Question

Calcium crystallises in face-centred cubic unit cell with $a=0.556nm$. Calculate density if:
(i) it contained $0.1$% Frenkel defect.
(ii) it contained $0.1$% Schottky defect.

Answer 1

(i) Frenkel defect does not alter the density of solid.

Given that,

Edge length, $a=0.556nm=0.556\times {10}^{-7}cm$

Number of atoms per unit cell, $Z=4$ Note: since fcc lattice.

Now,

$\text{Density, d}=\frac{M\times Z}{a^3\times N_A}=\frac{40\times 4}{(0.556\times {10}^{-7}{)}^3\times 6.02\times {10}^{23}}$

$\text{Density, d}=1.546g/c{m}^3$

(ii) Schottky defect lowers the density of solid.

Now,

$Z_{eff}=4-\frac{4\times 0.1}{100}=3.996$

$\text{Density, d}=\frac{40\times 3.996}{(0.556\times {10}^{-7}{)}^3\times 6.02\times {10}^{23}}$

$\text{Density, d}=1.545g/c{m}^3$.