Explain how much portions of an atom located at (i) corner and (ii) body centre of a cubic unit cell is part of its neighbouring unit cell.

Cubic Unit cell:

• In a simple cubic unit cell, atoms occupy the corner position of a cubic structure.
• So, each corner atom of the unit cell is connected by 8 other atoms of the unit cell.
• The effective contribution of each corner atom in one unit cell can be given as $\frac{1}{8}$, because one atom is shared with 8 neighbouring atoms.
• There are 8 corner atoms in one unit cell each with a contribution of $\frac{1}{8}$. so, the total effective atom in one unit cell will be $8\times \frac{1}{8}=1$.
• But in the body centre cubic unit cell. apart from corner atoms, there is one atom present at the centre of the cubic unit cell.
• The central atom is not shared by any other unit cell because it is at the centre of the cube. so its effective contribution is 1.

So, corner atoms have a contribution of $\frac{1}{8}$ while the body centre atom has a contribution of $1$ atom.