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

Catalytical effect vs cluster size

Face-centred cubic metal [001] [010] [100] 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. Looser packing. Lowest surface energy. 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. (100) type face (111) 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 Here we are plotting:

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