Question

In diamond, the lattice is fcc with $C$ atoms occupying lattice point as well as some of the voids. Which of the following statement $(s)$ is/are correct about diamond structure-
I. In the diamond lattice, half of $T.$ voids (tetrahedral) are occupied.
II. $\%$ age space occupied (Packing efficiency) is $74\%$ III. All octahedral voids are occupied in diamond

• A. Only I
• B. Only III
• C. I, II & III
• D. Only II

Answer 1

Answer: (A)

Effective No. of $C$ atoms per unit cell

$=8\times \frac{1}{8}+6\times \frac{1}{2}+4$

(at corner) (at face centres) (alt. T.V.) $=8$

$P.F.=\frac{\text{ Vol. occupied by atoms }}{\text{ Total vol. of cube }}=\frac{8\times \frac{4}{3}\pi r^3}{a^3}$

$=\frac{8\times \frac{4}{3}\pi r^3}{{\left(\frac{8r}{\sqrt{3}}\right)}^3}$



$2r=\frac{\sqrt{3}a}{4}$

$P.F.=8\times \frac{4}{3}\pi r^3\times \frac{3\sqrt{3}}{8r\times 8r\times 8r}$

$P.FP.F\simeq 0.34$

$\Rightarrow (34\%)$