Teaching

PY3105 is a one-semester undergraduate course in solid-state physics, covering the basis of electrons and phonons in solids, in addition to crystal structure and its experimental probes.

The course begins by building on elementary quantum mechanics to elucidate the physics of chemical bonding in molecules and solids, before introducing the emergence of electronic band structure in periodic systems. Considering the Kronig-Penney model as a prototypical "crystal", and by introducing the tight-binding method, we discuss fundamental properties of band structures and consider the basic properties of metals, insulators and semiconductors.

The second section of the course is concerned with thermal properties and lattice vibrations. We begin by recapitulating the Einstein and Debye models of the heat capacity of quantum mechanical solids, before considering the impact of band electrons via the Drude-Sommerfeld model. We then briefly discuss Fermi surfaces, and consider high-level trends in the properties of thermoelectric materials. Lattice vibrations are then studied via the classical mechanics of coupled atoms in exemplar one-dimensional crystals. This allows to straightforwardly introduce the dynamical matrix in addition to the phonon phase and group velocities, and to distinguish between acoustic and optical phonon modes. This section of the course is completed by considering the thermal expansion of solids, which is rooted in anharmonic lattice dynamics, and realistic examples for real materials are discussed.

Finally, we formalise the concepts of lattice and crystal structure, which are encountered informally earlier in the course. We define a crystal structure as a combination of a lattice and basis, and discuss examples of lattice and crystal systems that appear in common and technologically important materials. The concepts of reciprocal lattice and Brillouin zone are defined, and the emergence of the reciprocal lattice as the Fourier transform of the lattice is demonstrated. The course concludes with an introduction to x-ray diffraction and neutron scattering as experimental probes of the crystal structure of real materials. Lattice planes and Miller indices are introduced, and the equivalence between the Laue condition for wave scattering from a crystal lattice and Bragg's law for diffraction is demonstrated. The concept of the structure factor is introduced, and its calculation described for several exemplar crystal structures.

Level: 3rd year (B.Sc. Physics, B.Sc. Astrophysics, B.Sc. Physics & Mathematical Sciences, B.Sc. Chemical Physics)

Placeholder - Maxwell's equations in differential form and their consequences: electromagnetic waves in vacuum, dielectrics and conductors, reflection, refraction and dispersion, waveguides, radiation from accelerating charges, and the relativistic formulation of electrodynamics.

Level: 4th year (B.Sc. Physics, B.Sc. Astrophysics, B.Sc. Physics & Mathematical Sciences, B.Sc. Chemical Physics)