VOLUME 90.NUMBER 5 PHYSICAL REVIEW LETTERS week ending 7 FEBRUARY 2003 with equal strength.It is also noteworthy that the stress mal spikes play any significant role in the RIF process. relaxation for creation of either defect at 10 K occurs. Previous theories of RIF have assumed that thermal more or less,in steps.After an initially slow response to spikes are the primary mechanism of stress relaxation, adding defects,a rapid relaxation occurs,followed by and indeed,ion beam mixing in metals is usually domi- another slow response.This avalanchelike behavior was nated by thermal spike diffusion.We address this question also observed for the low-energy recoil events,but not for by first noting that the time (i.e.,dose)constant for the high-energy events.Presumably,the higher density of stress relaxation in the defect injection simulations is defects produced in each of the higher-energy events,or 0.03 dpa,which corresponds in our defect production local heating,suppresses this behavior.As seen in Fig.3 at calculations to 0.75 eV/atom.We consider,therefore,the 400 K this behavior is also suppressed.While we have not average energy required to raise an atom above a charac- yet examined the cause of this behavior,the fact that the teristic temperature,T,at which the viscosity is suffi- width of the step is 30 injected defects in a cell con- ciently low for relaxation to occur during a thermal spike. taining 16000 atoms suggests that a concentration of For simulated CuTi,T=800 K.Thus,for a 500 eV recoil 0.2%defects leads to an instability and subsequent event,for example,there need be over 700 such atoms to relaxation. compete with the defect mechanism.Results for the A quantitative comparison was made between the flow number of liquid atoms produced in recoil events are caused by defect creation at 10 K with that by recoil events illustrated in Table I An atom is considered liquid if it, by calculating the flow per Frenkel pair.For the injection and its neighbors,each has a kinetic energy equal to simulations this is straightforward since the number of 3/2kgT.A peak in this number is observed at short defects is known.For the recoil events we assume that the time 0.1-0.2 ps,followed by a long tail.The peak is threshold energy for defect production is 10 ev,as indi- due to a rapid outward expansion,or microexplosion, cated in Fig.2,and employ the Kinchin-Pease expression surrounding the recoil site,while the tail is due to local to calculate the number of Frenkel pairs per recoil event heating.Both numbers scale with energy above 500 ev [16].We find the rather remarkable result that,to within with the ratio of liquid atoms to energy being 1.2 eV per the uncertainties,simulations of both injection of defects atom and the ratio of atoms in the microexplosion to and the recoil events yield H=3x 10-9(Padpa)-1 recoil energy =0.8 ev per atom.Both ratios are close where dose is measured in normalized units of displace- to that deduced for the inserted defects. ments per atom,i.e.,the atomic fraction of Frenkel pairs. These several results indicate that three separate While this extremely close agreement must be somewhat mechanisms may contribute to stress relaxation,creation fortuitous,owing to the uncertainties in the threshold of point defects,atomic reorganization around a micro- energy and the Kinchin-Pease model,it illustrates that explosion,and local melting.In metals they appear the creation of point defects in recoil events is sufficient to operate with nearly the same efficiency and above in itself to induce the observed stress relaxation. 500 eV;they all scale linearly with recoil energy. We next compare our value of H=3x Below 500 eV,the thermal spike mechanism does not 10-9(Padpa)-obtained by MD simulation,with pub- appear viable since the cooling rate is too fast,less than lished experimental measurements of RIF on the metallic 0.3 ps;consequently,either defect production or the mi- glasses,Ni7sB14Sis and Zr65Cu27.5Al75,and glassy SiO2: croexplosion mechanisms must dominate.Since the mi- for 6.3 MeV proton irradiation of the Ni-based metallic croexplosion,ie.,a local excitation at the site of the glass H=4X 10-9(Padpa)[6];for 700 keV Kr irra- newly created Frenkel pair,always accompanies the ad- diation of the Zr-based glass,H2.6 X 10-(Padpa)-1 dition of a Frenkel pair in a recoil event,we refer to the [7,8];and for a series of MeV ion irradiations of different two simply as defect production.We find that,despite the mass projectiles on SiO2,H=2.8 x 10-9(Padpa)-1 [5]. different mechanisms of RIF its value remains constant For the normalization to dpa in these irradiations,we over the entire energy range of our simulations,100 eV to have used the displacement energy of 10 ev in the 10 keV.This further illustrates that the local melting Kinchin-Pease model.Remarkably,H has nearly the mechanism can be no more efficient than defect produc- same value for these very disparate irradiations as for tion.For this reason,RIF in the 6.4 Mev p-irradiated the simulations.Notice,for example,that the primary recoil spectrum for 6.3 MeV proton irradiation of the Ni- based glass is strongly weighted toward low energies;half TABLE I.Number of atoms during the microexplosion NM. the Frenkel pairs are produced in recoils below a charac- number of liquid atoms N and lifetime r as a function of teristic energy,T1/2,of 400 eV.For the 700 keV bombard- damage energy Ep. ment of Zr6sCu27.5Al75,T1/2 exceeds 20 keV.Moreover, Ep [keV] 0.1 0.5 1.0 3.0 10 the glass temperature for these metallic glasses is NM 80 763 1709 4549 13865 ≈400°C,whereas it is over1l00°C in SiO2 N 0 320 840 2450 8050 While a defect model appears to explain a variety of experimental results for RIF we consider whether ther- [fs] 180 1100 2100 3000 6000 055505-3 055505-3with equal strength. It is also noteworthy that