The number of octahedral voids per lattice site in a lattice is __________

The number of octahedral voids per lattice site in a lattice is $1$

Step 1: Formula:

• Let us assume the structure of $\mathrm{FCC}$

$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{octahedral}\mathrm{voids}\mathrm{per}\mathrm{lattice}\mathrm{site}=\frac{\mathrm{Octahedral}\mathrm{Voids}}{\mathrm{Lattice}\mathrm{site}}$

Step 2: Finding octahedral voids:

$\mathrm{Octahedral}\mathrm{voids}=\mathrm{Edge}\mathrm{centre}+\mathrm{Body}\mathrm{centre}$

$$\begin{gathered} =12+1 \\ =13 \end{gathered}$$

Step 3: Finding Lattice sites:

$\mathrm{Lattice}\mathrm{sites}=\mathrm{corner}+\mathrm{face}\mathrm{center}$

$$\begin{gathered} =8+6 \\ =14 \end{gathered}$$

$\mathrm{The}\mathrm{number}\mathrm{of}\mathrm{octahedral}\mathrm{voids}\mathrm{per}\mathrm{lattice}\mathrm{site}=\frac{\mathrm{Octahedral}\mathrm{Voids}}{\mathrm{Lattice}\mathrm{site}}$

$$\begin{gathered} =\frac{13}{14} \\ =0.928\simeq 1 \end{gathered}$$

Hence, the number of octahedral voids per lattice site in a lattice is $1$