Where the cell edge length the right triangle the face
3.4 Metallic Crystal Structures  ●  35 

of BCC unit cells with the atoms represented by hard sphere and reducedsphere models, respectively. Center and corner atoms touch one another along cube diagonals, and unit cell length a and atomic radius R are related through
(3.3) 



EXAMPLE PROBLEM 3.1
Calculate the volume of an FCC unit cell in terms of the atomic radius R.
a
the atoms touch one another across a facediagonal the length of which is 4R. Since the unit cell is a cube, its volume is a3, where a is the cell edge length.
The FCC unit cell volume VC may be computed from
VC � a3� (2R �2)3� 16R3�2 (3.4)
APF �total sphere volume total unit cell volume� VS 

Both the total sphere and unit cell volumes may be calculated in terms of the atomic radius R. The volume for a sphere is ���R3, and since there are four