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

(i)$\bf{face-centered\:cubic}$ :
on unit cell of face- centered cubic , there are 8 atoms in corner , 6 atoms in face centre. so, total number of atoms are (8 + 6) = 14 .
hence, total number of lattice points = 14

(ii) $\bf{face-centered\: tetragonal}$ : One unit cell of face- centered tetragonal has 8 lattice points are corners and 6 lattice points at faces, total 14 lattice points. you can say it is similar case of (i)

(iii) $\bf{body-centered cubic}$ :
one unit cell of body - centered cubic, there are 8 atoms at corners and one atom in body centre. so, total number of atoms in one unit cell of body centered cubic is 9.
hence, total number of lattice points = 9