week ending VOLUME 90.NUMBER 5 PHYSICAL REVIEW LETTERS 7 FEBRUARY 2003 calculations are in excellent agreement with experimental o with surface 1015 -x without surface results.Thermal spike models of RIF were carefully analyzed by determining the number of atoms in the liquid and were shown to be at most as efficient as point defects,and then in only some cases. 0.9 10~16 3 0.8 We are grateful for grants of computer time from 0. NCSA and NERSC.The research was supported by the 0.6 0.5 U.S.Department of Energy,Division of Materials a Science,under Grant No.DEFG02-91-ER45439,and 1017 0.001 100 through the University of California under subcontract 0.001 0.0100.1001.00010.0 100.0 B341494. Damage energy [keV] FIG.4.The dependence of the average radiation-induced diffusivity g on the damage energy.The inset shows how the ratio of the diffusivities of Ti and Cu change with damage *Electronic address:smayr@uiuc.edu energy. Electronic address:yinona@uiuc.edu Permanent address:Institut fur Materialwissenschaft, TU Darmstadt,64287 Darmstadt,Germany. Ni7sB4Sis glass,despite its low recoil energy spectrum, Electronic address:averback@uiuc.edu is equally efficient as 700 kev Kr irradiation of the [1]C.Volkert,J.Appl.Phys.70,3521 (1991). Zr6sCu27.sAl7.5 glass.Additional experiments on other [2]E.Snoeks,T.Weber,A.Cacciato,and A.Polman,J.AppL metallic glasses using different ions to determine the Phys.78.4723(1995) universality of the value of H=3 x 10-9(Padpa) [3]E.Snoeks,A.Polman,and C.A.Volkert,Appl.Phys. would be valuable.While the simulations have been per- Lett65,2487(1994). formed only on metallic glasses,the results appear to [4]M.L.Brongersma,E.Snoeks,T.van Dillen,and explain why the value for RIF is the same in SiO2,whose A.Polman,J.Appl.Phys.88,59(2000). value of Te greatly exceeds that for the metallic glasses, [5]M.L.Brongersma,E.Snoeks,and A.Polman,Appl. and for which thermal spikes are not expected.It is Phys.Lett71,1628(1997). [6]P.Jumg,J.Appl.Phys.86,4876(1999). simply because the energy to create a Frenkel pairs [7]S.G.Mayr and R.S.Averback,Phys.Rev.Lett.87, does not vary by more than a factor of 2 in most materials 196106(2001). and defect production is at least as efficient a flow mecha- [8]S.G.Mayr and R.S.Averback,unpublished results nism as the thermal spike.Perhaps our result that defect (2002). production can account for RIF should not be considered [9]E Snoeks,A.van Blaaderen,T.van Dillen,C.M. surprising since a relaxation dose of 0.03 dpa (see Fig.3) van Kats,and M.L.B.A.Polman,Adv.Mater.12,1511 implies that a volume equal to 33 atomic volumes,or a (2000). sphere of radius 0.33 nm surrounding the Frenkel pair, [10]H.Trinkaus,J.Nucl.Mater.223,196 (1995). undergoes relaxation,as the Frenkel pair relaxes.In [11]PARCAS was written by K.Nordlund;see,e.g., crystalline materials the spontaneous relaxation volume K.Nordlund and R.S.Averback,Phys.Rev.B 56,2421 is≈100 atomic volumes or r≈0.5nm[171. (1997). As a final consideration of thermal spikes,we plot the [12]M.J.Sabochick and N.Q.Lam,Scr.Metall.Mater.24, 565(1990). mean square displacement per atom,per dpa,as a [13]F Spaepen,in Physics of Defects,edited by R.Balian, function of recoil energy;see Fig.4.The value is seen M.Kleman,and J.P.Poirier (Elsevier,Amsterdam, to increase with energy up to I kev and then it be- 1981). comes constant.Similar behavior is observed for the ratio [14]M.J.Norgett,M.T.Robinson,and IM.Torrens,Nucl. of the Cu and Ti diffusion coefficients,Dri/Dcu(Fig.4). Eng.Des.33,50(1975). We know from our simulations,moreover,that this ratio is [15]A.J.E.Foreman,C.A.English,and W.J.Phythian, near unity in liquid CuTi.We conclude,therefore,that the Philos.Mag.A 66,671(1992). thermal spike becomes increasingly important with en- [16]While the Kinchin-Pease expression is known to over- ergy up to 1 keV,when local melting becomes significant. estimate the number of stable Frenkel pairs by a factor of The behavior for RIF,in contrast,becomes independent of 3 owing to stimulated recombination in the thermal energy by 100 eV suggesting that the increasing impor- spike,these unstable defects,as well as the stable ones, contribute to the viscous flow. tance of the thermal spike has little influence on the RIF [17]H.J.Wollenberger,in Vacancies and Interstitials in In conclusion,the MD simulations illustrate that Metals,edited by A.Seeger,D.Schumacher, radiation-induced viscous flow results primarily by the W.Schilling,and J.Diehl (North-Holland, creation of point defects,which act as flow defects.The Amsterdam,1970). 