Question

$CaS$ exists in a cubic close packed arrangement of $S^{2-}$ ions in which $C{a}^{2+}$ ions occupy $1/2$ of the available tetrahedral holes. How many $C{a}^{2+}$ and $S^{2-}$ ions are contained in the unit cell?

• A. $1,1$
• B. $2,4$
• C. $4,4$
• D. $4,2$

Answer 1

Answer: (C)

$4,4$

In CCP structure, $S^{2-}$ ions are present at corner and face centre. Thus number of $S^{2-}$ ions are= $8\times \frac{1}{8}$ (corner)$+6\times \frac{1}{2}$ (face centre)

$S^{2-}$ ion= $1+3=4$ ions

as $2$ tetrahedral voids are present in $1$ body diagonal, there are $4$ body diagonal in a unit cell.

Thus total tetrahedral voids are $2\times 4=8$. As $C{a}^{2+}$ are present in $\frac{1}{2}$ of tetrahedral voids. Thus number of $C{a}^{2+}$ ions present= $\frac{8}{2}=4$

$C{a}^{2+}⟶4$

$S^{2-}⟶4$