Question
Calculate the packing efficiency of metal crystal that has simple cubic structure.
✓
Answer
Step 1 : Radius of sphere : In simple cubic lattice, the atoms (spheres) are present at eight corners and in contact along the edge in the unit cell.
If ‘a’ is the edge length of the unit cell and ‘r’ is the radius of the atom, then
a = 2r or r = a/2
If ‘a’ is the edge length of the unit cell and ‘r’ is the radius of the atom, then
a = 2r or r = a/2
scc structure
Step 2 : Volume of sphere :
Volume of one particle = $\frac{4 \pi}{3} \times r^3$
$=\frac{4 \pi}{3} \times( a / 2)^3=\frac{\pi a^3}{6}$
Step 3 : Total volume of particles : Since the unit cell contains one particle. Volume occupied by one particle in unit cell = $\frac{\pi a^3}{6}$
Step 4 : Packing efficiency :
Packing efficiency
$=\frac{\text { Volume occupied by particles in unit cell }}{\text { Volume of unit cell }} \times 100$
$=\frac{\pi a^3 / 6}{a^3} \times 100$
$=\frac{3.142 \times 100}{6}=52.36 \%$
∴ Packing efficiency = 52.36%
Percentage of void space = 100 – 52.36
= 47.64%
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