As discussed elsewhere,59,63,65 in-cascade vacancy clustering in iron is quite low (~10% of NRT) when a NN criterion for clustering is applied. This was identified as one of the differences between iron and copper in the comparison of these two materials reported by Phythian and coworkers.59 However, when the coordinates of the surviving vacancies in 10, 20, and 40keV cascades were analyzed, clear spatial correlations were observed. Peaks in the distributions of vacancy-vacancy separation dis­tances were obtained for the second and fourth NN locations.64 These radial distributions are shown in Figure 19. Similar results were obtained from the analysis of the vacancy distributions in higher energy cascades at 100 and 600 K. The peak observed for vacancies in second NN locations is consistent with the di-vacancy binding energy being greater for second NN (0.22 eV) than for first NN (0.09 eV).90 The reason for the peak at fourth NN is presumably related to this also since two vacancies that are second NN to a given vacancy would be fourth NN. In addi­tion, work discussed by Djurabekova and coworkers91 indicates that there is a small binding energy between two vacancies at the fourth NN distance.

Sonic
shock wave "V
(nondestructive)
separation ^

Transonic shock-= Spaghetti

wave limit

(d)

Figure 18 Schematic representation of cascade development leading to the formation of interstitial and vacancy clusters formation. Reproduced from Calder, A. F.; Bacon, D. J.; Barashev, A. V.; Osetsky, Yu. N. Phil. Mag. 2010, 90, 863-884.

An example of a locally vacancy-rich region in a 50keV, 100 K cascade is shown in Figure 20, where the region around a collection of 14 vacancies has

vacancy within the fourth NN spacing of 1.66a0, where a0 is the iron lattice parameter. The ‘cluster’ is shown in two views: a 3D perspective view and an orthographic projection (—x) in Figure 20. Such an arrangement of vacancies is similar to some of the vacancy clusters observed by Sato and coworkers in field ion microscope images of irradiated tungsten.9 Since the time period of the MD simulations is too short to allow vacancies to jump (<100 ps), the possi­bility that these closely correlated vacancies might collapse into clusters over somewhat longer times has

been investigated using MC simulations. The vacancy coordinates at the end ofthe MD simulations were extracted and used as the starting configuration in MC cascade annealing simulations. The expecta­tion of vacancy clustering was confirmed in the MC simulations, where many of the isolated vacancies had clustered within 70 ms.90,

The energy and temperature dependence of in-cascade vacancy clustering as a fraction of the NRT displacements is shown in Figure 21 for cas­cade energies of 10-50 keV. Results are shown for clustering criteria of first, second, third, and fourth NN. A comparison of Figure 21 and Figure 12 demonstrates that in-cascade vacancy clustering in iron remains lower than that of interstitials even when the fourth NN criterion is used. This is consis­tent with the experimentally observed difficulty of forming visible vacancy clusters in iron as discussed by Phythian and coworkers,59 and the fact that only relatively small vacancy clusters are found in positron annihilation studies of irradiated ferritic alloys.94 However, it should be pointed out that work with more recently developed iron potentials finds less dif­ference between vacancy and interstitial clustering.74 The cascade energy dependence of vacancy cluster­ing is similar to that of interstitials; there is essentially zero clustering at the lowest energies but it rapidly increases with cascade energy and is relatively inde­pendent of energy above ^10 keV. However, vacancy clustering decreases as the temperature increases,

which is consistent with vacancy clusters being ther­mally unstable.

Fractional vacancy cluster size distributions are shown in Figure 22, for which the fourth NN clus­tering criterion has been used. Figure 22(a) illus­trates that the vacancy cluster size distribution shifts to larger sizes as the cascade energy increases from 10 to 50keV. This is similar to the change shown for interstitial clusters in Figure 13(a). There is a corresponding reduction in the fraction of single vacancies. However, as mentioned above, the effect of cascade temperature shown in Figure 22(b) and 22(c) is the opposite of that observed for interstitials. The magnitude of the temperature effect on the vacancy cluster size distributions also appears to be weaker than in the case of interstitial clusters. The fraction of single vacancies increases and the size dis­tribution shifts to smaller sizes as the temperature increases from 100 to 900 K for the 10keV cascades, and from 100 to 600 K for 20 keV cascades. Similar to the case of interstitial clusters, the effect of tempera­ture seems to be greater at 20 keV than at 10 keV.