56 POINT DEFECT MOVEMENT AND ANNEALING IN... 2427 produced in the cascade.The fact that very few vacancies ----Before rec. 102 5 keV Au were seen even in the 20 interstitial event indicates that the ■ ■ 0.5ps 10p5 presence of preexisting interstitials inhibits the creation of -20ps vacancies in a collision cascade:i.e..vacancies and intersti- --…50ps tials cannot coexist in the liquid core.Again,interstitial clus- ters were observed in the center of the cascade 10 We also simulated one event (run Au 9)in which we placed 20 interstitials and 20 vacancies as close to the center ◆◆一◆ of the cell as possible while retaining the 10 A minimum distance between them.After a 5 keV cascade event there 10 were 5 interstitials and 5 vacancies left in the cell,confirm- ing that damage anneals in the liquid core of the cascade. The surviving interstitials were located far away from the cascade center.whereas 4 of the vacancies were close to the 20 40 60 80 100 center. Distance from center(A) 3.Uniform defect distributions FIG.6.Pressure as a function of time in a 5 keV gold cascade as a function of the distance from the cascade center,evaluated simi- In the events described above,the final amount of damage larly as the temperature.The initial very high values are caused by was generally reduced by a cascade,but the effect was the strong collisions in the heart of the cascade.Near the end of the strongly dependent on the shape of the(somewhat artificial) cascade the pressure decreases towards the center of the cell due to initial defect distributions.To provide an estimate of what the presence of vacancies near the center. defect concentration is large enough to cause a reduction of the final number of defects,we simulated a number of events with a uniform defect concentration in the simulation cell initial interstitials were within the region of the cell which (the defects were introduced in the cell on random atom was liquid at some point of the cascade evolution.The vol- sites).The numbers of initial and final defects in these events ume of the liquid core (defined as the total volume of unit cells which contained liquid atoms at any time during the are listed in Table I as events Au 12-15. For 200+200 and 100+100 initial interstitials and vacan- simulation)was about 4%of the total volume or 4000 atomic cies the number of defects decreases as a result of a 5 keV volumes cascade.whereas for 50+50 initial defects the number in- As shown in Fig.4,the vacancies within the liquid core of creases.Considering only the defect-producing and anneal- the cascade cluster near the center of the cell.Similar behav- ing effect of the 5 keV cascades described above,we obtain ior was seen in the two events where preexisting vacancies were placed near the center of the simulation cell.The clus- that the equilibrium number of defects is of the order of tering in the center shows how the crystal regenerative pro- 1x 10-3.This result corresponds closely to experiments in cess favors the production of defect-free fcc lattice on reso- which defects were introduced randomly by proton irradia- lidification.Since the central region contains too few atoms tion and subsequently annealed by heavy ion irradiation.16 to form a perfect lattice,a vacancy cluster remains in the In a cascade event(run Au 10)with a large number of randomly distributed initial interstitials,only one vacancy is center.This result is similar to the copper cascade results of Kapinos and Bacon,which show clustering and loop forma- created,in good agreement with our earlier observation that tion of vacancies in samples with high initial vacancy interstitials appear to inhibit vacancy production.On the concentrations.14 other hand,in run Au 1I which had a large number of initial vacancies,six interstitials were produced,indicating that the In the event with no initial vacancies (Au 2).12 of the 50 initial interstitials got trapped in the liquid region and formed opposite is not necessarily true.This reflects the fact that an interstitial cluster in the center it.This shows that the newly produced interstitials are ejected from the liquid and avoid recombination,whereas vacancies are always pro- resolidification kinetics is sufficiently fast to avoid quench- duced in the liquid ing in defects and that the high-pressure gradient in the core of a cascade does not push the interstitials outwards,as might be expected.This is discussed further in Sec.IIIA4. 4.Damage at 600 K We also tested the behavior of interstitials near the cas- Since most practical ion irradiations are performed at tem- cade core.We simulated three 5 keV Au cascade events in peratures much higher than 0 K,we performed a few simu- which the cell contained 20,50,and 200 interstitials,placed lations at 600 K(runs Au 16-19).The initial defect distri- spherically around the center of the cell using the 10 Amini- butions were the same as in runs Au 2-5.Prior to the mum distance between defects(runs Au 6-8 in Table I).No initiation of a the cascade,the pressure in the cell was equili- vacancies were included in the initial cell in these events. brated to 0 kbar and the atoms were given realistic thermal In these cascades,the final cell contained 21,51,and 201 displacements by performing a 5 ps run at 600 K using a final interstitials,and a single vacancy in each case.The variable cell size and a pressure control algorithm.25 interstitials formed large clusters in all events,although a To check how many defects annihilate due to thermal few isolated interstitials were seen as well.In reference motion alone,two 50 ps runs were performed at a fixed events where a 5 keV event was simulated in an undisturbed temperature with no cascade in the cell.Run Au 19 was fcc lattice typically around 5 vacancies and interstitials were performed at 600 K and run