TMS 2012 presentation

Transcript

1. On the Factors Governing the Sink Strength of Semicoherent fcc-bcc Interfaces Kedarnath Kolluri and Michael Demkowicz Financial Support: Center for Materials at Irradiation and Mechanical Extremes (CMIME) at LANL, an Energy Frontier Research Center (EFRC) funded by U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences Acknowledgments: B. P. Uberuaga, A. Kashinath, A. Vattré, X.-Y. Liu, A. Misra, R. G. Hoagland, J. P. Hirth, M. A. Nastasi, and A. Caro
2. • Point defects (lets assume the cascade occurs in bulk) • arrive at the interface • reside and move at coherent regions of the interface until either • emit back into the bulk • embed into “non coherent” regions of the interface • dynamics of embedded defects Predicting interface sink efficiency: Beyond v.1 Cartoon of defect activity in radiation environment l2 b Db eff ⌫e E/kT Ac Dic eff l2 b Db eff Ac Dic eff
3. • Point defects (lets assume the cascade occurs in bulk) • arrive at the interface • reside and move at coherent regions of the interface until either • emit back into the bulk • embed into “non coherent” regions of the interface • dynamics of embedded defects UNKNOWN Cartoon of defect activity in radiation environment l2 b Db eff ⌫e E/kT Ac Dic eff l2 b Db eff Ac Dic eff Predicting interface sink efficiency: Beyond v.1
4. Interface sink efficiency: Formal definition Cartoon of defect activity in radiation environment where M2 µ2 M1 µ1 m13 m12 ⌘ = JI JI 0 Mi = Mb i [ Mb,I i Bulk mobilities Interface mobi Interface free energy µI J = Mrµ rµ = µbI @F I @n δ Interface thickness lets assume 1 as interface is rather sharp
5. Interface sink efficiency Cartoon of defect activity in radiation environment Hence, Interface free energy plays a crucial role in interface sink strength Goal: Determine interface free energy ⌘ = M h µbI @F I @n i M0µbI ⌘ = 1 @F I @⇢ µbI M2 µ2 M1 µ1 M3 µ3 m13 m12
6. Interface structure evolves Schematic of free energy of an interface ★ Interface structure evolves as defects interact with the interface Interface energy (f) Interfacial density (ρ) void phase transformation structure evolves f(⇢, . . . ) ⌘ = 1 @F I @⇢ µbI FI ⌘ (f(⇢, . . . ), Mi, m)
7. ★ Different interface regions may have different densities ★ Different density region have different free energies Interface sink efficiency change as structure evolves Interfacial density (ρ) Interface energy (f) µ v bulk µ i bulk void phase transformation structure evolves f(⇢, . . . ) FI ⌘ (f(⇢, . . . ), Mi, m) ⌘ = 1 @F I @⇢ µbI M2 µ2 M1 µ1 M3 µ3 m13 m12
8. Holy grail: Predict sink efficiency as interface structure evolves Schematic of interface free energy Point defect activity under radiation Interfacial density (ρ) Interface energy (f) µ v bulk µ i bulk void phase transformation structure evolves f(⇢, . . . ) FI ⌘ (f(⇢, . . . ), Mi, m) Goal: To determine in the context of interface structure • Interface free energy (factors that determine the energy functional) • Point defect mobilities that will determine the interface evolution ⌘(t) = 1 @F I @⇢ µbI M2 µ2 M1 µ1 M3 µ3 m13 m12
9. • Our focus is on • interfaces of immiscible fcc-bcc semicoherent metal systems Cu-Nb, Cu-V, Cu-Mo, Cu-Fe, and Ag-V (in both KS and NW) Methods and model systems • Atomistic simulations of few interfaces: Molecular dynamics (at 800 K) and statics, EAM potential, LAMMPS • Develop insights that may be used to develop figures of merits for classes of interfaces (111) fcc (110) bcc || ʪ110ʫ fcc ʪ111ʫ bcc || and Kurdjumov-Sachs (KS): (111) fcc (110) bcc || ʪ110ʫ fcc ʪ100ʫ bcc || and Nishiyama-Wassermann (NW):
10. General features of semicoherent fcc-bcc interfaces Cu-V ʪ110ʫ Cu ʪ111ʫ Nb ʪ112ʫ Cu ʪ112ʫ Nb An example of a semicoherent interface
11. View of the Interface
12. View of the Interface
13. View of the Interface
14. View of the Interface
15. View of the Interface
16. View of the Interface
17. General features of semicoherent fcc-bcc interfaces Cu-V ʪ110ʫ Cu ʪ111ʫ Nb ʪ112ʫ Cu ʪ112ʫ Nb An example of a fcc-bcc semicoherent interface Patterns corresponding to periodic “good” and “bad” regions
18. General features of semicoherent fcc-bcc interfaces Cu-V ʪ110ʫ Cu ʪ111ʫ Nb ʪ112ʫ Cu ʪ112ʫ Nb Interface contains arrays of misfit dislocations separating coherent regions
19. General features of semicoherent fcc-bcc interfaces ʪ110ʫ Cu ʪ111ʫ Nb ʪ112ʫ Cu ʪ112ʫ Nb Cu-Nb Cu-V Interface contains arrays of misfit dislocations separating coherent regions
