Question

a) Calculate the packing efficiency in a unit cell of Cubic Close Packing (CCP) structure?
b) Name the crystal defect which lowers the density in an ionic crystal?

Answer 1

a) For Cubic Close Packing (CCP) lattice, the relationship between the edge length a and the radius r of the unit cell is $a=\sqrt{8}r$
The volume of the unit cell is $a^3=(\sqrt{8}r{)}^3=8\sqrt{8}{r}^3$
The volume occupied by 1 atom is $\frac{4}{3}\pi r^3$
A CCP unit cell has 4 atoms per unit cell.
The volume occupied by 4 atoms is
$4\times \frac{4}{3}\pi r^3=\frac{16}{3}\pi r^3$
The packing efficiency $=\frac{\text{Volume occupied by atoms in a unit cell}}{\text{total volume of unit cell}}\times 100$
The packing efficiency $=\frac{\frac{16}{3}\pi r^3}{8\sqrt{8}{r}^3}\times 100=74.0$ %
b) Schottky defect (Vacancy defect) which lowers the density in an ionic crystal.