Department: PhysicsCredit value: 10 creditsCredit level: IAcademic year of delivery: 2022-23

## Pre-requisite modules

## Co-requisite modules

## Prohibited combinations

Occurrence | Teaching period |
---|---|

A | Spring Term 2022-23 |

This model will introduce a key concepts required in order to understand the properties of crystalline solids. The main aims are -

- the understanding of the structure of crystalline solids, including how it is experimentally determined, and that real materials exhibit departures from ideal crystallinity
- the role of lattice vibrations and phonons in the electrical and thermal properties of materials
- the development and detailed description of classical free electron theory to describe the electrical and thermal behaviour of metals

On completion of this course the student will be able to -

- Describe the structure of crystalline materials in terms of lattice and basis, and describe structural elements such as directions and planes using standard notations
- Understand the origins, nature and consequences of defects within otherwise ideal materials
- Understand the concept of reciprocal space and its role in describing and quantifying wave phenomena in solids
- Derive the conditions for x-rays to diffract from solids, including the concept of the structure factor
- Derive dispersion relations for vibrations in solids, and describe their interpretation in terms of both normal modes and phonons
- Understand how density of states and occupation can be used to calculate macroscopic properties of solids
- Describe the origins of the classical (Dulong-Petit) law of heat capacity, and discuss its failure at low temperature
- Understand the role of quantisation in describing low temperature lattice heat capacities, and discuss the Einstein and Debye models of heat capacity
- Explain the origins of thermal conductivity and thermal expansion of the lattice
- Derive results for electrical conduction, thermal conduction and heat capacity of a classical free electron gas, and describe its relevance to metallic systems
- Explain how application on quantum theory can resolve shortcomings in the classical model of free electron gasses
- Describe the successes and failures of a classical approach to free electron theory, including the positive sign of the Hall coefficient in some metals

- The concepts of point and translational symmetry
- The definition of crystal structures in terms of lattice and basis
- The use of Miller indices to index crystal planes in structures.
- The use of Miller indices to indicate direction and inter-planar spacing in a cubic crystals and derivation of expressions to do so.
- The Miller-Bravais system for indexing of hexagonal systems.
- Point Defects (vacancies, interstitials and impurities). Dislocations and Burgers vector. Stacking and planar defects (stacking faults and twins)
- The reciprocal lattice and Brillouin Zones, including the Wigner-Seitz construction. Extended, repeated and reduced zone schemes.
- Derivation of von Laue's approach for X-ray diffraction by crystals.
- Derivation and use of Bragg’s Law and the Ewald sphere.
- The structure factor and its relation to the reciprocal lattice.
- Use of the structure factor to determine crystal structure in a diffraction experiment.
- Lattice vibrations: the mathematical description of a vibrational wave for planes of atoms containing 1 or 2 atoms per unit cell and the derivation of the dispersion relation between and k, optical and longitudinal modes of vibration
- The concept of density of states and occupation. Their use in determining total and mean energies of a system.
- The breakdown of the classical Dulong-Petit Law for the specific heat capacity of a solid and introduction to the ideas of the Debye and Einstein models including the Debye temperature.
- Thermal conduction and expansion in a solid including the phonon contribution to the mean free path.
- Classical free electron theory (The Drude model) for the electrical and thermal properties of metals, and its limitations.
- Derivation of classical expressions for electrical conductivity, thermal conductivity, the electronic contribution to specific heat capacity, mean free path and the Wiedemann-Franz Law.
- Matthiessen’s Rule for the resistivity of metals.
- Hall effect and the sign of the Hall coefficient.
- Lattice vibrations: the mathematical description of a vibrational wave for planes of atoms containing 1 or 2 atoms per unit cell and the derivation of the dispersion relation between and k, optical and longitudinal modes of vibration
- The concept of density of states and occupation. Their use in determining total and mean energies of a system.
- The breakdown of the classical Dulong-Petit Law for the specific heat capacity of a solid and introduction to the ideas of the Debye and Einstein models including the Debye temperature.
- Thermal conduction and expansion in a solid including the phonon contribution to the mean free path.
- Classical free electron theory (The Drude model) for the electrical and thermal properties of metals, and its limitations.
- Derivation of classical expressions for electrical conductivity, thermal conductivity, the electronic contribution to specific heat capacity, mean free path and the Wiedemann-Franz Law.
- Matthiessen’s Rule for the resistivity of metals.
- The concept of a quantum electron gas and its application to metals
- Hall effect and the sign of the Hall coefficient.

Note - In addition to co-requisites above, students should also take either PHY00036I or PHY00091I

Task | % of module mark |
---|---|

Closed/in-person Exam (Centrally scheduled) |
80 |

Essay/coursework |
20 |

None

Task | % of module mark |
---|---|

Closed/in-person Exam (Centrally scheduled) |
100 |

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Hook JR and Hall HE; Solid State Physics (Wiley)***

Kittel C; Introduction to solid state physics (Wiley) ***