Question

In a AB unit cell (Rock salt type) assuming cations forms fcc lattice point, the :

• A. nearest neighbours of $A^{+}$ are $6B^{-}$ ions
• B. nearest neighbours of $B^{-}$ are $6A^{+}$ ions
• C. second nearest neighbours of $A^{+}$ are $12A^{+}$ ions
• D. packing fraction of AB crystal is $\frac{\sqrt{3}\pi }{8}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A nearest neighbours of $A^{+}$ are $6B^{-}$ ions
B nearest neighbours of $B^{-}$ are $6A^{+}$ ions
C second nearest neighbours of $A^{+}$ are $12A^{+}$ ions

Coordination number of both ions in Rock Salt type unit cell is 6 hence option A and B are correct
Second nearest neighbours of cation(present in the octahedral voids) are present in the nearest octahedral void, which are 12 in number.
Based on FCC crystal (like NaCl lattice), we have
Packing fraction $=\frac{(4\times \frac{4}{3}\pi r_{A^{+}}^3)+(4\times \frac{4}{3}\pi r_{B^{-}}^3)}{a^3}$
$=\frac{(4\times \frac{4}{3}\pi \frac{a^3(0.414{)}^3}{(2\sqrt{2}{)}^3})+(4\times \frac{4}{3}\pi \frac{a^3}{(2\sqrt{2}{)}^3})}{a^3}=0.79$

Hence, options A. B and C are correct while D is incorrect.