MD Simulations of Void Stability in a-Si Under Heavy Ion (Xe) Bombardment: Influence of He

1. MD Simulations of Void Stability in a-Si Under Heavy Ion (Xe) Bombardment: Influence of He Brent J. Heuser University of Illinois, Urbana, IL Work supported by DoE NEER Program Under Grant No. DE-FG07-01ID14121

2. Acknowledgements • Maria Okuniewski, Yinon Ashkenazy (Hebrew Univ.), Robert Averback (UIUC-MSE) • MCC IBM computer cluster, UIUC, Greg Bauer

3. Outline • Introduction—Why do we care about voids/bubbles in a-Si? • Background—Energetic ion damage process; MD basics; Interatomic potentials; Simulation details. • Results of void/bubble closure—Dependence on energy (@p=0) and He pressure (@E=2 keV). • Special case of unidirectional irradiation—Greater stability observed. • Model of void/bubble closure—Viscous flow and surface tension. • Conclusions—He bubbles are stable, voids are not.

4. Why do we care? • Inventory statistics (R.C. Ewing, Proc. Natl. Acad. Sci. 96, 1999, 3432) • Actinides dominate after 500 yrs.: 238Pu, 131Sm, 241Am • 239Pu and 237Np after several hundred yrs. • 960 MCi HLW from weapons production (>99% non-actinide; T1/2<50 yrs) • 30,200 MCi commercial spent fuel. • Pu from weapon dismantlement. • Waste storage media • Glass—modified borosilicate glasses. • Ceramics—Zircon • Requirements • Hold radioisotopes in matrix (in solution). • Structural integrity over thousands of years. • Barrier between environment and radioisotopes (leaching).

5. He introduction a + recoil Energetic recoil Potential Problems He bubbles Bubble formation leads to compressive stresses He Actinide Decay Cracking Rad. damage DV/V>0 Devitrification leads to compressive stresses

6. a-SiO2 vs. a-Si Property a-SiO2 a-Si Mass r [g/cc] 2.322.57 Number r (x1022 1/cc) 7.0 5.5 Tmelt1713 C 1414 C Bond Type Covalent Covalent 2 keV Xe TRIM Range ~50 A ~50 A Experience with Si potential

7. Outline • Introduction—Why do we care about voids/bubbles in a-Si? • Background—Energetic ion damage process; MD basics; Interatomic potentials; Simulation details. • Results of void/bubble closure—Dependence on energy (p=0) and He pressure (E=2 keV). • Special case of unidirectional irradiation—Greater stability observed. • Model of void/bubble closure—Viscous flow and surface tension. • Conclusions—He bubbles are stable, voids are not.

8. Energy Loss of Energetic Ion in a SolidTwo Components: Electronic (Ionization) and Nuclear (Collision/Displacement) Light ion (like He) dE/dx|e>>dE/dx|c Projectile path Projectile path Heavy ion (like Xe) dE/dx|c>>dE/dx|e Energy loss via ionization Displacement cascades

9. Displacement Cascade Details Projectile High density of Frenkel pairs (vacancies + interstitials) created in displacement cascade

10. Dvi MD Basics--Solve F=ma and F=-dU/dr Velocity distribution at T1 DRi=DT1vi DT1 DFi=S(-DU/DR )k Dvi=DT1DFi/m Updated vel. dist. @T2 vi(T2)=vi (T2)+Dvi DT2 DRi

11. Interatomic Potential in Detail High-energy processes like displacement cascades. ZBL potential here. Atom @ equil. wrt nearest neighbors Potential Energy, U(r) Near-equil., low-energy processes like diffusion, phase transformation. EAM, S-W potentials here. , r

12. Examples of MD 100 eV C60 incident on C nanotube lying on Pt K. Nordlund/U. Helsinki

13. Low energy self-ion impact on graphite K. Nordlund/U. Helsinki

14. 50 keV Xe incident on (100) Au surface K. Nordlund/U. Helsinki

15. 50 keV Xe incident on liquid Au surface K. Nordlund/U. Helsinki

16. Local plasticity near crack in Cu F. Abraham/IBM

17. Simulations Details 50,000 Si atom cell (~100 A on a side) Amorphous structure created by melt-quenching c-Si Periodic BCs 10 K skin 5 A thick 20 A Void/Bubble: He pressure 0-1 kbar Xe ion: 0.2-2 keV Uni- & multi-directional Interatomic Potentials He-He: L-J Si-He: Pure repulsive (ZBL) Si-Si: Stillinger-Weber Xe-He and Xe-Si: ZBL MD using PARCAS on a PC cluster 30 psec displacement phase (DV/V=0) 30 psec relaxation phase (p=0 @ boundary) ~1 cpu hour/psec/processor

