If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of

Question

If the unit cell of a mineral has cubic close packed (ccp) array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ions and n fraction of tetrahedral holes occupied by magnesium ions, m and n, respectively, are (Mineral is Spinel)

Professor PC Thomas Classes · Answer

The mineral is Spinel ($MgAl_2O_4$). For 4 $O^{2-}$ (ccp), there are 4 octahedral voids and 8 tetrahedral voids. To balance -8 charge, we need 2 $Al^{3+}$ and 1 $Mg^{2+}$. Thus, $m = 2/4 = 1/2$ and $n = 1/8$.