Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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In two dimensions, periodic unit cells can have one of five
basic shapes: general parallelogram, general rectangle, square,
60-120 degree rhombus, and generic rhombus. The last is often
described as a "centered" lattice, a rectangle with an
extra point in the middle, to bring out the rectangular nature of
||It's not too hard to see the rectangular pattern in a rhombic
lattice, but it can be very hard to see the patterns in three
dimensional lattices. At left, for example, is a cubic lattice with an extra
point in the center, a so-called body-centered lattice. At far left
is the simplest cell shape, but the cubic nature of the lattice is
totally impossible to see.
For this reason, three-dimensional lattices
must often be described as unit cells with additional
points. There are 14 basic unit cells in three dimensions, called
the Bravais Lattices.
- P - Primitive: simple unit cell
- F - Face-centered: additional point in the center of each
- I - Body-centered: additional point in the center of the
- C - Centered: additional point in the center of each end
- R - Rhombohedral: Hexagonal class only
|The F cell is very important because it
is the pattern for cubic closest packing. There is no C
cell because such a cell would not have cubic symmetry.
|A C cell would simply be a P cell with a
smaller cross-section, as shown below. An F cell would reduce to a
network of I cells.
|The R cell is unique to hexagonal crystals. The two interior
points divide the long diagonal of the cell in thirds. This is
the only Bravais lattice with more than one interior point. A
rhombohedron can be thought of as a cube distorted along one of
its diagonals. More information on
the rhombohedral lattice.
|The orthorhombic class is the only one with all four types of
Monoclinic and Triclinic Cells
|Monoclinic F or I cells could also be
represented as C cells. Any other triclinic cell can also
be represented as a P cell.
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Created 13 Oct 1997, Last Update 13 Oct 1997
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