Learning Objectives
- Classify solids based on bonding and crystallinity
- Understand crystal lattice, unit cells, and packing efficiency
- Calculate density from unit cell parameters
- Study imperfections in solids and their effects on properties
- Learn about electrical and magnetic properties of solids
Key Concepts
Classification of Solids
Crystalline solids: Regular, ordered arrangement. Sharp melting point. Anisotropic (direction-dependent properties). Examples: NaCl, diamond, ice.
Amorphous solids: Irregular arrangement. No sharp melting point (soften over a range). Isotropic. Examples: glass, rubber, plastics. Sometimes called pseudo-solids or supercooled liquids.
Types of Crystalline Solids
- Ionic: Cation-anion lattice. Hard, brittle, high MP. Conduct in molten/dissolved state. Example: NaCl, KNO₃.
- Covalent/Network: Atoms connected by covalent bonds. Very hard, very high MP. Poor conductors (except graphite). Example: diamond, SiO₂, SiC.
- Molecular: Molecules held by van der Waals/H-bonds. Soft, low MP. Non-conducting. Example: ice, I₂, naphthalene.
- Metallic: Metal ions in electron sea. Variable hardness, high conductivity, lustrous, malleable. Example: Cu, Fe, Au.
Crystal Lattice and Unit Cells
14 Bravais lattices in 7 crystal systems: cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, rhombohedral.
Cubic unit cells:
- Simple Cubic (SC): Atoms at corners. Z = 1. Coordination number = 6. Packing efficiency = 52.4%.
- Body-Centred Cubic (BCC): Corners + centre. Z = 2. CN = 8. PE = 68%.
- Face-Centred Cubic (FCC/CCP): Corners + face centres. Z = 4. CN = 12. PE = 74%.
Contribution of atoms: corner = 1/8, edge = 1/4, face = 1/2, body = 1.
Close Packing
HCP (ABAB...): Hexagonal close packing. PE = 74%.
CCP/FCC (ABCABC...): Cubic close packing. PE = 74%.
Voids: Tetrahedral voids = 2N (where N = number of atoms). Octahedral voids = N.
Radius ratio: tetrahedral void r = 0.225R; octahedral void r = 0.414R.
Density Calculation
ρ = ZM/(a³Nₐ), where Z = atoms per unit cell, M = molar mass, a = edge length, Nₐ = Avogadro's number.
Imperfections (Defects) in Solids
Stoichiometric (intrinsic) defects:
- Schottky defect: Equal cation and anion vacancies. Decreases density. Found in ionic compounds with similar cation/anion sizes (NaCl, KCl, CsCl).
- Frenkel defect: Ion displaced to interstitial site. Density unchanged. Found when cation is much smaller than anion (AgCl, AgBr, ZnS).
Non-stoichiometric defects:
- Metal excess (F-centre): Electron trapped in anion vacancy. Imparts colour (NaCl yellow, KCl violet).
- Metal deficiency: Cation vacancy balanced by higher oxidation state of another cation (FeO, FeS).
Electrical Properties
Conductors: ρ ~ 10⁻² to 10⁻⁸ Ω·m. Semiconductors: 10⁻⁶ to 10⁴ Ω·m. Insulators: > 10¹¹ Ω·m.
n-type semiconductor: Doped with Group 15 (extra electron). p-type: Doped with Group 13 (electron hole).
Summary
Solids are classified by bonding type (ionic, covalent, molecular, metallic) and crystallinity. Crystal structures are described by unit cells with specific packing efficiencies. FCC/HCP are most efficient at 74%. Density is calculated from unit cell parameters. Crystal defects (Schottky, Frenkel, F-centres) affect properties like density, colour, and conductivity.
Important Terms
- Unit Cell: Smallest repeating unit of a crystal lattice
- Coordination Number: Number of nearest neighbours
- Packing Efficiency: Fraction of space occupied by atoms
- Schottky Defect: Paired cation-anion vacancies
- Frenkel Defect: Ion displaced to interstitial site
- F-centre: Electron trapped in anion vacancy causing colour
Quick Revision
- SC: Z=1, CN=6, PE=52.4%; BCC: Z=2, CN=8, PE=68%; FCC: Z=4, CN=12, PE=74%
- ρ = ZM/(a³Nₐ)
- Tetrahedral voids = 2N; Octahedral voids = N
- Schottky: density ↓ (NaCl); Frenkel: density same (AgCl)
- n-type: Group 15 dopant; p-type: Group 13 dopant
- F-centre: NaCl → yellow, KCl → violet