If a solid $A B$ having $Z n S$ structure is heated so that the ions along two of the axis passing through the face centre particles are lost and bivalent ion ( $Z$ ) enters here to maintain the electrical neutrality so that the new formula unit becomes $A_{x} B_{y} Z_{c}$ . Find the value of $x + y - c$ .

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Solution

For ZnS structure, number of $B^{⊝}$ ions $=$ $4$ per unit cell (corner + face center)

Number of $A^{\oplus}$ $=$ $4$ per unit cell (in alternate tetrahedral voids)

Number of $B^{⊝}$ ion removed $=$ $4$ (two from each face center) $\times \frac{1}{2}$ (per face centre share) $= 2$

Number of $B r^{⊝}$ ions left $= 4 - 2 =$ $2$ per unit cell

Number of $Z^{2 -}$ ions entering in place of Be $= 1$

Formula $= A_{4} B_{2} Z_{1}$

$∴ x + y + c = 4 + 2 - 1 = 5$

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If a solid AB having ZnS structure is heated so that the ions along two of the axis passing through the face centre particles are lost and bivalent ion (Z) enters here to maintain the electrical neutrality so that the new formula unit becomes AxByZc. Find the value of x+y−c.