Overview
This lecture explains Bravais lattices, the 14 unique three-dimensional arrangements of atoms in crystals, their classifications, and important related concepts.
Bravais Lattice Basics
- Bravais lattices are 14 unique ways atoms can be arranged in 3D space within crystals.
- The repeating smallest group of atoms is called a unit cell.
- All lattice points in a Bravais lattice are indistinguishable and equivalent.
- Bravais lattices are named after Auguste Bravais.
Types of Bravais Lattices
- There are seven crystal systems: cubic, orthorhombic, tetragonal, monoclinic, triclinic, rhombohedral, and hexagonal.
- Cell sides (a, b, c) and angles (α, β, γ) characterize each system.
Cubic System
- a = b = c; α = β = γ = 90°
- Types: simple (P), body-centered (I), face-centered (F).
- Examples: polonium (simple), iron (body-centered), copper (face-centered).
Orthorhombic System
- a ≠b ≠c; α = β = γ = 90°
- Types: simple, base-centered, face-centered, body-centered.
- Examples: rhombic sulphur (simple), MgSO₄·7H₂O (base-centered), potassium nitrate (body-centered), barium sulfate (face-centered).
Tetragonal System
- a = b ≠c; α = β = γ = 90°
- Types: simple, body-centered tetragonal.
- Examples: stannic oxide (simple), titanium dioxide (body-centered).
Monoclinic System
- a ≠b ≠c; α = γ = 90°, β ≠90°
- Types: simple, base-centered monoclinic.
- Examples: monoclinic sulphur (simple), sodium sulfate decahydrate (base-centered).
Triclinic System
- a ≠b ≠c; α ≠β ≠γ ≠90°
- Only one type: primitive triclinic.
- Example: potassium dichromate.
Rhombohedral System
- a = b = c; α = β = γ ≠90°
- Only one type: primitive rhombohedral.
- Examples: calcite, sodium nitrate.
Hexagonal System
- a = b ≠c; α = β = 90°, γ = 120°
- Only one type: simple hexagonal.
- Examples: zinc oxide, beryllium oxide.
Key Terms & Definitions
- Bravais lattice — One of 14 unique 3D arrangements of points in space with all points equivalent.
- Unit cell — The smallest repeating structure in a crystal lattice.
- Lattice point/site — Position in the unit cell occupied by an atom, molecule, or ion.
- Space lattice — The 3D lattice structure of points in space, equivalent to Bravais lattices when considering space groups.
Action Items / Next Steps
- Memorize the 7 crystal systems and their defining parameters.
- Learn examples for each Bravais lattice type.
- Review differences between Bravais, space, and non-Bravais lattices.