week ending VOLUME 90.NUMBER 5 PHYSICAL REVIEW LETTERS 7 FEBRUARY 2003 Mechanisms of Radiation-Induced Viscous Flow:Role of Point Defects S.G.Mayr,*Y.Ashkenazy,"K.Albe,and R.S.Averbacks Department of Materials Science and Engineering,University of Illinois at Urbana-Champaign. 405 West Green Street,Urbana,Illinois 61801 (Received 10 July 2002:published 6 February 2003) Mechanisms of radiation-induced flow in amorphous solids have been investigated using molecular dynamics computer simulations.It is shown for a model glass system,CuTi,that the radiation-induced flow is independent of recoil energy between 100 ev and 10 keV when compared on the basis of defect production and that there is a threshold energy for flow of 10 eV.Injection of interstitial-and vacancylike defects induces the same amount of flow as the recoil events,indicating that point-defect- like entities mediate the flow process,even at 10 K.Comparisons of these results with experiments and thermal spike models are made. DOI:10.1103/PhysRevLett90.055505 PACS numbers:61.80.Az,61.80.Jh,61.82.Bg Experimental investigations of stress relaxation and interatomic potentials for Cu-Ti developed by Sabochick surface smoothing have illustrated that many amorphous and Lam [12].Two types of boundary conditions were solids undergo Newtonian flow during ion irradiations at used.One employed periodic boundary conditions in the temperatures far below their respective glass tempera- x-y direction and open surfaces in the z direction,while tures.This phenomenon,which occurs in materials with the other was periodic in three dimensions to avoid covalent [1],ionic [2-5],and metallic [6-8]bonding, surfaces.The first type had fixed boundaries in the x-y provides new opportunities for processing materials at direction and monitored the relaxation of the initial state the nanometer length scale [9]as well as having signifi- of stress,oo,as a function of the number of recoil events. cance for radiation waste storage through glass encapsu- The completely periodic cell used the same applied lation.While radiation-induced viscous flow has been stress,o,in the x-y direction and zero applied stress in widely explored experimentally,a comprehensive theo- the z direction.After each recoil event,performed under retical understanding of this behavior has been more constant volume conditions,the initial state of stress was difficult to achieve.For heavy ions in the regime when restored and the strain in the z direction obtained.Many electronic excitation dominates the stopping,thermal such events were then averaged.The fully periodic cell spike models provide a satisfactory description of the contained 2.56 X 105 atoms for all events,while the flow process since the energy dissipation is uniform and number of atoms in the cell with free surfaces increased typically greater than =1 kev/nm.For lower energy approximately linearly with recoil energy,using a ratio of ions,thermal spike models have also been invoked more than 25 atoms/eV.For both cells the atoms in the [5,10],but in this energy regime,the energy loss is much periodic boundaries were damped to simulate the loss of smaller and the energy distribution tends to be rather energy in infinite solids.The irradiations proceeded by inhomogeneous along the path of the ion.Thermal spike alternating between Cu and Ti recoils. models are therefore less attractive in this situation,since The viscosity during irradiation was determined in the the flow occurs within a few picoseconds or less of the case of periodic boundary conditions using the expression recoil event and large gradients in energies,densities,and stresses are present.Over the past decade,it has been E- -Edef, (1) recognized that molecular dynamics (MD)computer 67 simulations provide a realistic alternative approach to treat such many-body problems,and we apply this where e is the total biaxial strain,o is the applied biaxial method here to explore the mechanisms of radiation- stress,and n is the viscosity.The second term in Eq.(1) induced viscous fow.Our results show that radiation- represents possible changes in strain due to the introduc- induced flow does not,in fact,require thermal spikes tion of "defects"in the amorphous structure during an and that the creation of point defects is an equally,or, irradiation with flux,.