8.6: Brillouin Zones in Three Dimensions

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The extension to three dimensions is straightforward by the method outlined in the previous section. However, it is important to remember not to overlook important Bragg Planes. There is also a problem of representation, because the structure of the Zones in 3-D can be quite complicated and hard to visualise.

It is also important to remember that in 3-D the Zones all have the same volume, and that the volume corresponding to the 3rd Zone is the volume between the outer surface of the 2nd Zone and that of the 3rd Zone.

Representations of the Brillouin Zones corresponding to Simple Cubic (SC), Body Centred Cubic (BCC), Face Centred Cubic (FCC) lattices are linked to below. Use the buttons on the left hand side to select which Zone Surface to view, and use the arrow buttons to rotate the view about the [001] axis.

Simple Cubic

Body Centred Cubic

Face Centred Cubic