NEEP 541 – Damage and Displacements

1. NEEP 541 – Damage and Displacements Fall 2003 Jake Blanchard

2. Outline • Damage and Displacements • Definitions • Models for displacements • Damage Efficiency

3. Definitions • Displacement=lattice atom knocked from its lattice site • Displacement per atom (dpa)=average number of displacements per lattice atom • Primary knock on (pka)=lattice atom displaced by incident particle • Secondary knock on=lattice atom displaced by pka • Displacement rate (Rd)=displacements per unit volume per unit time • Displacement energy (Ed)=energy needed to displace a lattice atom

4. Formal model • To first order, an incident particle with energy E can displace E/Ed lattice atoms (either itself or through knock-ons) • Details change picture • Let (E)=number of displaced atoms produced by a pka

5. Formal Model

6. What is (E) • For T<Ed there are no displacements • For Ed <T<2Ed there is one displacement • Beyond that, assume energy is shared equally in each collision because =1 so average energy transfer is half of the incident energy

7. Schematic tka ska pka Energy per atom E E/2 E/4 E/2N 2 4 displacements 1 2N

8. Displacement model • Process stops when energy per atom drops below 2Ed (because no more net displacements can be produced) • So

9. Kinchin-Pease model  T Ed 2Ed Ec

10. More Rigorous Approach • Assume binary collisions • No displacements for T>Ec • No electronic stopping for T<Ec • Hard sphere potentials • Amorphous lattice • Isotropic displacement energy • Neglect Ed in collision dynamics

11. Kinchin-Pease revisited

12. Kinchin-Pease revisited

13. Kinchin-Pease revisited • Solution is: • For power law potential, result is:

14. Electronic Stopping • Repeat with stopping included • Hard sphere potentials Don’t need cutoff energy any more Hard sphere collision cross section (independent of E)

15. Comprehensive Model • Include all effects (real potential, electronic stopping) • Define damage efficiency:

16. Damage Efficiency