Crystal Viewer

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This Demonstration gives insight into the crystal symmetries of five standard crystal symmetries of pure elements. These lattice symmetries are


1) simple cubic SC (e.g., polonium);

2) face-centered cubic FCC (e.g., copper);

3) body-centered cubic BCC (e.g., iron);

4) hexagonal closed-packed HCP (e.g., helium);

5) diamond DIA (e.g., silicon).

The direction defines a plane to which this direction is perpendicular. This plane is called the crystal plane . The three values , , and are often referred to as Miller indices.


Contributed by: Nikolai Mikuszeit (March 2011)
Open content licensed under CC BY-NC-SA



The viewer not only allows studying the symmetry of specific planes, but also visualizes the density of the atoms in certain directions. This is important for a process called channeling (see the Wikipedia entry). In this case a (high-energy) atom or ion penetrates the crystal. If the atoms of the crystal have a low density in the direction of penetration, the penetration depth is probably high, and vice versa. One may say that in low-density directions channels open for the penetrating particle. Usually, these channels open in high-symmetry crystal directions. To visualize the effect of different cross sections, it is possible to change the size.


For more structures that appear in crystals of pure elements see N. W. Ashcroft and N. D. Mermin, Solid State Physics, Philadelphia: Sounders College Publishing, 1976.

C. Kittel, Introduction to Solid State Physics, 7th ed., New York: John Wiley & Sons, Inc., 1996.

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