py4007 lecture 3 - catalysts at the nanoscale, physics and chemistry converge
Post on 21-Dec-2015
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TRANSCRIPT
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
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.