<Dl> <Dd> a = 4 r 3 . (\ displaystyle a = (\ frac (4r) (\ sqrt (3))) \, .) </Dd> </Dl> <Dd> a = 4 r 3 . (\ displaystyle a = (\ frac (4r) (\ sqrt (3))) \, .) </Dd> <P> Knowing this and the formula for the volume of a sphere, it becomes possible to calculate the APF as follows: </P> <Dl> <Dd> A P F = N a t o m s V a t o m V c r y s t a l = 2 ⋅ 4 3 π r 3 (4 r 3) 3 = π 3 8 ≈ 0.680 174 76 . (\ displaystyle (\ begin (aligned) \ mathrm (APF) & = (\ frac (N_ (\ mathrm (atoms)) V_ (\ mathrm (atom))) (V_ (\ mathrm (crystal)))) = (\ frac (2 \ cdot (\ frac (4) (3)) \ pi r ^ (3)) (\ left ((\ frac (4r) (\ sqrt (3))) \ right) ^ (3))) \ \ (10pt) & = (\ frac (\ pi (\ sqrt (3))) (8)) \ approx 0.680 \, 174 \, 76 \,. \ end (aligned))) </Dd> </Dl>

Atomic packing factor (apf) in the case of copper crystal is