Question

Calculate the void fraction per unit volume of unit cell for such crystal.

• A. 0.236
• B. 0.67
• C. 0.45
• D. 0.82

Answer 1

The correct option is A 0.236

When the cation radii are greater or equal to 0.414 R, but less than 0.732 R, where R is the radius of an atom, the cations occupy the octahedral sites. Let us approximate it to 0.5
Thus, the radius of atom B is approximately equal to one half of the radius of atom A.
The packing fraction is $\frac{\text{volume occupied by the atoms}}{\text{total volume of the unit cell}}=\frac{4\times \frac{4}{3}\pi r^3+\frac{4}{3}\pi (\frac{r}{2}{)}^3}{(\frac{4r}{\sqrt{2}}{)}^3}=0.764$
The void fraction is $1-0.764=0.236$