1. PY4007 Lecture 3 - Catalysts
At the nanoscale, physics and chemistry converge

2. Catalytical effect vs cluster size

3. Face-centred cubic metal
[001]
[010]
[100]
Direction vectors take square brackets

4. FCC planes
This is a (100) plane in a FCC packed material

5. FCC planes
This is a (110) plane in a FCC packed material

6. FCC planes
This is a (111) plane in a FCC packed material

7. Surface energies of low-order planes
Closest packing.
Looser packing.
Lowest surface energy.
Higher surface energy.

8. Wulff construction
Equilibrium shape is the inner envelope of planes normal to, and passing through the end of, the free energy vectors.

9. Equilibrium Wulff shape
Create (111) faces to give truncated octahedron.
(100) type face
(111) type face

10. Variations of facet sizes

11. Multiply twinned particles

12. Decahedral and icosahedral MTPs
Made from 5 tetrahedral units
Made from 20 tetrahedral units

13. Strain in MTPs
7.5°

14. Cluster structure of Al13

15. Evaporation cluster source

16. Abundances of Na clusters

17. Closed electronic shells for Na clusters
Here we are plotting:

18. Metal-nonmetal transition in electronic states

19. Worked example
(a) Show that the Fermi energy for sodium is approximately 3.1 eV (density of Na is 970 kg m-3; atomic mass for Na is 23). [Hint: Assume a free-electron model for the valence electrons of sodium.]
(b) Hence derive an approximate expression for the temperature of the metal-nonmetal transition for a sodium cluster of diameter, d. Find this diameter at a temperature of 100 K.

20. Coulomb blockade