|| PH33510 |
|| CRYSTALLINE SOLID STATE PHYSICS |
|| 2003/2004 |
|| Dr Rudolf Winter |
|| Semester 1 |
|| Professor Geraint Vaughan |
|| PH21510 , PH22010 , PH23010 |
| Course delivery
|| Lecture || 20 lectures |
|| Seminars / Tutorials || 2 workshops |
|Assessment Type||Assessment Length/Details||Proportion|
|Semester Exam||3 Hours End of semester examinations ||80%|
|Semester Assessment|| Course Work: Assessed homework Deadline (by week of Semester): Week 6||10%|
|Semester Assessment|| Course Work: Assessed homework Deadline (by week of Semester): Week 11||10%|
After taking this module students should be able to:
describe the experimental basics of crystal structure determination
understand the concept of translational invariance and point symmetry of crystals
determine the reciprocal lattice from the real space lattice for cubic structures and appreciate the importance of unit cells in each case
understand the origins of atomic vibrations and thermal properties
distinguish acoustic from optical modes at edges of the Brilllouin zone
understand electronic energy bands and the relevance of the Fermi level for distinguishing metals from insulators and of the Fermi surface in describing the electrical and optical properties of metals
describe the different types of magnetism and the role of the exchange interaction in distinguishing these
understand the basis and application of the spin resonance techniques ESR and NMR
appreciate the critical temperature and magnetic field constraints of superconductivity and the notion of flux quantisation and quantum interference
describe the essential differences between Low Tc and High Tc superconductors
The physics of crystalline materials has had a major impact on present day society. Semiconductors, metals and magnetic materials have all found particular use in microcomputers, displays and telecommunications. This module on crystalline solid state physics falls into three main sections. The fist lays the ground work and introduces the main concepts used in crystallography viz. atomic structure, reciprocal space, translational invariance and scattering. The second deals with the vibrational and electronic structure and the way these relate to the atomic structure and form the basis for our understanding of thermal, electrical and optical properties of crystalline materials. The third part extends these ideas further to include the properties of metals, magnetic materials and superconductors.
PROBING THE STRUCTURE OF CRYSTALLINE SOLIDS
Bragg's Law and Wavenumber. Laue, Single Crystal and Powder Diffraction. Pros and cons of X-rays, neutrinos and electrons as probes of periodic structures.
3 DIMENSIONAL GEOMETRY OF CRYSTALS
Crystal lattice, Unit Cell, Translational Invariance and Basis. Reciprocal Space. Scattering of a Plane Wave by a crystalline solid, Laue Conditions and Bragg's Law. Miller Indices, Crystal Planes and Stereograms. Bravais lattices and common cubic structures. Wigner-Seitz Cells and Brillouin Zones for cubic structures. Structure Factor, Atomic Form Factor and Crystallography.
VIBRATIONAL PROPERTIES OF SOLIDS
Atomic Vibrations, Phonons, Bose-Einstein statistics. Experimental probes - inelastic neutron and light Scattering. Dispersion Relations for a monatomic lattice. Phonon Modes within the Brillouin Zone. Diatomic lattice, optic and acoustic modes, Raman and Brillouin Scattering. Vibrational Density of States and Debye Model versus spectra for cubic structures.
ELECTRONIC BAND THEORY
Free electron gas, Electronic Density of States, Fermi-Dirac statistics and transport in simple cubic metals. Nearly Free Electron Model, Band Structure, Metals and Insulators. Fermi Surface of cubic metals and its measurement (De Haas-van Alphen Effect). Optical and Electrical properties of Metals.
Magnetisation, susceptibility and diamagnetism. Permanent electronic dipoles, paramagnetism and electron paramagnetic resonance (EPR). Ideal magnetic gas and Curie-Weiss Law. Exchange interaction, ferromagnetism and antiferromagnetism. Nuclear dipoles and Nuclear Magnetic Resonance (NMR).
Tc and Bc and the Meissner Effect. Type I and Type II superconductors. London Equation. Phonon exchange, Cooper pairs and superconductivity energy gaps. Flux quantisation and Josephson Effect, quantum interference and SQUIDS. Metal oxide High Tc superconductors.
** Recommended Text
HP Myers Introductory Solid State Physics
Taylor & Francis
** Supplementary Text
SR Elliott The Physics and Chemistry of Solids
This module is at CQFW Level 6