PHYS2531 Thermal and Condensed Matter Physics (2010/11)
Content
Crystals, Vibrations and X-rays
13 lectures + 4 examples classes in Michaelmas Term
Syllabus: Crystallography and diffraction: Lattices, 7 crystal systems, the 14 Bravais lattices, point groups, space groups, Miller indices. X-ray generation, characteristic spectra, absorption laws. Neutron generation. Scattering from point sources and periodic lattices. Elastic and inelastic scattering, atomic scattering factor and its angular dependence. Bragg's law, Laué equations. Amplitude-phase description of scattering from a unit cell. Systematic absences. Intensities of diffracted rays. Powder diffractometry, single crystal diffractometry, neutron methods. Vibrations in solids. Failure of the static latice model to account for all solid state physics phenomena. Waves on a 1-D elastic string and in rows of atoms. Dispersion relations for monatomic and diatomic rows. Group phase velocity. Brillouin zone. Optical and acoustic phonons. Heat capacity in solids . Temperature dependence of heat capacity and some examples. Theories: a) classical thoery, and equipartition. Degrees of freedom. Dulong - Petit heat capacity. b) Einstein theory. Physical assumptions and deviation. c) Debye theory. Density of states. Physical assumptions and derivation. Use of the results to determine temperature dependence of heat capacity.
Textbooks:
The Solid State, H.M. Rosenberg (OUP, 3rd Ed.), B
Elements of X-ray Diffraction, B.D. Cullity (Addison-Wesley, 2nd Ed.), B
Introduction to Solid State Physics, C. Kittel (Wiley, 7th Ed.), B
An Introduction to X-ray Crystallography, M.M. Woolfson (CUP, 2nd Ed.), B
Principles of Solid State Physics, R.A. Levy (Academic Press) B
The Crystal Structure of Solids, P.J. Brown and J.B. Forsyth (Arnold), B
Thermodynamics and Statistical Mechanics
12 lectures + 4 examples classes in Michaelmas and Epiphany Terms
Syllabus: Basic ideas: temperature, zeroth law and equations of state. Definitions and mathematical methods. The first law of thermodynamics. Definitions of heat capacities and applications of the first law. Entropy and the second law of thermodynamics. Cyclic processes: Carnot and other engines. Thermodynamic functions: Maxwell's relations and their applications. Equilibrium and phase transitions. The third law of thermodynamics. Other applications of thermodynamics. Introduction to statistical basis of entropy: the second law of thermodynamics revisited. The background to statistical mechanics: microstates and macrostates. Boltzmann's distribution function. Classical gases. Bose-Einstein and Fermi-Dirac statistics.
Textbooks:
Statistical Mechanics: a survival guide, M. Glazer and J. Wark (OUP), B
Concepts in Thermal Physics, S.J. Blundell and K.M. Blundell (OUP), B
Electrons in Solids
13 lectures + 4 examples classes in Epiphany Term
Syllabus: Introduction and classical Drude Model: Review of resistivity variation, current carriers in solids, postulates of classical free electron theory, electrical and thermal conductivity, Wiedemann-Franz Law, plasma oscillations. Sommerfeld (or Fermi Gas) Model: Postulates of quantum mechanical free electron model, Pauli exclusion principle, Fermi-Dirac distribution, the Fermi level, density of states in one dimension, occupation of energy states, density of states in three dimensions, average energy of Fermi gas and Fermi surface for free electrons. Applications of Fermi gas model: Electronic heat capacity, electrical and thermal conductivity. Breakdown of the free electron model and effect of periodic lattice on nearly-free electrons: positive Hall coefficients, nearly-free electron model and concept of forbidden energy gaps. Applications of band theory: Classification of metals, semiconductors and insulators. The concepts of effective mass and of holes.
Textbooks:
Introduction to Solid State Physics, C. Kittel (Wiley, 8th Ed.), E
Solid State Physics, N.W. Ashcroft and N.D. Mermin (Thomson Learning), R
The Solid State, H.M. Rosenberg (OUP, 3rd Ed.), R
Introduction to the Physics of Electrons in Solids, B.K. Tanner (CUP), B
Revision
3 lectures in Easter Term, one by each lecturer.
Teaching methods
Lectures: 2 one-hour lectures per week
Examples classes: These provide an opportunity to work through and digest the course material by attempting exercises and assignments assisted by direct interaction with the lecturers and demonstrators. Students will be divided into four groups, each of which will attend one one-hour class every two weeks.
Problem exercises: See http://www.dur.ac.uk/physics/students/problems/