Simple Cubic
In the Simple Cubic (SC) unit cell
there is one lattice point at each of the eight corners of
a cube. Unit cells in which there are lattice points only
at the eight corners are called primitive. In general, the
number of lattice points is denoted by the letter "Z"; thus, for SC, Z
= 1.
(crossed stereo pair)
Let a host atom of radius r occupy
each lattice point, and assume that each atom touches as many adjacent
atoms as possible (in this case, there are six such contacts).
Then each of the three unit cell edges is equal to the sum of two atomic
radii: a = b = c = 2r. The volume of the cell is thus
Vc = 8r3
In a simple cubic cell, there is one
host atom wholly inside the cube, because each of the eight corner atoms
contributes one eighth of an atom to the cell interior. In general,
the total volume of the cell which is occupied by the host atoms is
Vs = 4/3pr3.Z.
The packing efficiency of a
lattice is defined as the ratio Vs:Vc.
Thus, for SC, the packing efficiency is about 52%.
If you have the Chime
plugin installed in your browser, click here
to interact with the unit cell.
Previous - Next