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# Statistical & Solid State Physics - PHY00054I

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• Department: Physics
• Module co-ordinator: Dr. Paul Davies
• Credit value: 20 credits
• Credit level: I
• Academic year of delivery: 2023-24
• See module specification for other years: 2024-25

## Module summary

Physics aims to understand the properties of matter at both microscopic and macroscopic scales. This module provides a bridge between these two extremes. Statistical mechanics gives us a framework to understand macroscopic behaviour of systems based on the properties of their constituent particles. Solid state physics is your first application of this idea as you explain bulk material properties such as thermal and electrical conductivity by considering the interaction of individual atoms and electrons.

## Related modules

Pre-requisites:  Thermodynamics and Electromagnetism or Equivalent

Co-requisites: Quantum, Nuclear and Particle Physics or Equivalent.

## Module will run

Occurrence Teaching period
A Semester 2 2023-24

## Module aims

This module explores powerful techniques which link the microscopic world to macroscopic, observable physics of bulk systems.

In Statistical Mechanics we will develop formalisms of equilibrium statistical mechanics from fundamental considerations of the microscopic states available to the system, and relate statistical mechanics to the classical thermodynamic descriptions of heat, work, temperature and entropy. Statistical mechanics will be used to derive formulae for the internal energy, entropy, specific heat, free energy and related properties of classical and quantum-mechanical systems, and to apply these formulae to a variety of realistic examples.

In solid state physics we will build up the theory of solid, crystalline matter using the approaches of statistical mechanics; deriving the macroscopic theory of matter starting from microscopic models and assumptions. We will explore how many key physical behaviours in solids can be reduced to simple quantised wave phenomena, allowing us to explain many of the most familiar properties of solids by starting from basic assumptions.

## Module learning outcomes

• Determine macroscopic properties of materials via statistical models of their constituent particles

• Understand classical and quantum distributions and solve problems utilising them

• Apply statistical methods to explore real systems such as solids

• Describe the microscopic ordering of crystalline materials using the formal language of lattices and structures

• Explain how wave propagation in crystals can lead to an understanding of their structural, thermal and electrical properties

• Apply simple models of electron behaviours in solids which allow the description of insulating, metallic and semiconducting materials

## Module content

Statistical Mechanics

The statistics of thermodynamics: probability theory, microstates (quantum states) and macrostates of a system, degeneracy W, postulates of statistical mechanics, statistical interpretation of entropy and temperature, isolated systems and the microcanonical ensemble.

Non-isolated systems with variable energy: statistical nature of equilibrium, definition of temperature and entropy in the canonical ensemble, Boltzmann distribution, partition function Z and the connection to thermodynamics, examples of non-interacting systems (e.g. vacancies in solids; paramagnet, systems of harmonic oscillators), equipartition theorem, distinguishable and indistinguishable particles.

Ideal gas: Partition function of monatomic gas, density of states, classical gas law, Maxwell-Boltzmann speed distribution, molecular gases (rotation and vibration), thermodynamic properties.

Vibrational heat capacity of solids: Quantisation of phonon modes, labelling of modes using wavevector k; density of states, Einstein and Debye models

Non-isolated systems with variable number of particles: Grand canonical ensemble, chemical potential, Gibbs distribution.

Identical particles: Fermions and bosons, Fermi and Bose distributions, Bose-Einstein condensation, applications to free-electron metals (fermions), Blackbody radiation (Planck Formula).

Solid State

Structure: Lattice and basis, Bravais lattices, unit cells, common structures, directions, planes, defects, the reciprocal lattice

Determination of structure via diffraction: The interaction of waves with a periodic array of scatterers, Bragg’s law, the Laue condition, structure factors, single crystal and powder diffraction

Dynamics: Dispersion relations of 1d monatomic and diatomic chains, the Brillouin zone, phonons, lattice heat capacity, lattice thermal conductivity, the qualitative effects of anharmonicity in the interatomic potential

Electronic Effects: Quantum free electron theory, Fermi energy, Drude-Sommerfeld model of electrical conductivity, electronic heat capacity, electronic thermal conductivity

Band Theory: Qualitative description of the nearly free electron model, bands, insulators, metals, semiconductors, effective mass, holes, the Hall effect, intrinsic and extrinsic semiconductors, carrier concentrations

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Statistical & Solid State Physics
3 hours 80
Essay/coursework
Physics Practice Questions
N/A 20

Other

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Statistical & Solid State Physics
3 hours 80

## Module feedback

'Feedback’ at a university level can be understood as any part of the learning process which is designed to guide your progress through your degree programme. We aim to help you reflect on your own learning and help you feel more clear about your progress through clarifying what is expected of you in both formative and summative assessments.

A comprehensive guide to feedback and to forms of feedback is available in the Guide to Assessment Standards, Marking and Feedback. This can be found at:

https://www.york.ac.uk/students/studying/assessment-and-examination/guide-to-assessment/

The School of Physics, Engineering & Technology aims to provide some form of feedback on all formative and summative assessments that are carried out during the degree programme. In general, feedback on any written work/assignments undertaken will be sufficient so as to indicate the nature of the changes needed in order to improve the work. Students are provided with their examination results within 25 working days of the end of any given examination period. The School will also endeavour to return all coursework feedback within 25 working days of the submission deadline. The School would normally expect to adhere to the times given, however, it is possible that exceptional circumstances may delay feedback. The School will endeavour to keep such delays to a minimum. Please note that any marks released are subject to ratification by the Board of Examiners and Senate. Meetings at the start/end of each semester provide you with an opportunity to discuss and reflect with your supervisor on your overall performance to date.

Our policy on how you receive feedback for formative and summative purposes is contained in our Physics at York Taught Student Handbook

Solid State

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

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

Statistical Mechanics

Glazer M and Wark J: Statistical Mechanics: A Survival Guide (Oxford University Press)***

Bowley R and Sánchez M: Introductory statistical mechanics (Oxford University Press)***

Blundell SJ and KM: Concepts in Thermal Physics (Oxford University Press)**

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.