NEEP 541 Damage and Displacements Fall 2003 Jake

NEEP 541 – Damage and Displacements Fall 2003 Jake Blanchard

Outline n Damage and Displacements n n n Definitions Models for displacements Damage Efficiency

Definitions n n n 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

Formal model n n n 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

Formal Model

What is (E) n n n For T<Ed there are no displacements For Ed <T<2 Ed 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

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

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

Kinchin-Pease model Ed 2 Ed Ec T

More Rigorous Approach n n n n 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

Kinchin-Pease revisited

Kinchin-Pease revisited

Kinchin-Pease revisited n Solution is: n For power law potential, result is:

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

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

Damage Efficiency