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.

 

Leave a Reply

Your email address will not be published. Required fields are marked *