Crystal Lattices and Unit Cell

In solid state chemistry, the arrangement of particles in a crystalline solid is highly ordered and repetitive. This regular 3D arrangement is called a crystal lattice, and the smallest repeating unit that defines the lattice is called a unit cell.

What is a Crystal Lattice?

A crystal lattice is a geometric pattern formed by atoms, ions, or molecules in crystalline materials. Each point (called a lattice point) represents the position of a particle. The lattice extends in 3D space.

Key Features of a Crystal Lattice:

• Highly ordered, periodic structure
• Repeats in three dimensions
• Each lattice point is fixed
• Types include cubic, hexagonal, etc.

What is a Unit Cell?

The unit cell is the smallest part of a lattice that repeats in all directions to create the full crystal.

• Edge lengths: a, b, c
• Angles: α, β, γ

Remember: Crystal properties depend on the unit cell geometry.

Types of Unit Cells (Cubic System)

• Simple Cubic (SC): Atoms at corners. Coordination number: 6.
• Body-Centered Cubic (BCC): Corners + one in center. Coordination number: 8.
• Face-Centered Cubic (FCC): Corners + face centers. Coordination number: 12.

Calculations Involving Unit Cells

• Edge Length (a): Related to atomic radius.
• Density (ρ):
  ρ = (Z × M) / (a³ × NA)
  Where Z = number of atoms/unit cell, M = molar mass, a = edge length, N_A = Avogadro’s number.
• Packing Efficiency: Space occupied by atoms vs total volume.

Importance

• Determines mechanical, electrical properties
• Used in X-ray crystallography
• Vital in designing functional materials

Conclusion: Understanding crystal lattices and unit cells helps explain the structure and properties of solid materials, making them crucial in modern science and technology.

MCQ Quiz

1. Which type of unit cell has atoms at corners and face centers?
   A. SC     B. BCC     C. FCC     D. None
   ✅ Explanation: FCC includes atoms at corners and all face centers.
2. The number of atoms per unit cell in BCC is:
   A. 1     B. 2     C. 4     D. 6
   ✅ Explanation: BCC has 1 atom at center and 8 corners × 1/8 = 2 total.

True / False

• Crystal lattice is random and disordered.
  ❌ False – It is highly ordered and periodic.
• Unit cells repeat in 3D to form the whole crystal.
  ✅ True
• FCC unit cells have lower coordination number than BCC.
  ❌ False – FCC has 12, BCC has 8.

Internal & External Links

• Crystal Structures – Wikipedia
• Crystal Lattice & Unit Cells – LibreTexts