neep 541 damage and displacements fall 2003 jake blanchard
DESCRIPTION
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 atomTRANSCRIPT
NEEP 541 – Damage and Displacements
Fall 2003Jake Blanchard
Outline Damage and Displacements
Definitions Models for displacements Damage Efficiency
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
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
Formal Model
m
d
m
d
m
d
T
Ed
dd
T
Ed
T
Ed
dTTET
dEEENR
dEdTTETENR
dTdETEENTR
),()(
)()(
),()()(
),()()(
0
0
0
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
Schematic
pka
skatka
displacements
1 2 4 2N
Energy per atom
E E/2 E/4 E/2N
Displacement model Process stops when energy per atom
drops below 2Ed (because no more net displacements can be produced)
So
d
N
dN
ETE
or
ET
22)(
22
Kinchin-Pease model
T
Ed 2Ed Ec
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
Kinchin-Pease revisited
E
EE
EE
dTTTEE
E
dTTTEEEdTE
EE
spherehardEETE
dTTTETEdTETE
TTEE
0
00
00
)()(1)(
)()()()()(
;1;)(),(
)()(),()(),(
)()()(
Kinchin-Pease revisited
E
E
d
E
E
E
E
E
E
EE
E
E
d
d
d
d
d
dTTEE
EE
dTTE
dTE
dTE
E
dTTE
E
dTTdTTE
TEwdwwdTTE
2
2
2
0
0
00
0
0
)(22)(
)(2202)(
)(2)(
)()(
;)()(
Kinchin-Pease revisited Solution is:
For power law potential, result is:dEEE2
)(
d
d
s
d
EEE
EEE
s
EsEE
257.0)(3
252.0)(2
122
)( 11
Electronic Stopping Repeat with stopping included Hard sphere potentials
dd
e
ENk
EEE
EkdxdE
241
2)(
Hard sphere collision cross section (independent of E)
Don’t need cutoff energy
any more
Comprehensive Model Include all effects (real potential,
electronic stopping) Define damage efficiency:
3/1
22
4/36/1
88.0/2
4.04.313.011)(
2)()(
Zaa
aeZE
E
EEEE
B
d
Damage Efficiency