Show that the atomic packing factor for BCC is 0.68.

wwe are asked to prive the atomic pavking factor APF for BCC is 0.68

solution

APF is given by equation (3.3) in the form

APF =nVs/Vc

whenn is the number of atoms per unit cell and for BCC n=2.0, Vs is the volume of the atom and it is given by 43π3³ and Vc is the volume of the unit cell and for BCC Vc=a³ where a is the side of the cube. From equation 3.4

we could get a by

a=4R/√3

where R is the radius of the atom. Now let us olug the expression inyo equation (1) to get APF

APF = nVs/Vc

=2.0(4/3πR³) / (4R/√3)³

=2.0(4/3πR³) / (4/√3)³ R³

=0.68