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
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and VRMLs are owned and copyright
by
Barbara L. Sauls and Frederick C. Sauls
1998.
Contact the owners for individual permission
to use. blsauls@rs01.kings.edu