Question

1) Define atomic packing(APF) factor calculate APF for simple cubic cell
2) calculate APF for Body centered cubic crystal. (BCC)
3) calculate APF for face centered cubic crystal. (FCC)​

Answer 1

1)

proven mathematically that for one-component structures, the most dense arrangement of atoms has an APF of about 0.74

2)

bcc structure each atom has c1=8 c 1 = 8 nearest neighbours (coordination number) at a distance of dc1=2r=√32a≈0.866a(3) (3) d c 1 = 2 r = 3 2 a ≈ 0.866 a and c2=6 c 2 = 6 next-nearest neighbours at a distance of dc2=a≈2.3r≈1.15dc1.

3)

For fcc and hcp structures, the atomic packing factor is 0.74