PY4007 Lecture 3 - Catalysts

At the nanoscale, physics and chemistry converge

Catalytical effect vs cluster size

Face-centred cubic metal

[100]

[010]

[001]

Direction vectors take square brackets

FCC planes

This is a (100) plane in a FCC packed material

FCC planes

This is a (110) plane in a FCC packed material

FCC planes

This is a (111) plane in a FCC packed material

Surface energies of low-order planes

Closest packing.

Lowest surface energy.

Looser packing.

Higher surface energy.

Wulff construction

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

Equilibrium Wulff shape

Create (111) faces to give truncated octahedron.

(111) type face

(100) type face

Variations of facet sizes

Multiply twinned particles

Decahedral and icosahedral MTPs

Made from 5 tetrahedral units

Made from 20 tetrahedral units

Strain in MTPs

7.5°

Cluster structure of Al13

Evaporation cluster source

Abundances of Na clusters

Closed electronic shells for Na clusters

1 NENEN

Here we are plotting:

NN 1

Metal-nonmetal transition in electronic states

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.

Coulomb blockade