the stress relaxation for creation of either defect at 10 K occurs, more or less, in steps. After an initially slow response to adding defects, a rapid relaxation occurs, followed by another slow response. This avalanchelike behavior was also observed for the low-energy recoil events, but not for the high-energy events. Presumably, the higher density of defects produced in each of the higher-energy events, or local heating, suppresses this behavior. As seen in Fig. 3 at 400 K this behavior is also suppressed. While we have not yet examined the cause of this behavior, the fact that the width of the step is 30 injected defects in a cell con￾taining 16 000 atoms suggests that a concentration of 0:2% defects leads to an instability and subsequent relaxation. A quantitative comparison was made between the flow caused by defect creation at 10 K with that by recoil events by calculating the flow per Frenkel pair. For the injection simulations this is straightforward since the number of defects is known. For the recoil events we assume that the threshold energy for defect production is 10 eV, as indi￾cated in Fig. 2, and employ the Kinchin-Pease expression to calculate the number of Frenkel pairs per recoil event [16]. We find the rather remarkable result that, to within the uncertainties, simulations of both injection of defects and the recoil events yield H  3 10 9 Pa dpa 1, where dose is measured in normalized units of displace￾ments per atom, i.e., the atomic fraction of Frenkel pairs. While this extremely close agreement must be somewhat fortuitous, owing to the uncertainties in the threshold energy and the Kinchin-Pease model, it illustrates that the creation of point defects in recoil events is sufficient in itself to induce the observed stress relaxation. We next compare our value of H  3 10 9 Pa dpa 1 obtained by MD simulation, with pub￾lished experimental measurements of RIF on the metallic glasses, Ni78B14Si8 and Zr65Cu27:5Al7:5, and glassy SiO2: for 6.3 MeV proton irradiation of the Ni-based metallic glass H 4 10 9 Pa dpa 1 [6]; for 700 keV Kr irra￾diation of the Zr-based glass, H 2:6 10 9 Pa dpa 1 [7,8]; and for a series of MeV ion irradiations of different mass projectiles on SiO2, H  2:8 10 9 Pa dpa 1 [5]. For the normalization to dpa in these irradiations, we have used the displacement energy of 10 eV in the Kinchin-Pease model. Remarkably, H has nearly the same value for these very disparate irradiations as for the simulations. Notice, for example, that the primary recoil spectrum for 6.3 MeV proton irradiation of the Ni￾based glass is strongly weighted toward low energies; half the Frenkel pairs are produced in recoils below a charac￾teristic energy, T1=2, of 400 eV. For the 700 keV bombard￾ment of Zr65Cu27:5Al7:5, T1=2 exceeds 20 keV. Moreover, the glass temperature for these metallic glasses is 400 C, whereas it is over 1100 C in SiO2. While a defect model appears to explain a variety of experimental results for RIF, we consider whether ther￾mal spikes play any significant role in the RIF process. Previous theories of RIF have assumed that thermal spikes are the primary mechanism of stress relaxation, and indeed, ion beam mixing in metals is usually domi￾nated by thermal spike diffusion.We address this question by first noting that the time (i.e., dose) constant for stress relaxation in the defect injection simulations is 0:03 dpa, which corresponds in our defect production calculations to 0:75 eV=atom. We consider, therefore, the average energy required to raise an atom above a charac￾teristic temperature, Tc, at which the viscosity is suffi- ciently low for relaxation to occur during a thermal spike. For simulated CuTi, Tc  800 K. Thus, for a 500 eV recoil event, for example, there need be over 700 such atoms to compete with the defect mechanism. Results for the number of liquid atoms produced in recoil events are illustrated in Table I. An atom is considered liquid if it, and its neighbors, each has a kinetic energy equal to 3=2kBTc. A peak in this number is observed at short time 0:1–0:2 ps, followed by a long tail. The peak is due to a rapid outward expansion, or microexplosion, surrounding the recoil site, while the tail is due to local heating. Both numbers scale with energy above 500 eV, with the ratio of liquid atoms to energy being 1.2 eV per atom and the ratio of atoms in the microexplosion to recoil energy 0:8 eV per atom. Both ratios are close to that deduced for the inserted defects. These several results indicate that three separate mechanisms may contribute to stress relaxation, creation of point defects, atomic reorganization around a micro￾explosion, and local melting. In metals they appear to operate with nearly the same efficiency and above 500 eV; they all scale linearly with recoil energy. Below 500 eV, the thermal spike mechanism does not appear viable since the cooling rate is too fast, less than 0.3 ps; consequently, either defect production or the mi￾croexplosion mechanisms must dominate. Since the mi￾croexplosion, i.e., a local excitation at the site of the newly created Frenkel pair, always accompanies the ad￾dition of a Frenkel pair in a recoil event, we refer to the two simply as defect production. We find that, despite the different mechanisms of RIF, its value remains constant over the entire energy range of our simulations, 100 eV to 10 keV. This further illustrates that the local melting mechanism can be no more efficient than defect produc￾tion. For this reason, RIF in the 6.4 MeV p-irradiated TABLE I. Number of atoms during the microexplosion NM, number of liquid atoms NL and lifetime  as a function of damage energy ED. ED [keV] 0.1 0.5 1.0 3.0 10 NM 80 763 1709 4549 13 865 NL 0 320 840 2450 8050  [fs] 180 1100 2100 3000 6000 PHYSICAL REVIEW LETTERS week ending VOLUME 90, NUMBER 5 7 FEBRUARY 2003 055505-3 055505-3