1. NEEP 541 – Interatomic Potentials
Fall 2003
Jake Blanchard

2. Outline Interatomic Potentials Impact Parameter Potentials
Closest Approach

3. Binary Collisions Energetic particle strikes stationary particle V1f1
V10 M2 M1 2
V2f

4. CM System M1
u1F
u10 1 M1 M2 2
u20
u2F M2

5. Final Velocities M1
v1f
u1f  1 2
u2f
v2f 1 M2

6. Results

7. Potential Collisions
V1f
V10 1 M1 p M2 2
V2f
p=impact parameter

8. Potential Interactions

9. Potentials Overlap of electrons leads to repulsion Mechanisms:
Electrostatic repulsion due to charge imbalance
Closed shell repulsion resulting from Pauli exclusion principle

10. Interatomic Potentials
V(r) r
attractive
repulsive

11. Functions Large separation: Born-Mayer Very close: Coulomb
Medium range: modified Coulomb

12. Screening Radius

13. Hard Sphere
“billiard ball”

14. Screened Coulomb
Ignores closed shell repulsion

15. Power Law

16. Thomas-Fermi
Moliere

17. Using Potentials Most scattering occurs near closest approach
Hence, one can use single potential
Distance of closest approach determines “best” potential
Low E: Born-Mayer
Medium E: Inverse square
High E: Coulomb
Best overall is Thomas-Fermi

18. Cu-Cu

19. Collisions
Distance of Closest Approach
V10
V20 M2 M1

20. Distance of Closest Approach

21. Distance of Closest Approach
At closest approach, Er=0 (g=0)
 = distance of closest approach
0 = distance of closest approach for p=0

22. Example – Coulomb