Question

Calculate the number of particles (atoms) per units cell in a FCC crystal lattice?

Answer 1

The no. of particles (atoms) per units cell in a FCC crystal lattice is 4.
A fcc unit cell has atoms present at 8 corners and 6 face centers. Each atom at corner is shared by 8 unit cells. Hence, it contributes one eight to a unit cell. Each atom at face center is shared by 2 unit cells. Hence, it contributes one half to a unit cell.
The no. of particles (atoms) per units cell in a FCC crystal lattice is $8\times \frac{1}{8}+6\times \frac{1}{2}=1+3=4$