Question

The type of holes occupied by $A{l^{3 + }}$ ions is.
A.Tetrahedral
B.Octahedral
C.Both A and B
D.None of the above

Answer 1

Hint: In $(MgA{l_2}{O_4}){O^{2 - }}$ , ${O^{2 - }}$ ions are considered to form a face centred array, within the unit cell, $M{g^{2 + }}$ ions occupy tetrahedral interstices between ${O^{2 - }}$ ions, the smaller $A{l^{3 + }}$ ions are sited in octahedral interstices.

Complete step by step answer:
The important class of oxides consisting of two types of metal ions arranged in CPP pattern is Spinel. The normal spinel has $\dfrac{1}{8}$ of the tetrahedral holes occupied by one type of metal ion and $\dfrac{1}{2}$ of the octahedral hole occupied by another type of metal ion. Such a spinel is formed by $A{l^{3 + }}$ in the tetrahedral holes.
 $(MgA{l_2}{O_4}){O^{2 - }}$ Forming FCC, $M{g^{2 + }}$ filling $\dfrac{1}{8}$ of tetrahedral voids and $A{l^{3 + }}$ taking half of octahedral voids. In an inverse spinel structure, ${O^{2 - }}$ ion form FCC lattice, ${A^{2 + }}$ ions occupy $\dfrac{1}{8}$ of the tetrahedral voids and trivalent cation occupies $\dfrac{1}{8}$ of the tetrahedral voids and ¼ of the octahedral voids.
These cations sub lattices only partly fill the available interstices and the remaining positions are generally considered to accommodate interstitial ions.

Note: The spinel is the normal spinel since $M{g^{2 + }}$ ion is in the tetrahedral field and ion is in the tetrahedral field. We know that in one FCC lattice unit cell, the number of atoms or ions occupying the lattice point is 4 and at the same time the effective tetrahedral holes are 8 and octahedral holes is 4.