A compound is formed by $X$ and $Y$ elements. Atoms of $Y$ (anions) from hcp lattice. Atoms of $X$ (cations)…
A compound is formed by $X$ and $Y$ elements. Atoms of $Y$ (anions) from hcp lattice. Atoms of $X$ (cations) are in some octahedral holes. The formula of the compound is $X Y_3$. What is the fraction of octahedral holes unoccupied by $X$ ?
$\frac{1}{2}$
$\frac{2}{3}$
$\frac{3}{4}$
$\frac{1}{5}$
Solution
$\because$ Number of octahedral voids $=$ Number of lattice point
$\because$ Given formula is $X Y_3$ means.
three octahedral voids are filled against each lattice point (particle).
$\because 3$ octahedral voids fill $=1$ full part of $Y_3$.
$\because 1$ octahedral voids fill $=\frac{1}{3}$ part of $Y_3$.
$\therefore$ Unoccupied fraction of voids $=1-\frac{1}{3}=\frac{2}{3}$