In a $A_x B_y$ crystal structure, $A^{+y}$ ions occupy all the tetrahedral voids and…
In a $A_x B_y$ crystal structure, $A^{+y}$ ions occupy all the tetrahedral voids and $\mathrm{B}^{-\mathrm{x}}$ ions make $\mathrm{BCC}$ unit cell: What is the formula of the compound?
$\mathrm{A}_4 \mathrm{~B}_2$
$\mathrm{A}_2 \mathrm{~B}_4$
$\mathrm{A}_2 \mathrm{~B}_2$
$\mathrm{A}_4 \mathrm{~B}_4$
Solution
Number of $\mathrm{A}^{+\mathrm{y}}$ ions $=2 \times$ number of atoms per unit cell.
Number of $\mathrm{B}^{-\mathrm{x}}$ ions $=2(\mathrm{BCC})$ per unit cell.
$\Rightarrow$ Number of $\mathrm{A}^{+\mathrm{y}}$ ions $=2 \times 2=4$
$\Rightarrow$ Formula $=\mathrm{A}_4 \mathrm{~B}_2$