055505-4 055505-4Ni78B14Si8 glass, despite its low recoil energy spectrum, is equally efficient as 700 keV Kr irradiation of the Zr65Cu27:5Al7:5 glass. Additional experiments on other metallic glasses using different ions to determine the universality of the value of H  3 10 9 Pa dpa 1 would be valuable. While the simulations have been per￾formed only on metallic glasses, the results appear to explain why the value for RIF is the same in SiO2, whose value of Tg greatly exceeds that for the metallic glasses, and for which thermal spikes are not expected. It is simply because the energy to create a Frenkel pairs does not vary by more than a factor of 2 in most materials and defect production is at least as efficient a flow mecha￾nism as the thermal spike. Perhaps our result that defect production can account for RIF should not be considered surprising since a relaxation dose of 0.03 dpa (see Fig. 3) implies that a volume equal to 33 atomic volumes, or a sphere of radius 0.33 nm surrounding the Frenkel pair, undergoes relaxation, as the Frenkel pair relaxes. In crystalline materials the spontaneous relaxation volume is 100 atomic volumes or r 0:5 nm [17]. As a final consideration of thermal spikes, we plot the mean square displacement per atom, per dpa, , as a function of recoil energy; see Fig. 4. The value is seen to increase with energy up to 1 keV and then it be￾comes constant. Similar behavior is observed for the ratio of the Cu and Ti diffusion coefficients, DTi=DCu (Fig. 4). We know from our simulations, moreover, that this ratio is near unity in liquid CuTi. We conclude, therefore, that the thermal spike becomes increasingly important with en￾ergy up to 1 keV, when local melting becomes significant. The behavior for RIF, in contrast, becomes independent of energy by 100 eV, suggesting that the increasing impor￾tance of the thermal spike has little influence on the RIF. In conclusion, the MD simulations illustrate that radiation-induced viscous flow results primarily by the creation of point defects, which act as flow defects. The calculations are in excellent agreement with experimental results. Thermal spike models of RIF were carefully analyzed by determining the number of atoms in the liquid and were shown to be at most as efficient as point defects, and then in only some cases. We are grateful for grants of computer time from NCSA and NERSC. The research was supported by the U.S. Department of Energy, Division of Materials Science, under Grant No. DEFG02-91-ER45439, and through the University of California under subcontract B341494. *Electronic address: smayr@uiuc.edu † Electronic address: yinona@uiuc.edu ‡ Permanent address: Institut fu(r Materialwissenschaft, TU Darmstadt, 64287 Darmstadt, Germany. x Electronic address: averback@uiuc.edu [1] C. Volkert, J. Appl. Phys. 70, 3521 (1991). [2] E. Snoeks, T. Weber, A. Cacciato, and A. Polman, J. Appl. Phys. 78, 4723 (1995). [3] E. Snoeks, A. Polman, and C. A. Volkert, Appl. Phys. Lett. 65, 2487 (1994). [4] M. L. Brongersma, E. Snoeks, T. van Dillen, and A. Polman, J. Appl. Phys. 88, 59 (2000). [5] M. L. Brongersma, E. Snoeks, and A. Polman, Appl. Phys. Lett. 71, 1628 (1997). [6] P. Jung, J. Appl. Phys. 86, 4876 (1999). [7] S. G. Mayr and R. S. Averback, Phys. Rev. Lett. 87, 196106 (2001). [8] S. G. Mayr and R. S. Averback, unpublished results (2002). [9] E. Snoeks, A. van Blaaderen, T. van Dillen, C. M. van Kats, and M. L. B. A. Polman, Adv. Mater. 12, 1511 (2000). [10] H. Trinkaus, J. Nucl. Mater. 223, 196 (1995). [11] PARCAS was written by K. Nordlund; see, e.g., K. Nordlund and R. S. Averback, Phys. Rev. B 56, 2421 (1997). [12] M. J. Sabochick and N. Q. Lam, Scr. Metall. Mater. 24, 565 (1990). [13] F. Spaepen, in Physics of Defects, edited by R. Balian, M. Kleman, and J. P. Poirier (Elsevier, Amsterdam, 1981). [14] M. J. Norgett, M.T. Robinson, and I. M. Torrens, Nucl. Eng. Des. 33, 50 (1975). [15] A. J. E. Foreman, C. A. English, and W. J. Phythian, Philos. Mag. A 66, 671 (1992). [16] While the Kinchin-Pease expression is known to over￾estimate the number of stable Frenkel pairs by a factor of 3 owing to stimulated recombination in the thermal spike, these unstable defects, as well as the stable ones, contribute to the viscous flow. [17] H. J. Wollenberger, in Vacancies and Interstitials in Metals, edited by A. Seeger, D. Schumacher, W. Schilling, and J. Diehl (North-Holland, Amsterdam, 1970). 0.001 0.010 0.100 1.000 10.0 100.0 Damage energy [keV] 10-17 10-16 10-15 ξ [cm2/dpa] with surface without surface 0.001 100 0.5 0.6 0.7 0.8 0.9 D(Ti)/D(Cu) FIG. 4. The dependence of the average radiation-induced diffusivity  on the damage energy. The inset shows how the ratio of the diffusivities of Ti and Cu change with damage energy. PHYSICAL REVIEW LETTERS week ending VOLUME 90, NUMBER 5 7 FEBRUARY 2003 055505-4 055505-4