## Pre-requisite modules

## Co-requisite modules

## Prohibited combinations

Occurrence | Teaching cycle |
---|---|

A | Spring Term 2020-21 |

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 | Length | % of module mark |
---|---|---|

Essay/courseworkPhysics Practice Questions |
N/A | 14 |

University - closed examinationSolid State Physics I |
1.5 hours | 86 |

None

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

University - closed examinationSolid State Physics I |
1.5 hours | 86 |

Physics Practice Questions (PPQs) - You will receive the marked scripts in problem classes or via your pigeon holes. Feedback solutions will be provided on the VLE or by other equivalent means from your lecturer. As feedback solutions are provided, normally detailed comments will not be written on your returned work, although markers will indicate where you have lost marks or made mistakes. You should use your returned scripts in conjunction with the feedback solutions.

Exams - You will receive the marks for the individual exams from eVision. Detailed model answers will be provided on the intranet. You should discuss your performance with your supervisor.

Advice on academic progress - Individual meetings with supervisor will take place where you can discuss your academic progress in detail.

Online VLE tests throughout module will provide feedback on understanding and progress

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

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