18. 2 keV Xe Displacement with 1 kbar He Color: Distance Displaced Size: Energy

19. 1 keV Xe Displacement with 0.1 kbar He

20. Outline • Introduction—Why do we care about voids/bubbles in a-Si? • Background—Energetic ion damage process; MD basics; Interatomic potentials; Simulation details. • Results of void/bubble closure—Dependence on energy (@p=0) and He pressure (@E=2 keV). • Special case of unidirectional irradiation—Greater stability observed. • Model of void/bubble closure—Viscous flow and surface tension. • Conclusions—He bubbles are stable, voids are not.

21. Void Closure w/ He2 keV Xe

22. P=0 5 events Effect of He Gas Pressure on Closure2 keV Xe Initial P=1 kbar 5 events

23. Effect of He on Closure 2 keV Xe: 1 kbar He 1 keV Xe: 0.1 kbar He

24. Void Closure w/o He

25. Void Closure w/o He

26. Outline • Introduction—Why do we care about voids/bubbles in a-Si? • Background—Energetic ion damage process; MD basics; Interatomic potentials; Simulation details. • Results of void/bubble closure—Dependence on energy (@p=0) and He pressure (@E=2 keV). • Special case of unidirectional irradiation—Greater stability observed. • Model of void/bubble closure—Viscous flow and surface tension. • Conclusions—He bubbles are stable, voids are not.

27. Initial After 2 After 1 displ. After 3 After 4 After 5 Evolving Void Morphology—No He(Incident 2 keV Xe along z axis) Void

28. Initial After 2 After 1 displ. After 3 After 4 After 5 Evolving Void Morphology—No He

29. Evolving Void Morphology—No He Continued After 6 After 7

30. Initial After 1 displ. After 2 After 3 After 4 After 5 Evolving Void Morphology—0.1 kbar He

31. Initial After 2 After 1 displ. After 3 After 4 After 5 Evolving Void Morphology—1 kbar He

32. Comparision of Void Morphologies after Displacements 1 kbar No He 0.1 kbar

33. Outline • Introduction—Why do we care about voids/bubbles in a-Si? • Background—Energetic ion damage process; MD basics; Interatomic potentials; Simulation details. • Results of void/bubble closure—Dependence on energy (@p=0) and He pressure (@E=2 keV). • Special case of unidirectional irradiation—Greater stability observed. • Model of void/bubble closure—Viscous flow and surface tension. • Conclusions—He bubbles are stable, voids are not.

34. Time Scale t<0.3 ps ~0.5-5 ps >10 ps Elongated void shape becomes stable wrt further closure. Molten Region Why? Void Reduced curvature along walls Inhibits further mass transport during subsequent displace- ments. Molten Region Liquid Si goes here because surface tension is reduced by concave surface. Mass flow from molten region to concave void surfaces. Incident Ion Model of Void Elongation/Stability in Simulations

35. Incident Ion Effect of Changing the Incident Ion Direction Elongated void less stable wrt further closure.

36. Effect of He Gas Expect effect of He gas when gas pressure roughly equals surface tension of a:Si This happens at about 0.05 kbar He

37. Viscous Flow Theory Energy dissipated by viscous flow; dEF/dt =(1/2)|2|dV162R(R/r)3 Rate of loss of surface energy; dES/dt8(R2/r) Equating; r = (/2) Radius decrease prop. to time

38. Conclusions • He filled voids (bubbles) are stable under heavy ion bombardment for gas pressures greater than or equal to approximately 0.1 kbar. • Void closure (no He case) scales with energy at high E, but not at low E. • A chain of two or more displacement events at the same location near a spherical void or low-pressure He bubble will induce elongation.