Diamond and Zinc-Blende Crystal Structure Viewer: You may find this site helpful for visualizing the dimaond and zinc-blende crystal structures.  You can select common elemental and compound semiconductors from the drop down list, or by selecting "more" from the list you can click on elements from columns III, IV or V to view a variety of semiconductors.  By clicking and dragging the mouse pointer on the unit cell you can rotate it to allow viewing from different directions.

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Bravais Lattice Viewer This viewer allows you to display and rotate the 14 different Bravais Lattices.
Crystal Structures You may find this site helpful for visualizing different crystal structures as well as planes and directions with-in them. The site includes a JAVA applet that lets you rotate and change the size of the crystal (both the number of "atoms" and the space between them). Hints on how to use the different features are included after the lists of different crystal types on the main page.

I suggest that if you are trying to visualize the diamond structure you also try using the zincblende viewer. Zincblende differs from diamond in that the two interpenetrating fcc sublattices have different atoms. The viewer gives them different colors, which makes the interior atoms of the diamond cubic unit cell easier to distinguish from the corner and face-center atoms.

You may also find it useful to remember that for cubic lattices a plane with a given set of Miller indices is perpendicular to the direction with the same Miller indices.

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EE331 | Electrical Engineering