In non stoichiometric defects ratio of cation and anion is not same that is represented by chemical ideal formula, this is due to variable oxidation nos of cation. Transition elements show variable oxidation nos.

For $$bcc$$  lattice body diagonal $$ = a\sqrt 3 .$$
The distance between the two oppositely charged ions
$$\eqalign{ & = \frac{a}{2}\sqrt 3 \cr & = \frac{{387 \times 1.732}}{2} \cr & = 335\,pm \cr} $$

In antiferromagnetic substances, their domains are oppositely oriented and cancel out each other's magnetic moment.

The given properties are shown by covalent solids which are network solids and very hard with high melting point. They are insulators in solid as well as in molten state.

$$\eqalign{ & \rho = \frac{{ZM}}{{{N_A}V}} \cr & Z = \frac{{\rho {N_A}V}}{M} \cr & = \frac{{2 \times 6 \times {{10}^{23}} \times {{\left( {5 \times {{10}^{ - 8}}} \right)}^3}}}{{75}} \cr & Z = 2,\,{\text{which represents }}bcc{\text{ structure}} \cr & \therefore r = \frac{{\sqrt 3 }}{4}a = \frac{{\sqrt 3 }}{4} \times 5 = 2.165\mathop {\text{A}}\limits^{\text{o}} = 216.5\,pm \approx 217\,pm \cr} $$

For body centred cubic lattice $$Z=2$$
Atomic mass of unit cell $$ = 133 + 80 = 213\,a.m.u$$
Volume of cell $$ = {\left( {436.6 \times {{10}^{ - 10}}} \right)^3}c{m^3}$$
$$\eqalign{ & {\text{Density,}} \cr & \rho = \frac{{ZM}}{{{a^3}{N_A}}} \cr & = \frac{{2 \times 213}}{{{{\left( {436.6 \times {{10}^{ - 10}}} \right)}^3} \times 6.02 \times {{10}^{23}}}} \cr & = 8.50\,g/c{m^3} \cr} $$

Octahedral sites are occupied by $$N{a^ + }\,ions$$   in $$NaCl$$  structure.

$${\text{For}}\,fcc\,{\text{unit}}\,{\text{cell,}}\,4r = \sqrt 2 \,{\text{a}}\,{\text{;}}\,{\text{r}} = \frac{{\sqrt 2 \times 361}}{4} = 127\,pm$$

$$\eqalign{ & AB = \frac{{\sqrt 3 a}}{2}\,\,{\text{(nearest)}} \cr & AC = a\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(next - nearest)}} \cr & CD = \sqrt 2 a\,\,\,{\text{(next - next - nearest)}} \cr} $$

For $$fcc$$  arrangement, distance of nearest neighbour
$$\eqalign{ & \left( d \right)\,\,{\text{is}}\,\,\frac{a}{{\sqrt 2 }} \cr & = \frac{{862}}{{1.414}} \cr & = 609.6\,pm \cr} $$