φ.Dividing by中yields in many cases,more efficient mechanism.Within this framework,a number of experimental results from differ- deoH dede! (2) ent systems are quantitatively explained. do 6 do Irradiation-induced flow was obtained by simulating the response of an amorphous (a-)CuTi alloy to an ap- whereH=1/(no)is the radiation-induced fluidity plied stress during a series of monoenergetic events at (RIF),and the fundamental quantity in this study.For 10 K.The MD code PARCAS [11]was employed with the calculations of stress relaxation,we use 055505-1 0031-9007/03/90(5)/055505(4)$20.00 2003 The American Physical Society 055505-1Mechanisms of Radiation-Induced Viscous Flow: Role of Point Defects S. G. Mayr,* Y. Ashkenazy,† K. Albe,‡ and R. S. Averbackx Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, 405 West Green Street, Urbana, Illinois 61801 (Received 10 July 2002; published 6 February 2003) Mechanisms of radiation-induced flow in amorphous solids have been investigated using molecular dynamics computer simulations. It is shown for a model glass system, CuTi, that the radiation-induced flow is independent of recoil energy between 100 eV and 10 keV when compared on the basis of defect production and that there is a threshold energy for flow of 10 eV. Injection of interstitial- and vacancylike defects induces the same amount of flow as the recoil events, indicating that point-defect￾like entities mediate the flow process, even at 10 K. Comparisons of these results with experiments and thermal spike models are made. DOI: 10.1103/PhysRevLett.90.055505 PACS numbers: 61.80.Az, 61.80.Jh, 61.82.Bg Experimental investigations of stress relaxation and surface smoothing have illustrated that many amorphous solids undergo Newtonian flow during ion irradiations at temperatures far below their respective glass tempera￾tures. This phenomenon, which occurs in materials with covalent [1], ionic [2–5], and metallic [6–8] bonding, provides new opportunities for processing materials at the nanometer length scale [9] as well as having signifi- cance for radiation waste storage through glass encapsu￾lation. While radiation-induced viscous flow has been widely explored experimentally, a comprehensive theo￾retical understanding of this behavior has been more difficult to achieve. For heavy ions in the regime when electronic excitation dominates the stopping, thermal spike models provide a satisfactory description of the flow process since the energy dissipation is uniform and typically greater than 1 keV=nm. For lower energy ions, thermal spike models have also been invoked [5,10], but in this energy regime, the energy loss is much smaller and the energy distribution tends to be rather inhomogeneous along the path of the ion. Thermal spike models are therefore less attractive in this situation, since the flow occurs within a few picoseconds or less of the recoil event and large gradients in energies, densities, and stresses are present. Over the past decade, it has been recognized that molecular dynamics (MD) computer simulations provide a realistic alternative approach to treat such many-body problems, and we apply this method here to explore the mechanisms of radiation￾induced viscous flow. Our results show that radiation￾induced flow does not, in fact, require thermal spikes and that the creation of point defects is an equally, or, in many cases, more efficient mechanism. Within this framework, a number of experimental results from differ￾ent systems are quantitatively explained. Irradiation-induced flow was obtained by simulating the response of an amorphous (a-)CuTi alloy to an ap￾plied stress during a series of monoenergetic events at 10 K. The MD code PARCAS [11] was employed with the interatomic potentials for Cu-Ti developed by Sabochick and Lam [12]. Two types of boundary conditions were used. One employed periodic boundary conditions in the x-y direction and open surfaces in the z direction, while the other was periodic in three dimensions to avoid surfaces. The first type had fixed boundaries in the x-y direction and monitored the relaxation of the initial state of stress, 0, as a function of the number of recoil events. The completely periodic cell used the same applied stress, 0, in the x-y direction and zero applied stress in the z direction. After each recoil event, performed under constant volume conditions, the initial state of stress was restored and the strain in the z direction obtained. Many such events were then averaged. The fully periodic cell contained 2:56 105 atoms for all events, while the number of atoms in the cell with free surfaces increased approximately linearly with recoil energy, using a ratio of more than 25 atoms=eV. For both cells the atoms in the periodic boundaries were damped to simulate the loss of energy in infinite solids. The irradiations proceeded by alternating between Cu and Ti recoils. The viscosity during irradiation was determined in the case of periodic boundary conditions using the expression _   6  _ def; (1) where  is the total biaxial strain,  is the applied biaxial stress, and is the viscosity. The second term in Eq. (1) represents possible changes in strain due to the introduc￾tion of ‘‘defects’’ in the amorphous structure during an irradiation with flux, _ . Dividing by _ yields d d  H 6  ddef d ; (2) where H  1= _  is the radiation-induced fluidity (RIF), and the fundamental quantity in this study. For calculations of stress relaxation, we use PHYSICAL REVIEW LETTERS week ending VOLUME 90, NUMBER 5 7 FEBRUARY 2003 055505-1 0031-9007=03=90(5)=055505(4)$20.00  2003 The American Physical Society 055505-1