Module Specifications..
Current Academic Year 2023 - 2024
Please note that this information is subject to change.
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Repeat examination Array |
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Description To introduce the student to the structure of crystalline solids and diffraction techniques for structure determination. To provide an understanding of bonding in solids. To provide a basic grounding in thermal, electrical and electronic (including bandstructure), magnetic and superconducting properties of solids. In the case of thermal, electrical and electronic properties the module will explore both classical physics and quantum mechanical approaches and compare the two in terms of agreement with experimental results. | |||||||||||||||||||||||||||||||||||||||
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Learning Outcomes 1. The student will be able to explain the concepts of unit cell, basis, lattice and crystal structure. 2. The student will be able to describe the different types of bonding in solids. 3. The student will be able to discuss experimental methods to determine crystal structure. 4. The student will be able to describe and explain the Drude and Free Electron models of conduction in solids. 5. The student will be able to describe and explain the basic thermal, electrical and electronic (including bandstructure), magnetic and superconducting properties of solids and will be able to describe and explain the limitations of the classical approach to the thermal, electrical and electronic properties and the improvements which a quantum mechanical approach yields in terms of agreement with experiments. 6. Apply physical principles to solve numerical problems based on the physical properties of solids. | |||||||||||||||||||||||||||||||||||||||
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml |
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Indicative Content and Learning Activities
STRUCTURE OF CRYSTALLINE SOLIDS:Discussion of crystal structures, including unit cell, basis, lattice (and Bravais lattices) and overall crystal structure. Examples such as SC, FCC, BCC and HCP are presented and discussed, including issues such as packing fraction etc. Miller indices. X-ray diffraction techniques and their application to crystal structure determination. Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class.CHEMICAL BONDING IN SOLIDS:Discussion of the main types of binding in solids, including ionic (including the concept of the Madelung constant), covalent (including molecular orbitals, bonding and anti-bonding states and a brief introduction to hybridisation) and metallic bonding. The topics of hydrogen and van der Waals bonding will also be covered. Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class.ELECTRONIC PROPERTIES OF METALS, CLASSICAL APPROACH:Discussion of classical Drude model, electrical conductivity, thermal conductivity due to electrons, collision time and mean free path of electrons, classical thermal and drift velocities, Hall effect. Further discussion of Wiedemann-Franz law and Lorenz constant and the other deficiencies of the classical Drude approach (including positive Hall coefficients, absence of electron scattering from individual atom/ion cores as key determinant of mean free path close to interatomic spacing etc.) Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class.THERMAL PROPERTIES OF SOLIDS:Discussion of the general concepts of thermal expansion, specific heat capacity and thermal conductivity and how these can be understood on the basis of vibrations of atoms/ions in the lattice and the asymmetry of the potential energy curve governing vibrations. Discussion of classical theory of specific heat (Dulong-Petit) and the failures of this model for both lattice and electrical contributions to specific heat and thermal conductivity. Introduction and discussion of Einstein and Debye models and the associated quantum mechanical concept of phonons for specific heat capacity and comparison with experimental data. Discussion of lattice thermal conductivity and derivation of standard relation and introduction of concept of mean free path and collision time of phonons and temperature variation of lattice thermal conductivity. Normal and Umklapp processes are NOT covered. Introduction to electronic contribution to thermal conductivity of metals. Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class.ELECTRONIC PROPERTIES OF METALS, QUANTUM APPROACH:Discussion of the origin of energy bands based on a tight binding model. Introduction of Bloch theorem and Bloch functions in periodic potentials and associated k-vector. Introduction of Wilson classification of solids according to band theory. Discussion of Free Electron Model and application of simple quantum mechanics (particle in a box) and Fermi-Dirac statistics to solids. Discussion of Fermi level, Fermi temperature, Fermi velocity and Fermi wavevector and comparison with Drude model thermal velocity etc. Introduction of concept of density of states. Discussion of electron contribution to specific heat capacity in quantum model, and derivation of dependence on temperature, plus comparison with Drude model and experiments. Discussion of electrical conductivity in free electron model, and the mean free path in context of Fermi velocity, and link to Bloch theorem and scattering from defects/phonons. Revisiting electron contribution to thermal conductivity and Wiedemann-Franz Law in light of Free Electron model and comparison with experiment. Revisiting Hall effect and positive Hall coefficients, discussion of effective mass and negative effective mass at top of bands, holes and consequences for Hall effect. Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class.MAGNETIC PROPERTIES OF SOLIDS:Discussion of atomic origin of magnetism based on a simple Bohr-model approach. Introduction of quantum theory and L, S, mL, mS, J and mJ dipole moments and Hund’s rules and Lande g-factor for multi-electron atoms. Definitions of magnetic quantities such as susceptibility, relative permeability etc. and the classification of magnetic materials responses based on these quantities. Discussion of diamagnetism and Larmor model, and mention of magnetic levitation. Discussion of paramagnetism and Pauli and Curie models (including derivation of susceptibilities in both cases) for metals and fixed ion systems, respectively. Discussion of magnetic ordering, ferromagnetism, ferrimagnetism etc. Introduction and motivation of concept of exchange interaction and Weiss molecular field, derivation of Curie-Weiss Law. Discussion of ferromagnetic behaviour, including magnetic domains, hysteresis, soft and hard magnets etc. Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class.INTRODUCTION TO SUPERCONDUCTIVITY (Time permitting):Discussion of discovery of zero resistivity during low temperature conductivity studies by Kammerlingh Onnes. Discussion of the effect of temperature and magnetic field on superconducting states and the concepts of critical temperature, field and current density. Introduction of supercurrent persistence time. Introduction of the Meissner Effect and brief discussion of difference between a perfect conductor and a superconductor. Discussion of the isotope effect and Type I and Type II superconductors phenomenologically. Brief introduction to BCS Theory and Cooper Pairs, connection to isotope effect and the concept of the superconducting band gap. Brief mention of high temperature superconductivity (the coverage of this section will be dependent on time available). Tutorials will be provided on the topics above involving simple numerical problems. Indicative solutions will be provided online following the tutorial class. | |||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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Other Resources None | |||||||||||||||||||||||||||||||||||||||
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| Date of Last Revision | 03-JUN-11 | ||||||||||||||||||||||||||||||||||||||
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