Py4007 lecture 3 catalysts
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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

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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

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


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


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