Aims:
To provide an introduction to the physics of condensed matter and, in particular, to the structure of crystalline, quasi-crystalline and amorphous materials, and to the thermal, electronic and magnetic properties of solids. |
Assessable learning outcomes:
After the unit, each student should be able to:
Define the interatomic potential and explain how the various types of bonding arise. Explain the difference between a metal, insulator and semiconductor in terms of simple band theory. Describe the various defects present for elements with Van der Waals and metallic bonding and for simple ionic materials. Explain the origin of Dulong and Petit's law and derive an expression for the specific heat according to the Einstein model. Derive the dispersion relationships and density of vibrational states for monotomic and diatomic linear lattices. Discuss the Debye model for specific heat. Describe the origin of thermal expansion. Derive an expression for the energy levels for electrons in a metal, according to the free electron theory, and for the resulting electronic heat capacity. Define the terms Fermi energy, sphere, surface and wavevector. Outline how the nearly free electron theory leads to energy gaps and bands. Explain how band theory can account for the electrical conductivity of the elements in groups I - IV. Describe the conduction and optical absorption processes for intrinsic semiconductors. Explain what is meant by direct and indirect band gap semiconductors. Discuss the origin of localised and weakly bound excitons and account for their optical spectra. Discuss the origin of extrinsic semiconduction and the location of the resulting Fermi level. Explain what is meant by the Peltier coefficient and thermoelectric power. Derive a classical expression for diamagnetic susceptibility. Explain the quantum theory of paramagnetism and derive an expression for the paramagnetic susceptibility for a two-level system. Describe the various forms of magnetic ordering found in crystalline and amorphous solids. Explain the origin of the domain structure of a ferromagnet. |
Outline content:
An introduction is given to the structure and properties of modern materials (condensed matter), which includes the following topics: Introduction: Basic definitions; the states of matter; polymorphism; brief survey of the properties of metals, semiconductors and insulators; effect of impurities. Cohesion and Bonding: Electronic configurations of atoms and the periodic table; types of bonding; interatomic potentials; 8-N rule; relationship between bonding and properties; electron bands and conduction in metals, semiconductors and insulatiors. Qualitative discussion of crystal structure and Brillouin Zones Van der Waals and Metallic Systems: Spherical atom approximation; crystal structures (hcp, fcc, bcc and simple cubic); number of atoms in the unit cell; co-ordination number; packing density; point, line and interfacial defects and their effect on properties; alloys. Thermal Properties: Dulong and Petit law; Einstein Model; linear monatomic and diatomic lattices; sound wave limit; phonons; vibrational density of states; Debye model; thermal expansion. Free Electron Model: e-k relationship for a free electron; energy levels in 1, 2 and 3 dimensions; Fermi surface; density of states; occupancy at finite temperatures; electronic heat capacity; soft X-ray emission spectra. Metals, Insulators and Semiconductors: Band structure and conduction; Effective mass; positive holes; optical excitation; intrinsic semiconductors; direct and indirect band gaps; localised and delocalised excitons; Raman scattering; impurity levels and extrinsic conduction; variation of Fermi level with temperature. Thermal Conductivity: Peltier coefficient; thermoelectric power; thermal conductivity; phonon flow; geometrical scattering and 3-phonon processes; normal and umklapp processes; conduction at high and low temperatures. Magnetic Materials: Magnetic susceptibility; types of magnetism (brief survey of diamagnetism, paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism), Curie and N?el temperatures; typical susceptibility values. |