• Week 1. Crystal structure
  • Course information
  • Symmetries
  • Translational invariance
  • Lattices in 2D, 3D
  • 14 Bravais lattices
  • Unit cells
  • Wigner-Zeitz cell
  • Atoms in crystals
  • Planes in crystals, Miller indexes
  • Directions
  • Typical structures
• Week 2. Reciprocal lattice
  • Periodic functions
  • Reciprocal lattice
  • Geometrical properties of reciprocal lattice
  • Brillouin zone
• Week 3. Bragg reflection, Phonons
  • Bragg reflection
  • Laue condition
  • Bonding in crystals
  • Phonons
  • Sound waves
• Week 4. Phonons in 1D
  • Energy, forces, equations of motion
  • Solution of equations of motion, waves
  • Spectrum
  • Long-wave limit
  • Number of oscillators, Brillouin zone
• Week 5. Chain of two types of atoms. Quantum definition of phonons
• Week 6+7. Heat capacity

• Heat capacity of lattice vibrations
  • Oscillator
  • Phonons
• Free electron gas
  • Fermi level
  • Heat capacity
  • Effective mass
  • Conductivity
  • Thermal conductivity
  • Wiedemann-Franz law
• Band structure
  • Bloch's theorem (includes the proof, which was skipped on lecture)
  • Nearly free electrons
  • Tight binding approach
  • Effective mass
  • Holes

Exam questions with answers, Part 1