Question

Calculate the number of atoms per unit cell in

(a) Aluminum (FCC)

(b) Alpha-iron (BCC)

Answer 1

a]

FCC ---->

a] Atoms on the face

There are 6 faces

Each face centred atom contributes 1/2

Number of atoms = 6*1/2 = 3

b] Atoms at the corners

There are 8 atoms

Each cornered atom contributes 1/8th

NUmber of atoms = 1/8 *8 = 1

Total number of atoms per unit cell = 3+1 = 4 (In FCC)

Number of Al atoms = 4 per unit cell

b]

BCC --->

a] One body centered atom

b] 8 atoms at the corners of unit cell

Each corner atom contributes 1/8th of unit cell

Total atoms = 1+8*1/8 = 2

Number of atoms per unit cell = 2

Number of alpha-iron atoms in a unit cell = 2