As mentioned above in Section 1.11.4.2, Bacon and coworkers84,107 have shown that the number of stable
point defects produced in many materials follows a simple power-law dependence over a broad range of cascade energies (see eqn [3]). This behavior is shown in Figure 32 for several pure metals and Ni3Al.107 This figure also includes a line labeled NRT that is obtained from eqn [2] if the displacement threshold is taken as 40 eV, which is the recommended average value for iron.16 The difference between the NRT and Fe lines reflect the ratio plotted in Figure 9. As the displacement threshold is different for different metals (e. g., 30 eV is recommended for Cu16), the other lines should not be compared directly with the NRT values. When normalized using the appro­priate NRT displacements, the difference in the sur­vival ratio between Fe and Cu can be seen in Figure 33.61 Although the stable defect production in the other metals may be either somewhat lower or higher than in iron, the behavior is clearly similar across this group of bcc, fcc, and hcp materials. As the energies involved in displacement cascades are so much greater than the energy per atom in a perfect lattice or the vacancy and interstitial formation ener­gies, it is not surprising that ballistic defect produc­tion would be similar.

In-cascade clustering behavior shows a stronger variation between metals than does total defect sur­vival. The fraction of surviving interstitials contained in clusters is shown in Figure 34 for some of these

Ep (keV)

same metals as in Figure 32.107 Although defect formation does not seem to correlate with crystal structure in Figure 32, there is some indication that this may not be the case with interstitial clustering. The lowest clustering fraction is seen in bcc Fe, while the close-packed Cu (fcc) and hcp (Ti, Zr) materials yield higher values. Ti and Zr exhibit nearly the same value. Ni3Al, which is nominally close-packed is more similar to iron. This may be a result of the ordered structure and some impact of antisite defects on inter­stitial clustering. However, there is insufficient data available to make any definitive conclusions.

A further comparison of vacancy and interstitial clustering in Fe and Cu is provided by Figure 35,61 which provides histograms of the cluster size distri­butions for two different cascade energies at 100 K. The interstitial cluster size distributions are shown in (a) and (c) for Fe and Cu, respectively, and the corresponding vacancy cluster size distributions are shown in (b) and (d). Note the scale difference on the abscissa between Figure 35(a and b) and Figure 35(c and d). In addition to having a higher fraction of surviving defects in clusters, copper clearly produces much larger clusters of both types. It is clear that some of these differences are related to either the crystal structure and/or such basic parameters as the stacking fault energy. Many of the large vacancy clus­ters in fcc copper, which has a low stacking fault energy, are large stacking fault tetrahedra (generally imperfect). Similarly, large faulted SIA loops are observed in Cu. Figure 36 illustrates the difference observed between iron and copper in typical 20 keV cascades at 100 K. The final damage state is shown for Fe in (a) and Cu in (b). The simulation cells have an edge length of 50 lattice parameters in both cases. The copper cascade is clearly more compact and exhibits more point defect clustering.

While comparisons of iron and copper have been thoroughly explored in the literature,59,61,107,139 there have also been studies on materials such as zirconium, which is relevant to nuclear fuel cladding.70,107,140,141 Figure 37 provides an example of the differences in point defect clustering between Fe and hcp Zr. The average number of SIAs and vacancies in clusters per cascade as a function of cascade energy at 100 K is shown for (a) zirconium and (b) iron.107 Note the difference in scale on both the number in clusters and the cluster size, and that the highest cascade energy is 20 keV in (a) and 49 keV in (b). In both metals the probability of clustering increases with cascade energy, and the size of the largest cluster similarly increases. As indicated by the fact that there are more single vacancies than single interstitials, a greater fraction of SIAs are in clusters. Similar to the Fe-Cu comparison, there is significantly more clustering in close-packed Zr than in bcc Fe.