Question

A hypothetical AX type of ceramic material is known to have a density of 3.55 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.39 nm. The atomic weights of the A and X elements are 90.5 and 37.3 g/mol, respectively. On the basis of this information, which one of the following crystal structures is possible for this material?a) fluoriteb) zinc blendc) cesium chloride

Answer 1

Explanation:

For AX type ceramic material, the number of formula per unit cells is as follows.

         $\rho = \frac{n'(A_{c} + A_{A})}{V_{C}N_{A}}$

or,     $n' = \frac{\rho a^{3}N_{A}}{(A_{c} + A_{A})}$

where,   n' = no. of formula units per cell

           $A_{c}$ = molecular weight of cation = 90.5 g/mol

           $A_{a}$ = molecular weight of anion = 37.3 g/mol

          $V_{c}$ = volume of cubic cell = 3.55 $g/cm^{3}$

           a = edge length of unit cell = $3.9 \times 10^{-8} cm$

        $N_{A}$ = Avogadro's number = $6.023 \times 10^{23}$

          $\rho$ = density = 3.55 $g/cm^{3}$

Now, putting the given values into the above formula as follows.

           $n' = \frac{\rho a^{3}N_{A}}{(A_{c} + A_{A})}$

                      = $\frac{3.55 g/cm^{3} \times (3.9 \times 10^{-8})^{3} \times 6.023 \times 10^{23}}{(90.5 + 37.3)}$

                     = 0.9

                    = 1 (approx)

Therefore, we can conclude that out of the given options crystal structure of cesium chloride is possible for this material.