The rationale for investigating the impact of free surfaces on cascade evolution is the existence of an influential body of experimental data provided by experiments in which thin foils are irradiated by high-energy electrons and/or heavy ions.98-106 In most cases, the experimental observations are carried out in situ by TEM and the results of MD simulations are in general agreement with the data from these experiments. For example, some material-to-material differences observed in the MD simulations, such as differences in in-cascade clustering between bcc iron and fcc copper, also appear in the experimental data.59,107,108 However, the yield of large point defect clusters in the simulations is lower than would be expected from the thin foil irradiations, particularly for vacancy clusters. It is desirable to investigate the source of this difference because of the influence this data has on our understanding of cascade damage formation.

Both simulations81,97,109,110 and experimental work105,106 indicate that the presence of a nearby free surface can influence primary damage formation. For example, interesting effects of foil thickness
have been observed in some experiments.105 Unlike cascades in bulk material, which produce vacan­cies and interstitials in equal numbers, the number of surviving vacancies in surface-influenced cascades can exceed the number of interstitials because of interstitial transport to the surface. This could lead to the formation of larger vacancy clusters and account for the differences in visible defect yield observed between the results of MD cascade simula­tions conducted in bulk material and the thin-film, in situ experiments. Initial modeling work reported by Nordlund and coworkers81 and Ghaly and Averback109 demonstrated the nature of effects that could occur, and Stoller and coworkers97,100 subse­quently conducted a study involving a larger number of simulations at 10 and 20keV to determine the magnitude of the effects.

To carry out the simulations,97,100 a free surface was created on one face of a cubic simulation cell containing 250 000 atom sites. Atoms with sufficient kinetic energy to be ejected from the free surface (sputtered) were frozen in place just above the surface. Periodic boundary conditions are otherwise imposed. Two sets of nine 100 K simulations at 10keV were carried out to evaluate the effect of the free surface on cascade evolution. In one case, all the PKAs selected were surface atoms and, in the other, PKA were chosen from the atom layer 10a0 below the free surface. The PKA in eight 20keV, 100 K simulations were all surface atoms. Several PKA directions were used, with each of these directions slightly more than 10° off the [001] surface normal.

Figure 25 provides a representative example of a cascade initiated at the free surface. The peak damage state at 1.1 ps is shown in (a), with the final damage state at ~15 ps shown in (b). The large number of apparent vacancies and interstitials in

Figure 25(a) is due to the pressure wave from the cascade reaching the free surface. With the constrain­ing force of the missing atoms removed, this pressure wave is able to displace the near-surface atoms by more than 0.3a0, which is the criterion used to choose atom locations to be displayed. As mentioned above, a similar pressure wave occurs in bulk cascades, making the maximum number of displaced atoms much greater than the final number of displacements. Most of these displacements are short-lived, as shown in Figure 26, in which the time dependence of the defect popula­tion is shown for three typical bulk cascades, one surface-initiated cascade, and one cascade initiated 10a0 below the surface. The effect of the pressure wave persists longer in surface-influenced cascades, and may contribute to stable defect formation.

The number of surviving point defects (normalized to NRT displacements) is shown in Figure 2 7 for both bulk and surface cascades, with error bars indicating the standard error of the mean. The results are simi­lar at 10 and 20keV. Stable interstitial production in surface cascades is not significantly different than in bulk cascades; the mean value is slightly lower for the 10 keV surface cascades and slightly higher for the 20 keV case. However, there is a substantial increase in the number of stable vacancies produced, and the change is clearly significant. It is particularly worth noting that the number of surviving interstitials and vacancies is no longer equal for cascades initiated at the surface because interstitials can be lost by sputter­ing or the diffusion of interstitials and small glissile
interstitial clusters to the surface. Reducing the num­ber of interstitials leads to a greater number of sur­viving vacancies, as less recombination can occur.

In-cascade clustering of interstitials is also rela­tively unchanged in the surface cascades (e. g., see Figures 4 and 5 in Stoller11 ). The effect on in­cascade vacancy clustering was more substantial. The vacancy clustering fraction per NRT (based on the fourth NN criterion discussed above) increased from ~-0.15 to 0.18 at 10 keV and from ^0.15 to 0.25 at 20 keV. Moreover, the vacancy cluster size distribu­tions changed dramatically, with larger clusters pro­duced in the surface cascades. The free surface effect on the vacancy cluster size distributions obtained at 20 keV bulk is shown in Figure 28. The largest vacancy cluster observed in the bulk cascades con­tained only six vacancies, while the surface cascades had clusters as large as 21 vacancies. This latter size is near the limit of visibility in TEM, with a diameter of almost 1.5 nm. Overall, these results imply that cascade defect production in bulk material is different from that observed in situ using TEM. More research such as that by Calder and coworkers111 is required to fully assess these phenomena, particularly for higher cascade energies, in order to improve the ability to make quantitative comparisons between simulations and experiments.