|3.4 Metallic Crystal Structures||●||35|
of BCC unit cells with the atoms represented by hard sphere and reduced-sphere models, respectively. Center and corner atoms touch one another along cube diago-nals, and unit cell length a and atomic radius R are related through
EXAMPLE PROBLEM 3.1
Calculate the volume of an FCC unit cell in terms of the atomic radius R.
the atoms touch one another across a face-diagonal 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