**CRYSTAL LATTICES**

**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:**

**Squares**
**Rectangles**
**Hexagons**
**Squares**

**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.**

**Rectangles**

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

**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**
**Stoichiometry**
**Packing & Geometry**
**Simple Cubic Metals**
**Close Packed Structures**
**Body Centered Cubic**
**Cesium Chloride**
**Sodium Chloride**
**Rhenium Oxide**
**Niobium Oxide**
*Except as otherwise noted, all images and movies
are owned and copyright
by*
*Dr. Barbara L. Sauls and Dr. Frederick C. Sauls
1998.*
*Contact the owners for individual permission
to use. barbarasauls@kings.edu*