A crystal is a repeating array. In describing this structure we must distinguish between the pattern of repetition (the lattice type) and what is repeated (the unit cell).

The most fundamental property of a crystal lattice is its symmetry. If we initially limit ourselves to 2 dimensions for simplicity, three types are:


A square lattice may be visualized like this. 
Each "stuff" represents a unit cell - the unit of repetition in the crystal.

If you were in one of the unit cells and looked out, you would see the same "stuff"  at 0, 90, 180, and 270 degrees because a square repeats itself at 90 degree intervals - each 1/4 rotation.

A rectangular lattice repeats at 0 and 180 degrees. We find "stuff" farther away at 90 and 270 degrees.

A hexagonal lattice repeats every 1/6 rotation or 60 degrees.

The "stuff" in the unit cells can be virtually anything. Here we have:

   A square "eye" lattice.

    A square "foot" lattice.
A hexagonal "foot" lattice. 

Look again at the "stuffed" hexagons.  Notice that the unit cells completely fill the surface.
If the unit cells were seen in 3 dimensions, they would completely fill the space.

This is an important restriction as it prevents certain arrangements such as pentagonal unit cells, as shown below.


Do you see that this type of arrangement is not possible?
The unit cells must completely fill the surface  and have no overlap.


In 3 dimensions, the ideas are similar;  unit cells stack like boxes, filling the space, making the crystal.

The different colors are just to show the separate boxes - each unit cell is identical.


 Cubic                                       Hexagonal
Click here to go to the next page.
Structure of Crystals
Crystal Lattices
Unit Cells
From Unit Cell to Lattice
From Lattice to Unit Cell
Packing & Geometry
Simple Cubic Metals
Close Packed Structures
Body Centered Cubic
Cesium Chloride
Sodium Chloride
Rhenium Oxide
Niobium Oxide
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Dr. Barbara L. Sauls and Dr. Frederick C. Sauls  1998.
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