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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.

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Py4007 lecture 3 catalysts
PY4007 Lecture 3 - Catalysts

At the nanoscale, physics and chemistry converge



Face centred cubic metal
Face-centred cubic metal

[001]

[010]

[100]

Direction vectors take square brackets


Fcc planes
FCC planes

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


Fcc planes1
FCC planes

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


Fcc planes2
FCC planes

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


Surface energies of low order planes
Surface energies of low-order planes

Looser packing.

Closest packing.

Lowest surface energy.

Higher surface energy.


Wulff construction
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
Equilibrium Wulff shape

Create (111) faces to give truncated octahedron.

(100) type face

(111) type face




Decahedral and icosahedral mtps
Decahedral and icosahedral MTPs

Made from 5 tetrahedral units

Made from 20 tetrahedral units








Worked example
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.



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