Many of the physical properties of materials reflect the same symmetries as their crystal structure. In this series of lectures we will introduce the concepts of how the symmetries of materials are classified. The information described here partially follows the information contained in Grundmann, Chapter 3, and Yu and Cardona, Chapter 2.

Graphics from Mark McClure, http://www.uncp.edu/home/mcclurem/lattice/index.htm
Some Useful Links:
Symmetry@Otterbein College: An excellent resource which provides a tutorial showing how the symmetry elements are defined and how one uses them to determine the point group for a particular structure.
Symmetry Tutorial: A good tutorial on symmetries by Dr. Steven Haefner at Wake Forest . Look in particular at the flow-chart for determining the point group from the symmetry elements for a structure.
Visualize atomic orbitals: A good Jmol view of 2s, 2p, 3d, and 4f atomic orbitals.
Visualize sp3 hybridized orbitals: A good Jmol view of sp3 hybridized orbitals.
Close Packed Structures: This site by Prof. Mark McClure at UNC Pembroke shows how one can construct hexagonal and cubic closed packed structures by AB and ABC stackings.
Visualizing the 14 Bravais Lattices: A good site from SUNY Buffalo which has many simulations of semiconductor-related things.
Diamond Crystal Structure (A4): A good site at NRL for visualizing diamond crystal structures (appropriate for Silicon and Germanium).
Zincblende Crystal Structure (B3): A good site at NRL for visualizing Zincblende crystal structures (appropriate for GaAs, AlAs, GaP, InP, InAs, etc)
Wurtzite Crystal Structure (B4): A good site at NRL for visualizing Wurtzite crystal structures (appropriate for CdS, ZnS, InAs, InP, etc).
Reading, Lectures and Activities
Below are the beginning of the short ~10 minute lectures on different topics. Each activity begins with a reading assignment, followed by a web-cast of the lecture which you can access by clicking on the screen image. After the lecture there is a short problem which is releated to the topic, which should be completed before beginning the next topic.
1. Atomic Orbitals and Crystal Symmetry
Read section 2.2 and 3.4 (minimum) of Grundmann's book before beginning these lectures. To see the lecture (10 minutes long) click on the picture below:

Problem 1: Assuming a regular tetrahedran of side A, what is (a) the length of the bonds to an atom centered inside the tetrahedra in terms of A, and (b) what are the angles between the four bond angles?
2. Close-Packed Crystal Structures
Read section 3.4 of Grundmann. Click on the picture below to see the lecture.

Problem 2: (a) Convince yourself that for both AB and ABC stacking the number of tetrahedral holes is twice that of the octahedral holes. (b) Show that for an fcc unit cell the number of tetrahedral holes is twice the number of atoms in an fcc unit cell. Remember that the atom at each corner is shared between EIGHT unit cells, and that the atom centered on the face is shared between TWO unit cells.
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Comments (4)
wadead@... said
at 10:13 am on Apr 7, 2009
Leigh, on the videos. Could you add a progress bar with the play pause button. This way we can come back to a specific position instead of listening to the entire video every time.
Leigh M Smith said
at 10:54 am on Apr 7, 2009
There should be one....I have been having problems with the Quicktime video plugin with IE8...all I see is a black bar instead of the scroll bar. You can still access it by hunting around with the mouse, but it is painful. It seems to work better with Chrome (the new Google browser) or Firefox.
Mohammad Montazeri said
at 11:12 am on Apr 7, 2009
I do have them (firefox 3).
wadead@... said
at 12:17 pm on Apr 7, 2009
I'm able to access them by hunting in the black area but i don't see the scroll bar, etc.. (note: I'm using Firefox 3.0.4 on Vista)
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