Au 20 at 670 K [the averageinitial interstitials were within the region of the cell which was liquid at some point of the cascade evolution. The vol￾ume of the liquid core ~defined as the total volume of unit cells which contained liquid atoms at any time during the simulation! was about 4% of the total volume or 4000 atomic volumes. As shown in Fig. 4, the vacancies within the liquid core of the cascade cluster near the center of the cell. Similar behav￾ior was seen in the two events where preexisting vacancies were placed near the center of the simulation cell. The clus￾tering in the center shows how the crystal regenerative pro￾cess favors the production of defect-free fcc lattice on reso￾lidification. Since the central region contains too few atoms to form a perfect lattice, a vacancy cluster remains in the center. This result is similar to the copper cascade results of Kapinos and Bacon, which show clustering and loop forma￾tion of vacancies in samples with high initial vacancy concentrations.14 In the event with no initial vacancies ~Au 2!, 12 of the 50 initial interstitials got trapped in the liquid region and formed an interstitial cluster in the center it. This shows that the resolidification kinetics is sufficiently fast to avoid quench￾ing in defects and that the high-pressure gradient in the core of a cascade does not push the interstitials outwards, as might be expected. This is discussed further in Sec. IIIA4. We also tested the behavior of interstitials near the cas￾cade core. We simulated three 5 keV Au cascade events in which the cell contained 20, 50, and 200 interstitials, placed spherically around the center of the cell using the 10 Åmini￾mum distance between defects ~runs Au 6–8 in Table I!. No vacancies were included in the initial cell in these events. In these cascades, the final cell contained 21, 51, and 201 final interstitials, and a single vacancy in each case. The interstitials formed large clusters in all events, although a few isolated interstitials were seen as well. In reference events where a 5 keV event was simulated in an undisturbed fcc lattice typically around 5 vacancies and interstitials were produced in the cascade. The fact that very few vacancies were seen even in the 20 interstitial event indicates that the presence of preexisting interstitials inhibits the creation of vacancies in a collision cascade; i.e., vacancies and intersti￾tials cannot coexist in the liquid core. Again, interstitial clus￾ters were observed in the center of the cascade. We also simulated one event ~run Au 9! in which we placed 20 interstitials and 20 vacancies as close to the center of the cell as possible while retaining the 10 Å minimum distance between them. After a 5 keV cascade event there were 5 interstitials and 5 vacancies left in the cell, confirm￾ing that damage anneals in the liquid core of the cascade. The surviving interstitials were located far away from the cascade center, whereas 4 of the vacancies were close to the center. 3. Uniform defect distributions In the events described above, the final amount of damage was generally reduced by a cascade, but the effect was strongly dependent on the shape of the ~somewhat artificial! initial defect distributions. To provide an estimate of what defect concentration is large enough to cause a reduction of the final number of defects, we simulated a number of events with a uniform defect concentration in the simulation cell ~the defects were introduced in the cell on random atom sites!. The numbers of initial and final defects in these events are listed in Table I as events Au 12–15. For 2001200 and 1001100 initial interstitials and vacan￾cies the number of defects decreases as a result of a 5 keV cascade, whereas for 50150 initial defects the number in￾creases. Considering only the defect-producing and anneal￾ing effect of the 5 keV cascades described above, we obtain that the equilibrium number of defects is of the order of 131023. This result corresponds closely to experiments in which defects were introduced randomly by proton irradia￾tion and subsequently annealed by heavy ion irradiation.16 In a cascade event ~run Au 10! with a large number of randomly distributed initial interstitials, only one vacancy is created, in good agreement with our earlier observation that interstitials appear to inhibit vacancy production. On the other hand, in run Au 11 which had a large number of initial vacancies, six interstitials were produced, indicating that the opposite is not necessarily true. This reflects the fact that newly produced interstitials are ejected from the liquid and avoid recombination, whereas vacancies are always pro￾duced in the liquid. 4. Damage at 600 K Since most practical ion irradiations are performed at tem￾peratures much higher than 0 K, we performed a few simu￾lations at 600 K ~runs Au 16–19!. The initial defect distri￾butions were the same as in runs Au 2–5. Prior to the initiation of a the cascade, the pressure in the cell was equili￾brated to 0 kbar and the atoms were given realistic thermal displacements by performing a 5 ps run at 600 K using a variable cell size and a pressure control algorithm.25 To check how many defects annihilate due to thermal motion alone, two 50 ps runs were performed at a fixed temperature with no cascade in the cell. Run Au 19 was performed at 600 K and run Au 20 at 670 K @the average FIG. 6. Pressure as a function of time in a 5 keV gold cascade as a function of the distance from the cascade center, evaluated simi￾larly as the temperature. The initial very high values are caused by the strong collisions in the heart of the cascade. Near the end of the cascade the pressure decreases towards the center of the cell due to the presence of vacancies near the center. 56 POINT DEFECT MOVEMENT AND ANNEALING IN . . . 2427