Week 3

Lecture 19, 15 April, 10.00-12.00, FL51

Dynamics of lattice: phonons.

Reading.

Review questions.

1. Explain concept of phonons and how they are related to normal modes. Derive distribution function for phonons.
2. Derive Drude-Petit formula for the specific heat of a lattice. When and why does this formula disagree with the experiment?
3. Derive formula for the energy of the phonon gas. Use this formula for derivation of the phonon specific heat at low temperature.
4. What is the Debye approximation and in what limit does it become exact? Define Debye temperature, wave vector and frequency.
5. Discuss the Einstein model for the specific heat. In which temperature range it is useful?

Lecture 20, 18 April, 13.15-15.00, FL51

Thermodynamics and kinetics of phonons.

Reading.

Review questions.

1. Derive formula for the phonon density of states. How is this formula approximated in Debye's theory?
2. Derive temperature dependence for a total number of phonons (use Debye approximation).
3. Discuss the role of phonons in the heat transport. What is the thermal conductivity of perfect crystal? Why?
4. Write down Boltzmann kinetic equation for phonons in a relaxation time approximation. Caclulate thermal conductivity. Discuss temperature dependence of thermal conductivity.
5. Discuss mechanisms of thermal resistance.
6. Discuss phonon-phonon scattering. What is the physical mechanism behind it? What is the Umklapp process?

Home task.