Body-centred cubic (BCC) lattice — atoms per unit cell In crystallography of metals, how many atoms are effectively contained in one unit cell of a body-centred cubic (BCC) space lattice?

Introduction / Context:
Unit cell atom counting is fundamental in materials science and solid-state physics. It underpins density calculations, slip system enumeration, and understanding coordination numbers and packing efficiency. For body-centred cubic (BCC) structures (e.g., alpha iron), correctly counting atoms per unit cell prevents serious property miscalculations.

Given Data / Assumptions:

• BCC lattice has atoms at the eight cube corners and one atom at the body centre.
• Each corner atom is shared among eight neighboring unit cells.
• Counting is for the effective number of atoms wholly contained within one unit cell.

Concept / Approach:
Corner atoms contribute 1/8 of an atom per unit cell because each is shared by 8 cells. With 8 corners, the total contribution is 8 * (1/8) = 1 atom. The body-centre atom belongs entirely to that cell and contributes 1 atom. Adding these yields 2 atoms per unit cell. This count differs from coordination number (number of nearest neighbors), which for BCC is 8, and from the number of atoms intersecting the cell faces (zero in BCC).

Step-by-Step Solution:

Verification / Alternative check:
Using atomic packing factor (APF) for BCC, APF = (2 * 4/3 * pi * r^3) / a^3 with a = 4r / sqrt(3) confirms the standard density relationships for BCC metals.

Why Other Options Are Wrong:

• 1 atom: ignores the body-centre atom.
• 4 atoms: corresponds to FCC, not BCC.
• 8 atoms: confuses coordination number with atoms per cell.
• 14 atoms: unrelated; sometimes appears in other contexts (e.g., number of atoms in certain polyhedra), not BCC atoms per cell.

Common Pitfalls:
Mixing “atoms per cell” with “coordination number”; forgetting to divide shared corner atoms by 8.

Final Answer: