PY4007 Lecture 3 - Catalysts. At the nanoscale, physics and chemistry converge. Catalytical effect vs cluster size. Face-centred cubic metal. . . . Direction vectors take square brackets. FCC planes. This is a (100) plane in a FCC packed material. FCC planes.
At the nanoscale, physics and chemistry converge
Direction vectors take square brackets
This is a (100) plane in a FCC packed material
This is a (110) plane in a FCC packed material
This is a (111) plane in a FCC packed material
Lowest surface energy.
Higher surface energy.
Equilibrium shape is the inner envelope of planes normal to, and passing through the end of, the free energy vectors.
Create (111) faces to give truncated octahedron.
(100) type face
(111) type face
Made from 5 tetrahedral units
Made from 20 tetrahedral units
Here we are plotting:
(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.