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PY4007 Lecture 3 - CatalystsPowerPoint Presentation

PY4007 Lecture 3 - Catalysts

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PY4007 Lecture 3 - Catalysts

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PY4007 Lecture 3 - Catalysts

At the nanoscale, physics and chemistry converge

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

Looser packing.

Closest 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

Strain in MTPs

7.5°

Closed electronic shells for Na clusters

Here we are plotting:

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.