PH207 - SOLID STATE PHYSICS

Program

1. Introduction: gases, liquids and solids; regularities in solids and crystals

2. Packing of spheres and packing fraction; basic crystal structures: simple cube, face centred cube, body centred cube and hexagonal closed packed

3. Discrete translations, lattice, primitive vectors and primitive cells; crystal as lattice + basis; Bravais lattices (handed out problem set n. 1)

4. Reciprocal lattice; first Brillouin zone; X-Ray diffraction

5. Von Laue condition; Bragg condition; Ewald construction; experimental methods (continuous spectrum; rotating crystal; powder camera) (handed out problem set n. 2)

6. Structure factor and atomic form factor; calculation of the structure factor for case of the Face Centred Cube structure; discussion of a powder camera experiment for a crystal with a simple cubic structure

7. Correction problem set number 1

8. Binding in general; ionic bond: Coulomb term, Mandelung constant, hard core repulsion (handed out problem set n. 3)

9. The Van der Vaals and Lennard-Jones potentials; phenomenological parameters and their determination

10. Hydrogen bonds; covalent bonds; mention of the metalic bond

11. Correction of problem set n. 2

12. Lattice vibrations; phonon-vibration duality; modes of a monoatomic chain in one dimension

13. Correction problem set n. 3

14. Mode of a biatomic chain: acoustic and optical branches (handed out problem set n. 4)

15. Acoustic and optical frequencies in the long wavelength limit and at the edge of the Brillouin zone; frequency bands and frequency gaps; amplitudes of the oscillations for the optical and acoustic modes

16. Absorbtion of photons by a crystal ("Reststrahlen"); crystals at finite temperature: the Dulong-Petit law confronts experiments

17. Correction problem set n. 4 (handed out problem set n. 5)

18. Statistical Mechanics of the Quantum oscillator; internal energy and heat capacity for a system of independent oscillators; the density of states

19. The Einstein model and its high and low temperature limits

20. The Debye model: density of states, internal energy, specific heat; the high and low temperature limits of the models (handed out problem set n. 6)

21. Correction of problem set n. 5; revision

22. Correction of problem set n. 6; revision

Problems