Question

In calcium fluoride, having the fluorite structure, the coordination numbers for calcium ion ($C{a}^{2+}$) and fluoride ion ($F^{-}$) are:

• A. $\text{4 and 8}$
• B. $\text{4 and 2}$
• C. $\text{8 and 4}$
• D. $\text{6 and 6}$

Answer 1

The correct option is C $\text{8 and 4}$

In fluorite structure, the $C{a}^{2+}$ forms the fcc lattice.

Thus, $C{a}^{2+}$ occupies the corners and face centres of the cube.
The number of $C{a}^{2+}$ ions in each unit cell is:
$\frac{1}{8}\times 8+\frac{6}{2}=4$

$F^{-}$ ion occupies all the tetrahedral voids of the fcc. There are 8 tetrahedral voids in fcc.
Thus, the number of $F^{-}$ ions in each unit cell is 8.

Here, each $F^{-}$ ion in tetrahedral void is surrounded by 4 $C{a}^{2+}$ ions and each $C{a}^{2+}$ ion is surrounded by 8 $F^{-}$ ion.

Thus, the coordination number of $F^{-}$ is 4 and coordination number of $C{a}^{2+}$ is 8.
$C.N.ofCa{F}_2=8:4$

Hence, option (a) is correct.