Question

Unit cells can be divided into two categories, primitive and centered unit cells.
(a) Differentiate between Unit Cell and Crystal Lattice?
(b) Calculate the number of atoms per unit cell in the following:
(i) Body centered cubic unit cell (bcc)
(ii) Face centered cubic unit cell (fcc)

Answer 1

(a)
A crystal lattice is the orderly array of points in space, i.e., a lattice is a structure of crystals where each lattice point represents an identical group of atoms.
A unit cell is a crystal structure that is the smallest group of atoms possessing the symmetry of the crystal. It is the fundamental unit of crystal lattice.
(b)
(i) Body centered cubic unit cell (bcc)
8 atoms are present at eight corners of the unit cell and one atom is present at the body center. Each corner atom contributes one eight to the unit cell. The contribution of atom at body center is 1. The number of atoms per unit cell $=8\times \frac{1}{8}+1=2$
(ii) Face centered cubic unit cell (fcc)
8 atoms are present at eight corners of the unit cell and 6 atoms are present at the face centers. Each corner atom contributes one eight to the unit cell. The contribution of atom at face center is one half. The number of atoms per unit cell $=8\times \frac{1}{8}+6\times \frac{1}{2}=4$