Neep 541 damage and displacements
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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 l.jpg

NEEP 541 – Damage and Displacements

Fall 2003

Jake Blanchard


Outline l.jpg
Outline

  • Damage and Displacements

    • Definitions

    • Models for displacements

    • Damage Efficiency


Definitions l.jpg
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


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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



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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


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Schematic

tka

ska

pka

Energy per atom

E

E/2

E/4

E/2N

2

4

displacements

1

2N


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Displacement model

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

  • So


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Kinchin-Pease model

T

Ed

2Ed

Ec


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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




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Kinchin-Pease revisited

  • Solution is:

  • For power law potential, result is:


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Electronic Stopping

  • Repeat with stopping included

  • Hard sphere potentials

Don’t need cutoff energy any more

Hard sphere collision cross section (independent of E)


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Comprehensive Model

  • Include all effects (real potential, electronic stopping)

  • Define damage efficiency: