Study Notes: Cubic Lattices
Introduction
A cubic lattice is one of the simplest and most symmetric types of crystal lattices. Atoms are arranged
at the corners of a cube, and depending on how additional atoms are placed, there are three main
types.
Simple Cubic (SC)
Arrangement: Atoms only at the cube’s corners.
Atoms per unit cell: 8 × 1/8 = 1
Coordination number: 6
Packing efficiency: ~52%
Example: Polonium (Po)
Body-Centered Cubic (BCC)
Arrangement: Atoms at the corners + one atom in the cube’s center.
Atoms per unit cell: 8 × 1/8 + 1 = 2
Coordination number: 8
Packing efficiency: ~68%
Examples: Iron (Fe), Chromium (Cr)
Face-Centered Cubic (FCC)
Arrangement: Atoms at the corners + one atom at the center of each cube face.
Atoms per unit cell: 8 × 1/8 + 6 × 1/2 = 4
Coordination number: 12
Packing efficiency: ~74%
Examples: Aluminum (Al), Copper (Cu), Gold (Au), Silver (Ag)
Important Parameters
Lattice Parameter (a): Edge length of the cube.
Atomic Radius (r):
• SC: r = a/2
• BCC: r = (√3/4)a
• FCC: r = (√2/4)a
Packing Efficiency Formula: Volume of atoms in unit cell ÷ Volume of unit cell × 100%
Comparison Table
Type
Atoms per Cell
Coordination Number
Packing Efficiency
Example
SC
1
6
52%
Polonium
BCC
2
8
68%
Iron, Chromium
FCC
4
12
74%
Copper, Aluminum, Gold, Silver
Key Takeaways
• Cubic lattices are highly symmetric and form the basis for understanding crystal structures.
• FCC has the highest packing efficiency and coordination number, making it very stable.
• Knowledge of lattice parameters helps in calculating density and other physical properties.