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NEEP 541 – Damage and Displacements. Fall 2003 Jake Blanchard. Outline. Damage and Displacements Definitions Models for displacements Damage Efficiency. Definitions. Displacement=lattice atom knocked from its lattice site

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### NEEP 541 – Damage and Displacements

Fall 2003

Jake Blanchard

• Damage and Displacements

• Definitions

• Models for displacements

• Damage Efficiency

• 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

• 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

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

tka

ska

pka

Energy per atom

E

E/2

E/4

E/2N

2

4

displacements

1

2N

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

• So

T

Ed

2Ed

Ec

• 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

• Solution is:

• For power law potential, result is:

• Repeat with stopping included

• Hard sphere potentials

Don’t need cutoff energy any more

Hard sphere collision cross section (independent of E)

• Include all effects (real potential, electronic stopping)

• Define damage efficiency: