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.) $=8$

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

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



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

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

$P.F\,\,\,P . F \simeq 0.34$

$\Rightarrow (34 \%)$