PH3702: Condensed Matter

Module Provider:

Physics

Number of credits:

10 [5 ECTS credits]

Level:

H (Honours)

Terms in which taught:

Autumn

Module Convenor:

Prof AC Wright

Pre-requisites:

Co-requisites:

Modules excluded:

Current from:

2005/6

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.

  • Additional outcomes:

    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.

    Brief description of teaching and learning methods:
    Typically two lectures will be given each week, followed by a workshop session.

    Contact hours:

      Autumn Spring Summer
    Lectures 20    
    Tutorials/seminars      
    Practicals 10    
    Other contact (eg study visits)      
           
    Total hours 30    
           
    Number of essays or assignments      
    Other (eg major seminar paper)      

    Assessment:
    Coursework
    Assessed workshop problems
    Relative percentage of coursework: 20%
    Examinations
    Formal University Examination:
    80%
    Requirements for a pass
    An average of at least 40%
    Reassessment arrangements
    1?-hour formal examination in June (following the conclusion of the degree course)

    Last updated: 23/Mar/2005

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