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 (R d )=displacements per unit volume per unit time Displacement energy (E d )=energy needed to displace a lattice atom

4. Formal model To first order, an incident particle with energy E can displace E/E d 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<E d there are no displacements For E d <T<2E d 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 pka ska tka displacements1 24 2N2N Energy per atomEE/2 E/4E/2 N

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

9. Kinchin-Pease model T EdEd 2E d EcEc

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

13. Solution is: For power law potential, result is:

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

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

16. Damage Efficiency