Q.Define unit cell. Calculate the number of particles per unit cell in Body centered cube and Face centered cube.

Number of Atoms per Unit Cell

Imagine you're stacking identical cubes to build a giant crystal. Each cube is a unit cell — the smallest repeating block of the crystal. The question is: how many whole atoms "belong" to one cube?

The trick is that atoms at the corners, edges, or faces of a cube are shared with neighbouring cubes. You can't count the same atom twice. So we need a fair way to divide each atom among the cubes that touch it.

The sharing rule

An atom's contribution to one unit cell depends on where it sits:

• Corner atom: Touched by 8 cubes (4 in the layer above, 4 below). Each cube gets $\frac{1}{8}$ of that atom.
• Face-centre atom: Shared by exactly 2 cubes (one on each side of the face). Each cube gets $\frac{1}{2}$.
• Edge-centre atom: Shared by 4 cubes (two along the edge direction, two stacked). Each cube gets $\frac{1}{4}$.
• Body-centre atom: Lies entirely inside one cube — no sharing. Contribution = 1.

Counting for the three basic cubic cells

Simple Cubic (SCC) — atoms only at the 8 corners.

Body-Centred Cubic (BCC) — 8 corners + 1 atom at the body centre.

Face-Centred Cubic (FCC) — 8 corners + 6 face centres.