20. Cu-Nb KS Cu-V KS ʪ110ʫ Cu ʪ112ʫ Cu 1 nm MDI • Two sets of misfit dislocations with Burgers vectors • Misfit dislocation intersections (MDI) where different sets of dislocations meet General features of semicoherent fcc-bcc interfaces
21. Defects on misfit dislocations are good traps to point defects 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 Cu-Nb KS Cu-Fe NW Cu-V KS 1 nm 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1 nm 1.4 nm Formation energy (eV) Angle with -ve x axis 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0 Cu-Nb KS Cu-Fe NW Cu-V KS 1 nm 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1 nm 1.4 nm Formation energy (eV) Angle with -ve x axis Different fcc-bcc semicoherent interfaces with misfit dislocations Vacancy formation energies (similar trend for interstitials as well)
22. Interface reconstruction dominated by MDI-point defect interactions Interface structure evolution depends on MDI interactions with point defects Formation energy (eV) Ag-V NW Cu-Nb KS Size of point defect cluster at an MDI -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -10 -8 -6 -4 -2 0 2 4 6 8 10 Cu-Mo KS B C A
23. Interface reconstruction dominated by MDI-point defect interactions Interface structure evolution depends on MDI interactions with point defects Formation energy (eV) Ag-V NW Cu-Nb KS Size of point defect cluster at an MDI -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -10 -8 -6 -4 -2 0 2 4 6 8 10 Cu-Mo KS B C A B’ A’ Cu-Nb
24. A’ B’ Cu-Mo Interface structure evolution depends on MDI interactions with point defects Interface reconstruction dominated by MDI-point defect interactions Formation energy (eV) Ag-V NW Cu-Nb KS Size of point defect cluster at an MDI -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -10 -8 -6 -4 -2 0 2 4 6 8 10 Cu-Mo KS B C A
25. Interface structure evolution depends on MDI interactions with point defects Interface reconstruction dominated by MDI-point defect interactions Formation energy (eV) Ag-V NW Cu-Nb KS Size of point defect cluster at an MDI -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 -10 -8 -6 -4 -2 0 2 4 6 8 10 Cu-Mo KS B C A C’ A’ Ag-V
26. Holy grail: Predict sink strength as interface structure evolves Schematic interface free energy Point defect activity under radiation ⌘ = 1 P Mi @F I @⇢ P MiµI i Interfacial density (ρ) Interface energy (f) µ v bulk µ i bulk void phase transformation structure evolves f(⇢, . . . ) M2 µ2 M1 µ1 M3 µ3 m13 m12 FI ⌘ (f(⇢, . . . ), Mi, m) Goal: To determine • Interface free energy (or factors) • point defect mobilities that will determine the interface evolution
27. Point defect migration along the interface depends on the distance between defects on misfit dislocations Point defects migrate from MDI to MDI by collective atomic motion Cu-Nb KS (a) (b) (c) 1 nm 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0. 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 Cu-Nb KS Cu-Fe NW Cu-V KS 1 nm 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 nm 1.4 nm 0.6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 W Cu-V KS 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1.4 nm Formation energy (eV) Angle with -ve x axis
28. Point defect migration along the interface depends on the distance between defects on misfit dislocations Point defects migrate from one dislocation defect to another by collective atomic motion 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 .4 0.6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 NW Cu-V KS 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1.4 nm Formation energy (eV) Angle with -ve x axis 1 nm Cu-V KS (a) (b) (c)
29. 1 nm Cu-Fe NW Point defects migrate along misfit dislocation lines 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 KS Cu-Fe NW Cu-V KS 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1 nm 1.4 nm Formation energy (eV) Angle with -ve x axis .6 0.8 1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 Cu-V KS 0.8 1 0 50 100 150 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.8 1 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.6 0.8 1 1.2 1.4 1.4 nm Formation energy (eV) Angle with -ve x axis
30. Summary • Interface sink strength is a dynamic, evolving property of the interface • In semicoherent fcc-bcc interfaces, interface sink strength depends on – Density of misfit dislocation intersections and other dislocation defects – The ability of the misfit dislocation intersections to trap point defects – Point defect transport along the interfaces • Distance between misfit dislocation defects • character of the misfit dislocations