Fundamentals of Ion-Solid Interaction - SPIRIT
Fundamentals of Ion-Solid Interaction - SPIRIT
Fundamentals of Ion-Solid Interaction - SPIRIT
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<strong>Ion</strong> mixing at precipitates<br />
R<br />
<br />
Atomic relocation<br />
probability per<br />
incident ion<br />
(Assumed to be<br />
isotropic)<br />
w r<br />
<br />
<br />
<br />
exp<br />
<br />
<br />
= (E ion,m ion,m target)<br />
Characteristic Relocation Length<br />
R<br />
Angular and spatial<br />
integration yields radial<br />
relocation field<br />
W r<br />
r<br />
r Atomic relocation is<br />
counteracted by diffusion.<br />
In local equilibrium<br />
K.-H. Heinig et al., Mat.Res.Soc.Proc. vol. 650 (2001)<br />
Institute <strong>of</strong> <strong>Ion</strong> Beam Physics and Materials Research Pr<strong>of</strong>. Wolfhard Möller<br />
r D 2 c<br />
<br />
- r jW<br />
2 r<br />
r r<br />
r<br />
<br />
D Diffusion Coefficient<br />
r j <strong>Ion</strong> Flux<br />
After minor approximations (e.g., r-R > )<br />
<br />
R <br />
<br />
<br />
R <br />
~<br />
c 1 ~<br />
c c R<br />
(Linearized) Gibbs-Thomson<br />
equation holds for ion mixing !<br />
with<br />
c ~<br />
<br />
c<br />
1 <br />
R 5<br />
/<br />
R <br />
1 <br />
~ c<br />
c<br />
<br />
<br />
Dc<br />
q 2<br />
<br />
4<br />
q Nr. <strong>of</strong> displacements per<br />
Atom and Unit <strong>of</strong> Time
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