Class 11 Chapter 6 Crystal Lattice And Unit Cell
Introduction
In Chapter 6 of Class 11 Chemistry, the concepts of crystal lattice and unit cell form the foundation of solid state chemistry. A clear understanding of these concepts helps explain the arrangement of particles in crystalline solids and their macroscopic properties.
Crystal Lattice
A crystal lattice is a three-dimensional array of points representing the periodic arrangement of constituent particles (atoms, ions or molecules) in a crystal. Each point, called a lattice point, has an identical environment.
Key Features
- Infinite repetition of a pattern in three dimensions.
- Defines symmetry and long-range order.
- Lattice points are purely geometrical; actual particles may occupy positions relative to these points.
Unit Cell
The unit cell is the smallest repeating unit of the crystal lattice that, when stacked in all directions, recreates the entire lattice without gaps.
Types of Unit Cells
- Primitive (P): Lattice points only at corners.
- Body-Centered (I): Corners + one at the center.
- Face-Centered (F): Corners + one at the center of each face.
- Base-Centered (C): Corners + one at the center of two opposite faces.
Unit Cell Parameters
- Edge lengths: a, b, c
- Interaxial angles: α (between b & c), β (between a & c), γ (between a & b)
- Volume formula for orthogonal cell:
V = a·b·c·sin(α)·sin(β)·sin(γ)(general expression)
Bravais Lattices
There are 14 distinct Bravais lattices, classified into seven crystal systems:
| Crystal System | Lattice Types |
|---|---|
| Cubic | P, I, F |
| Tetragonal | P, I |
| Orthorhombic | P, C, I, F |
| Monoclinic | P, C |
| Triclinic | P |
| Hexagonal | P |
| Trigonal (Rhombohedral) | P |
Miller Indices
Miller indices (hkl) denote crystallographic planes and directions:
- Reciprocal of intercepts of the plane with axes (a/h, b/k, c/l).
- Integral values with common factors removed.
- Important for describing cleavage planes and diffraction patterns.
Example: (100) plane cuts the a-axis at one lattice constant and is parallel to b and c axes.
Conclusion
Crystal lattice and unit cell concepts provide the geometric framework for understanding the internal structure of crystalline solids. Mastery of Bravais lattices and Miller indices is essential for predicting and explaining material properties in solid state chemistry.
