3/PH/LH
CONDENSED MATTER 2
Aim
The aim of this unit is to provide an introduction to the electronic and magnetic properties of
solids.
Summary
The course includes the following topics:
Introduction: Brief summary of important concepts from Condensed Matter 1.
Free Electron Model: -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.
Nearly Free Electron Model: Energy bands in 1, 2 and 3 dimensions; energy gap.
Reciprocal Lattice and Brillouin Zones: Revision of material from Condensed Matter 1;
extended, reduced and repeated zone schemes; elements of groups I-IV; reduced and repeated
Brillouin zones in 2 and 3 dimensions; bcc and fcc lattices.
Electronic Conduction in Metals: Effect on Fermi sphere; impurity and phonon scattering;
normal and Umklapp processes; electron mobility; Hall effect.
Insulators and Semiconductors: 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;
(amorphous semiconductors; hydrogenated amorphous silicon).
Thermal Effects: Peltier coefficient; thermoelectric power; thermal conductivity; phonon flow;
geometrical scattering and 3-phonon processes; normal and Umklapp processes; conduction at
high and low temperatures.
Reciprocal Lattice Revisited: Comparison of use of reciprocal lattice and Brillouin zones to
describe various scattering processes; elastic and inelastic scattering; scattering of X-rays,
neutrons, electrons photons and phonons.
Magnetic Materials: Magnetic susceptibility; types of magnetism (brief survey of diamagnetism,
paramagnetism, ferromagnetism, antiferromagnetism, ferrimagnetism), Curie and Nel
temperatures; typical susceptibility values.
Diamagnetic and Paramagnetic Materials: Classical theory of diamagnetism; Larmor
precession; diamagnetic susceptibility; origin of permanent magnetic moments (brief summary
of material required from atomic and molecular physics courses); quantum theory of
paramagnetism; paramagnetic susceptibility; Curie law; Brillouin function.
Ferromagnetism, Antiferromagnetism and Ferrimagnetism: Origin of exchange field; mean
field approximation; magnetic susceptibility of ferromagnetic material above Curie
temperature; Curie-Weiss law; exchange integral; antiferromagnetic sublattices; paramagnetic
susceptibility of antiferromagnetic material above Néel temperature; (revision of neutron
diffraction by magnetic materials; helimagnetism; magnons; inelastic magnetic neutron
scattering; domains and hysteresis; amorphous magnetism).
Neutron Diffraction/Scattering: Nuclear reactor source; neutron energy and wavelength;
neutron scattering amplitude; location of light atoms; atoms of neighbouring atomic number;
magnetic scattering.
Intended learning outcomes
On completion of this unit each student should be able to:
 Derive an expression for the energy levels for electrons in a metal, according to the freeelectron theory, and for the resulting electronic heat capacity;
 Define the terms Fermi energy, sphere, surface and wave-vector;
 Describe the origin of the electrical conductivity for a metal in terms of the displacement of
the Fermi sphere and show that this leads to Ohm’s law;
 Describe the origin of the Hall effect and derive an expression for the Hall cofficient;
 Outline how the nearly-free-electron theory leads to energy gaps and bands;
 Define the Brillouin zone and describe the extended, reduced and repeated zone schemes;
 Explain how band theory can account for the electrical conductivity of the elements in
groups I-IV;
 Explain the role of normal and umklapp processes in determining the electrical conductivity
of metals;
 Derive the first Brillouin zones for simple, face-centred and body-centred cubic metals;
 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 localized and weakly bound excitons and account for their optical
spectra;
 Discuss the origin of extrinsic semiconduction and the location of the resulting Fermi
energy;
 Explain what is meant by the Peltier coefficient and thermoelectric power;
 Describe the origin of thermal conductivity, explaining the role of normal and umklapp
processes;
 Derive a classical expression for diamagnetic susceptibility;
 Explain the quantum theory of paramagnetism and derive an expression for the
paramagnetic susceptibility of a two-level system;
 Describe the various forms of magnetic ordering found in crystalline and amorphous solids
and derive an expression for the paramagnetic susceptibility of ferromagnetic and anti
ferromagnetic materials above the Curie/Néel temperature;
 Describe the use of neutron scattering techniques to investigate magnetic materials;
 Explain what is meant by a magnon;
 Explain the origin of the domain structure of a ferromagnet
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Unit Code:
Department:s:
Pre-requisites:
Excluded Units:
Required for:
Convener:
Lecturer:
3/PH/LH
Physics
3/PH/AK
None
Modules:
PH814
Co-requisites:
None
Prof A C Wright
Prof A C Wright
Teaching and learning methods
Lectures, workshops, directed reading and problem solving.
Contact hours:
Lectures
20
Workshops
10
Assessment
Examinations:
Formal University Examination (1½ hour, June)
Continuous assessment:
Assessed workshop problems
End-of-Term Test
Weight
60%
20%
20%
Requirement for pass: An average of at least 40%
Re-assessment:
1½-hour formal examination in June (following the conclusion of the
degree course)
13 March 2001
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