Question

In a cubic lattice, the closed packed structure of mixed oxides of the lattice is made up of oxide ion; one eight of the tetrahedral voids are occupied by divalent ions (A²⁺) while one half of the octahedral voids are occupied by trivalent ions (B³⁺). What is the formula of the oxides?

Answer 1

Let there be n no. of O^2– in the crystal. So, Octahedral voids = n & Tetrahedral voids = 2n

A²⁺ ions = 1 / 8 × 2n = n / 4, B³⁺ ion = 1 / 2× n = n / 2 A²⁺: B³⁺ : O^2– = n / 4 : n / 2 : n = 1 : 2 : 4 

So the formula is AB₂O₄.