Question

How many lattice points are there in one unit cell of each of the following lattice ?

(i) Face-centred cubic

(ii) Face - centred tetragonal

(iii) Body - centred

Answer 1

Number of corner atoms per unit cell

= 8 corners atoms $\times \frac{1}{8}$ atom per unit cell

$=8\times \frac{1}{8}=1atom$

Number of face face centred atoms per unit cell

= 6 face centred atoms $\times \frac{1}{2}$ atom per unit cell

$6\times \frac{1}{2}=3$ atoms

$\therefore$ Total number of atoms (lattice point) = 1 + 3 = 4

(ii) As in (i)

No. of lattice points = 4

(iii) In bcc unit cell, number of corner atoms per unit cell

$=8corners\times \frac{1}{8}$ per corner atom

$=8\times \frac{1}{8}=1atom$

Number of atoms at body centre $=1\times 1$ = 1 atom

$\therefore$ Total number of atoms (lattice points) = 1 + 1 = 2