Description:
| Aims: The aims of this unit are to introduce students to the basic concepts and models of solid state physics, with an emphasis on crystalline, electronic and magnetic structure.
Learning Outcomes: After taking this unit the student should be able to:
* know the ways in which crystal structures are described formally and relate structures in real space to those in reciprocal space;
* describe how X-ray and neutron diffraction is related to the properties of the reciprocal lattice, and used in structural studies.
* discuss why classical theories of electrons in solids fail, and why they have to be treated quantum mechanically;
* explain the concept of density of states;
* describe how allowed and forbidden energy bands arise as a result of crystal potentials and how the properties of electrons in allowed energy bands determine the electrical and optical behaviour;
* appreciate the difference between metals, semiconductors and insulators;
* discuss the factors that control the electrical conductivity of metals and semiconductors;
* describe classical theories of diamagnetism, paramagnetism, and the ferromagnetic properties of materials;
* describe how crystalline structures vibrate, and the associated theories of heat capacity.
Skills: Numeracy T/F A, Problem Solving T/F A.
Content: Crystal structures (4 hours): Translational symmetry; lattices and basis, Miller indices. Diffraction of waves in crystalline structures; Bragg law, the reciprocal lattice and Brillouin zones. X-ray and neutron diffraction studies of crystal structures.
Free electron theory of solids (4 hours): The classical free electron theory and its failures. The quantum free electron theory (electrons as waves). The basic properties of metals; density of states and the Fermi sphere. The Hall effect.
Electronic structure of solids (5 hours): The effect of crystalline periodicity. Energy band diagrams and effective masses. The distinction between metals, semiconductors and insulators. Electrons and holes. Basic properties of semiconductors; the effects of doping, donors and acceptors.
Magnetism (3 hours): Permeability and magnetic susceptibility. The origin of magnetic moments in solids. Classical models of diamagnetism and paramagnetism. Ferromagnetism and the exchange interaction. Ferromagnetic M-H loops. Paul paramagnetism; and itinerant electron ferromagnetism in metals.
Lattice dynamics (4 hours): Optical and acoustic vibrations. Phonons. Classical and quantum theories of heat capacity.
|