Question

What is the crystal structure with the least atomic packing factor in metal?

Answer 1

Atomic packing factor

= (atoms/unit cell) x (volume/atom) / (volume/unit cell)

For simple cubic structure

atoms/unit cell = 8 x (1/8) = 1

Volume/atom = (4/3)(0.5a)³

Volume/unit cell = a³

a = side of cube

Atomic packing factor for simple cubic

= (1) x [ (4/3)(0.5a)³] / (a³)

= 0.52

For BCC structure

atoms/unit cell = 2

Volume/atom = (4/3)()³

Volume/unit cell = a³

Atomic packing factor for BCC

= (2) x [ (4/3)()³] / (a³)

= 0.68

For FCC structure

atoms/unit cell = 4

Volume/atom = (4/3)()³

Volume/unit cell = a³

Atomic packing factor for FCC

= (4) x [ (4/3)()³] / (a³)

= 0.74

Least atomic packing factor is for the simple cubic structure