Solid State
1. Introduction
Solids have definite shape and volume. This chapter explores the structure, packing, defects, and properties of crystalline solids.
2. Amorphous vs Crystalline Solids
| Property | Crystalline | Amorphous |
|---|---|---|
| Order | Long-range order | Short-range order |
| Melting point | Sharp | Gradual range |
| Anisotropy | Anisotropic | Isotropic |
| Cutting | Clean cleavage | Irregular fracture |
| Examples | NaCl, Diamond | Glass, Rubber |
3. Unit Cell and Crystal Lattices
A unit cell is the smallest repeating unit of a crystal lattice.
3.1 Types of Unit Cells
Primitive (Simple): 1 atom per unit cell. Body-Centred Cubic (BCC): 2 atoms per unit cell. Face-Centred Cubic (FCC): 4 atoms per unit cell.
3.2 Seven Crystal Systems
Cubic, Tetragonal, Orthorhombic, Hexagonal, Rhombohedral, Monoclinic, Triclinic.
4. Packing Efficiency
Simple cubic: 52.4% BCC: 68% FCC/HCP: 74% (maximum packing)
Packing efficiency = (Volume occupied by atoms/Volume of unit cell) × 100%.
5. Structures of Ionic Compounds
5.1 NaCl Structure (Rock Salt)
- FCC arrangement of Cl⁻ ions with Na⁺ occupying all octahedral voids.
- Each Na⁺ surrounded by 6 Cl⁻ and vice versa.
- Coordination number: 6:6.
- Examples: NaCl, KCl, AgCl.
5.2 CsCl Structure
- Body-centred cubic arrangement.
- Cl⁻ at corners, Cs⁺ at body centre (or vice versa).
- Coordination number: 8:8.
- The larger Cs⁺ ion fits in the larger cubic void (radius ratio > 0.732).
5.3 ZnS Structure (Zinc Blende)
- FCC arrangement of S²⁻ ions with Zn²⁺ occupying alternate tetrahedral voids.
- Only half the tetrahedral voids are occupied.
- Coordination number: 4:4.
5.4 Radius Ratio Rules
The ratio r_cation/r_anion determines the coordination number:
-
0.732: Cubic void (coordination 8) — CsCl type.
- 0.414 - 0.732: Octahedral void (coordination 6) — NaCl type.
- 0.225 - 0.414: Tetrahedral void (coordination 4) — ZnS type.
6. Voids
If anions form a closed-packed arrangement, cations occupy interstitial voids.
Tetrahedral void: Radius ratio 0.225 - 0.414. Octahedral void: Radius ratio 0.414 - 0.732.
'In FCC, there are 8 tetrahedral and 4 octahedral voids per unit cell.'
6. Defects in Solids
6.1 Point Defects
Stoichiometric defects: Frenkel defect (cation vacancy + interstitial), Schottky defect (equal cation-anion vacancies).
Non-stoichiometric defects: Metal excess (F-centres, colour centres) or metal deficiency.
Impurity defects: Foreign atoms in the crystal.
6.2 Effect of Defects
Defects alter electrical conductivity, density, and colour of crystals.
7. Electrical and Magnetic Properties
Conductors: σ = 10⁴ - 10⁶ ohm^{-1}cm^{-1}. Semiconductors: σ = 10^{-6} - 10⁴ ohm^{-1}cm^{-1}. Insulators: σ < 10^{-6} ohm^{-1}cm^{-1}.
Magnetic properties: Diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, ferrimagnetic.
8. Worked Problems
Problem 1: A metal has FCC structure with edge length 400 pm. Find atomic radius. Solution: For FCC, 4r = a√2 ⇒ r = a√2/4 = 400×1.414/4 = 141.4 pm.
Problem 2: Calculate the number of atoms in a BCC unit cell. Solution: BCC: 1 atom at each corner (8×1/8 = 1) + 1 body-centred atom = 2 atoms.
9. Common Mistakes
'Students often confuse the number of atoms per unit cell. Remember: corner atoms count 1/8, face-centred count 1/2, body-centred counts 1.'
10. ISC Exam Focus
| Topic | Theory Marks | Practical Marks |
|---|---|---|
| Unit cells and packing | 4 | 2 |
| Voids and radius ratio | 3 | 1 |
| Defects | 3 | 1 |
| Properties | 2 | 1 |
11. Self-Test Questions
- Distinguish between crystalline and amorphous solids with examples.
- Calculate the packing efficiency of a BCC unit cell.
- Explain Frenkel and Schottky defects with examples.
- A metal crystallises in FCC with edge length 500 pm. Find the atomic radius and density if atomic mass is 60 g/mol.
- What are F-centres? How do they affect the colour of crystals?
