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# NEEP 541 – Focusing and Channeling

NEEP 541 – Focusing and Channeling. Fall 2002 Jake Blanchard. Outline. Focusing Definitions Modeling Criteria Channeling Definitions Modeling Criteria. Definitions. focusing=energy transfer in near head on collisions along a row of close-packed atoms Larger distances covered

## NEEP 541 – Focusing and Channeling

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1. NEEP 541 – Focusing and Channeling Fall 2002 Jake Blanchard

2. Outline • Focusing • Definitions • Modeling • Criteria • Channeling • Definitions • Modeling • Criteria

3. Definitions • focusing=energy transfer in near head on collisions along a row of close-packed atoms • Larger distances covered • Less displacements produced (more heating) • Only seen at low energies

4. Schematic r0 D Angles must be small enough to keep collisions in a line

5. Criterion for Focusing • We must have n+1<n n+1 n

6. Difference Equation For focusing to take place

7. Potentials • The sphere radius is energy dependent • Use Born-Mayer potential • Use equivalent hard sphere model Hard sphere radius is equal to distance of closest approach in head on collision for Born-Mayer potential

8. Criteria for Focusing • Focusing occurs if: • For fcc metals, close packed direction is <110>

9. Example: Copper • For fcc metals, close packed direction is <110>

10. Displacement Effects • Let c=probability of either channeling or focusing effect (independent of energy)

11. Displacement Effects • Consider 10 keV PKA in Fe • c=0 gives 200 displacements • c=0.07 gives 100 displacements

12. What is the probability (c)? • Assume Copper • c will increase with decreasing energy

13. Channeling • Long distance displacement of energetic particles down open direction in lattice • Direction is same as for focusing • Channeling occurs between close-packed rows • Channel radius for fcc is approximately 0.3a0

14. Schematic

15. Diagram y D pN  x N atoms per period in lattice

16. Scattering • Each atom passed contributes a momentum change • Use impulse approximation

17. Scattering

18. 2-D channel 2 rows of atoms pi=p=Rch Scattering Born-Mayer

19. Scattering Period of oscillation

20. Criterion Critical angle

21. Channeling Notes • Simulations indicate 1-10% of PKAs channel • There is no upper limit on energy • When wavelength is about 2D, large angle collision is likely 300 eV for Cu

22. End of Channeling Event

23. Summary • Kinchin-Pease is used for displacements • Realistic cross sections reduce  by up to 50% • Electronic losses reduce displacements continuously • Focusing and channeling reduce  by up to 50%

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