Class 11 Chapter 6 Symmetry in Crystalline Solids Properties of Crystalline Solids
Introduction
Symmetry in crystalline solids underpins their classification into crystal systems and dictates many of their physical properties. In Chapter 6 of Class 11 Chemistry, you’ll learn how symmetry elements and operations define the repeating patterns in crystal lattices, and how these influence properties such as cleavage, optical behavior, and electrical conductivity.
Symmetry Elements & Operations
Rotation Axes (n-fold)
A rotation axis allows a crystal to be rotated by 360°/n and appear unchanged. Common axes are 2-, 3-, 4-, and 6-fold. For example, a 4-fold axis means a rotation of 90° maps the lattice onto itself.
Mirror Planes (σ)
A mirror plane reflects one half of the crystal onto the other. Planes can be vertical, horizontal, or diagonal relative to the unit cell axes.
Centre of Inversion (i)
An inversion center maps each point (x, y, z) to (–x, –y, –z). If present, the crystal is centrosymmetric, affecting properties like piezoelectricity (which requires non-centrosymmetry).
Rotation–Reflection Axes (Sn)
Also called improper axes, Sn combines rotation about an axis and reflection through a plane perpendicular to that axis. For instance, S4 rotates by 90° then reflects.
Seven Crystal Systems
| System | Axes & Angles | Example |
|---|---|---|
| Cubic | a = b = c; α = β = γ = 90° | NaCl, Diamond |
| Tetragonal | a = b ≠ c; α = β = γ = 90° | Sn, TiO2 (rutile) |
| Orthorhombic | a ≠ b ≠ c; α = β = γ = 90° | S8, K2SO4 |
| Hexagonal | a = b ≠ c; α = β = 90°, γ = 120° | Graphite, ZnO |
| Trigonal | a = b = c; α = β = γ ≠ 90° | Quartz (SiO2) |
| Monoclinic | a ≠ b ≠ c; α = γ = 90°, β ≠ 90° | Gypsum, Sugar |
| Triclinic | a ≠ b ≠ c; α ≠ β ≠ γ ≠ 90° | CuSO4·5H2O |
Physical Properties of Crystalline Solids
- Cleavage & Fracture: Defined planes of weakness correspond to lattice planes.
- Anisotropy: Direction-dependent properties, e.g., refractive index, conductivity.
- Optical Behavior: Birefringence in uniaxial/biaxial crystals.
- Mechanical Strength: Dependent on bond types and symmetry.
- Electrical & Thermal Conductivity: Varies along different crystallographic axes.
Conclusion
Symmetry considerations form the foundation for classifying crystalline solids into the seven lattice systems and predicting their physical behavior. Mastery of these concepts aids in understanding material properties across chemistry, physics, and materials science.
