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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

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## NEEP 541 – Focusing and Channeling

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**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 • Less displacements produced (more heating) • Only seen at low energies**Schematic**r0 D Angles must be small enough to keep collisions in a line**Criterion for Focusing**• We must have n+1<n n+1 n**Difference Equation**For focusing to take place**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**Criteria for Focusing**• Focusing occurs if: • For fcc metals, close packed direction is <110>**Example: Copper**• For fcc metals, close packed direction is <110>**Displacement Effects**• Let c=probability of either channeling or focusing effect (independent of energy)**Displacement Effects**• Consider 10 keV PKA in Fe • c=0 gives 200 displacements • c=0.07 gives 100 displacements**What is the probability (c)?**• Assume Copper • c will increase with decreasing energy**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**Diagram**y D pN x N atoms per period in lattice**Scattering**• Each atom passed contributes a momentum change • Use impulse approximation**2-D channel**2 rows of atoms pi=p=Rch Scattering Born-Mayer**Scattering**Period of oscillation**Criterion**Critical angle**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**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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