 7 summarizes the effect of

damage morphology from the viewpoint of the grain boundary and how the defect flow affects radiation — induced grain boundary segregation. Of the total defects produced by the energetic particle, a fraction appears as isolated, or freely migrating defects, and the balance is part of the cascade. The fraction of the ‘ballistically’ produced FPs that survive the cascade quench and are available for long-range migration is an extremely important quantity and is called the migration efficiency, e. These ‘freely migrating’ or ‘avail­able migrating’ defects10 are the only defects that will affect the amount of grain boundary segregation, which is one measure of radiation effects. The migra­tion efficiency can be very small, approaching a few percent at high temperatures. The migration effi­ciency, e, comprises three components:

gi v: the isolated point defect fraction,

8iv: clustered fraction including mobile defect clusters such as di-interstitials, and Z: fraction initially in isolated or clustered form after the cascade quench that is annihilated during subsequent short-term (>10~ns) intracascade thermal diffusion.

They are related as follows:

e = di + gi + Ci = dv + gv + Cv I11]

Figure 8 shows the history of defects born as vacan­cies and interstitials as described by the NRT model.

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Clustered point defect fraction (CDF) (div)

Due to significant recombination in the cascade, only a fraction (^30%) is free to migrate from the displacement zone. These defects can recombine out­side of the cascade region, be absorbed at sinks in the
matrix (voids, loops), or be absorbed at the grain boundaries, providing for the possibility of radiation — induced segregation.

The fraction of defects that will be annihilated after the cascade quench by recombination events among defect clusters and point defects within the same cascade (intracascade recombination), Z, is about 0.07, for a migration efficiency of 0.3 (see below for additional detail).10 The clustered fraction, d includes large, sessile clusters and small defect clusters that may be mobile at a given irradiation temperature and will be different for vacancies and interstitials. For a 5 keV cascade, di is about 0.06 and dv is closer to 0.18.10 Some of these defects may be able to ‘evaporate’ or escape the cluster and become ‘available’ defects (Figure 8).

This leaves g, the isolated point defect fraction that are available to migrate to sinks, to form clus­ters, to interact with existing clusters, and to partic­ipate in the defect flow to grain boundaries that gives rise to radiation-induced segregation. Owing to their potential to so strongly influence the irra­diated microstructure, defects in this category, along with defects freed from clusters, make up the freely migrating defect (FMD) fraction. Recall that electrons and light ions produce a large fraction of their defects as isolated FPs, thus increasing the likeli­hood of their remaining as isolated rather than clus­tered defects. Despite the equivalence in energy among the four particle types described in Figure 5, the average energy transferred and the defect pro­duction efficiencies vary by more than an order of magnitude. This is explained by the differences in the cascade morphology among the different parti­cle types. Neutrons and heavy ions produce dense cascades that result in substantial recombination during the cooling or quenching phase. However, electrons are just capable of producing a few widely spaced FPs that have a low probability of recombi­nation. Protons produce small widely spaced cas­cades and many isolated FPs due to the Coulomb interaction and therefore, fall between the extremes in displacement efficiency defined by electrons and neutrons.

The value of g has been estimated to range from 0.01 to 0.10 depending on PKA energy and irradia­tion temperature, with higher temperatures resulting in the lower values. Naundorf12 estimated the freely migrating defect fraction using an analytical treat­ment based on two factors: (1) energy transfer to atoms is only sufficient to create a single FP, and (2) the FP lies outside a recombination (interaction)

radius so that the nearby FPs neither recombine nor cluster. The model follows each generation of the collision and calculates the fraction of all defects produced that remain free. Results of calculation using the Naundorf model are shown in Table 1 for several ions of varying mass and energy. Values of Z range between 24% for proton irradiation to 3% for heavy ion (krypton) irradiation. Recent results,13 however, have shown that the low values of FMD efficiency for heavy ion or neutron irradiation cannot be explained by defect annihilation within the parent cascade (intracascade annihilation). In fact, cascade damage generates vacancy and interstitial clusters that act as annihilation sites for FMD, reducing the efficiency of FMD production. Thus, the cascade remnants result in an increase in the sink strength for point defects and along with recombination in the original cascade, account for the low FMD efficiency measured by experiment.