Body Centered Cubic
Pearson Symbol:
cI2
Strukturbericht Designation:
A2
Space Group:
Im3m (229)
In crystallography there are various common cubic's that appear. The body-centered cubic is an arrangement of atoms in a lattice where there is an atom positioned at each corner of a cube and directly in the center of the cube. The body-centered cubic is a "unit cell" which is repeated many times in each direction.
The body-centered cubic is much more compact that other types of cubics because of the alternating atom pattern that forms. This structure is very common among metals such as Iron and Sodium but is also found in the following elements : Li, K, V, Cr, Fe, Rb, Nb, Mo, Cs, Ba, Eu, and Ta.
A Unit Cell
o_________o
/| /|
/ | / |
o__|_______o |
| | o | |
| o_______|__o
| / | /
| / | /
o/_________o/
The circles in the above diagram represent one of the atoms at each corner of the cube. By definition, there is also an atom exactly in the center of the cube (bold) comprising the Body-Centered Cubic.
Because this is the basic unit comprising a very large crystal lattice, it is useful to determine the atoms per unit cell. However we do not count the portions of the atoms which lie outside the edges of the cube. So we have one atom completely inside the cube plus eight atoms (at each corner) where only one eighth is inside the cube.
1 + (1/8 * 8) = 2 atoms per unit cell
You can also calculate the size of the unit cell based of the radius of the atoms in the cell. In the body-centered cubic the atoms along the diagonal (crossing the center of the cube) are touching. Therefore if each atom has a radius of 'r' then the diagonal of the cubic is 4r.
Reference :
http://cst-www.nrl.navy.mil/lattice/struk/bcc.html
http://www.kings.edu/~chemlab/animation/bcc.html