Question

Calculate the number of atoms in fcc unit cell.

Answer 1

Number of atoms in face-centred cubic (fcc)

unit cell :

In this unit cell, there are 8 atoms at 8 corners and 6 atoms at 6 face centres. Each corner contributes 1/8th atom to the unit cell, hence due to 8 corners,

Number of atoms \(=\frac{1}{8}\times 8 =1.\)

Each face centre contributes half of the atom to the unit cell, hence due to 6 face centres, Number of atoms \(=\frac{1}{2}\times 6 =3.\)

\(\therefore\) Total number of atoms present in fee unit cell = 1 + 3 = 4.

Hence the volume of the unit cell is equal to the volume of four atoms.

Face centered unit cell

Answer 2

1. A face-centred cubic (fcc) unit cell has particles at the eight corners plus particles at the centre of its six faces.

2. Each particle present at the corner of a given unit cell is shared with seven other neighbouring unit cells. As a result, its contribution to the given unit cell is only 1/8.

Thus, the number of particles present at corners per unit cell 

= 8 corner atoms × 1/8 atom per unit cell

= 1

3. Each particle at the centre of the six faces is shared with one neighbouring cube. Thus, 1/2 of each face particle belongs to the given unit cell.

Thus, the number of particles present at faces per unit cell

= 6 atoms at the faces ×1/2 atom per unit cell

= 3

Therefore, fcc unit cell has one corner particle plus 3 face particles, making total of 4 particles per unit cell.