# Structure and Properties of Functional Materials

- Introduction
- Aims and Outcomes
- Important Dates
- Course Notes
- Homework and Exercise Sheets
- Assessment
- Recommended Reading
- Online Resources
- FAQ

**News flash**: solutions to the mid-term exam and solutions to Homework Set Omega are now available.

**Structure and Properties of Functional Materials** is a second-year module that is currently running for the first time in semester B, 2012–13. Continuing from Condensed Matter in first year, it will introduce more advanced concepts in condensed matter physics. We will discuss crystalline symmetry and show how it can be described in reciprocal space. This powerful mathematical formalism is the key to understanding properties of crystals ranging from the characteristic diffraction of X-ray, neutron or electron beams to the behaviour of electrons in the material and its vibrational modes, and we will examine each of these properties in turn. We will complete our survey of important material properties by discussing common magnetic behaviour in solids. This module will also include a field trip to the Rutherford Appleton Laboratory to see the experimental facilities used for the techniques discussed in class, including the Diamond synchrotron and the ISIS neutron source.

In 2012–13 the module organiser is Dr Anthony Phillips and the deputy module organiser Prof. David Dunstan.

## Module aims

This module will enable students to describe the atomic, electronic, and magnetic structure of materials, using real- and reciprocal-space descriptions as appropriate and understanding the links between the two. On the basis of these descriptions, students will be able to predict the properties of simple materials.

## Module outcomes

Students who successfully complete this course should be able to answer qualitative and quantitative questions on the topics identified in the module synopsis, displaying clarity in both mathematical and verbal exposition. In particular, they should be able to: classify the symmetry of simple structures; identify symmetries of a crystal structure from its diffraction pattern and vice versa; use the reciprocal space formalism to describe diffraction, phonons, and electronic structure; describe the experimental techniques of X-ray, neutron, and electron diffraction and inelastic neutron scattering and their applications; use appropriate models to explain the properties of and differences between insulators, metals, and semiconductors; derive and interpret phonon dispersion curves for simple systems; and use simple models to explain magnetic effects such as hysteresis in ferromagnets.

## Weekly timetable

**Lectures**: Mondays at 9 in Laws 1.12; Tuesdays at 11 in Laws 1.12; Wednesdays at 11 in Geography 2.20. (Note: no lectures on Thursdays despite the official timetable!)

**Problems classes**: Fridays at 10 in Francis Bancroft 1.08 with Asmi Barot. (Note: no classes at 11 despite the official timetable!)

**Office hours**: Mondays at 2 to 3 and Thursdays at 3 to 4 *(note change of time)* in GO Jones 3.10, or by appointment.

## Outline of topics

The following timetable is subject to change during the semester, but is provided as a general guide to the module:

7–28 January | Atomic structure (10 lectures) |

29 January – 12 February | Atomic motion (7 lectures) |

13 February |
Mid-term exam |

21 February (note change of date) |
Field trip to Rutherford Appleton Laboratory – please sign up here |

25 February – 12 March | Electronic structure (8 lectures) |

13–27 March | Magnetic structure (7 lectures) |

## Course notes

Course notes will be released online shortly after each lecture.

## Homework

- Set 1 (due Wednesday 16 January); solutions
- Set 2 (due Wednesday 23 January); solutions
- Set 3 (due Wednesday 30 January); solutions
- Set 4 (due Wednesday 6 February); solutions
**No homework due Wednesday 13 February due to midterm**- Set 5 (due Wednesday 6 March); solutions
- Set 6 (due Wednesday 13 March); solutions
- Set 7 (due Wednesday 20 March); solutions
- Set 8 (due Wednesday 27 March); solutions
- Set Omega (optional); solutions

## Exercise classes

- Week 1 (Friday 11 January); solutions
- Week 2 (Friday 18 January); solutions
- Week 3 (Friday 25 January); solutions
- Week 4 (Friday 1 February); solutions
- Week 5 (Friday 8 February); solutions
**No exercise classes weeks 6 (due to midterm) or 7 (reading week)**- Week 8 (Friday 1 March); solutions
- Week 9 (Friday 8 March); solutions
- Week 10 (Friday 15 March); solutions
- Week 11 (Friday 22 March); solutions

## Assessment

8 weekly homework sheets @ 1.875% each (not 10 of these!) |
15% |

Mid-term exam (45 minutes) | 5% |

Final exam (150 minutes) | 80% |

## Online resources

The following websites may be useful as supplementary study materials; this list will be augmented as we go through the module.

### General

- The Condensed Matter section of Georgia State University's "Hyperphysics" pages contains useful information about many topics covered in this module.

### Atomic structure

- Kevin Cowtan's Picture Book of Fourier Transforms
- Andrew Goodwin's notes from Cambridge IB Mineral Science
- Nicolas Schoeni and Gervais Chapuis' Java applet for Fourier transforms
- Liverpool notes on 3D crystallography
- DoITPoMS guide to Miller indices

## Recommended reading

It is not essential to buy any of the recommended reference books for this module, although if you *want* to own books on condensed matter physics these are all excellent choices. On the other hand, consulting a library copy is often a good idea to help clarify tricky concepts from lectures. Full section references will be announced at the beginning of the module: for those who wish to look through the material before we begin, chapter references are provided below.

We now have a recommended reference that covers (almost) all of the module material: David Sidebottom's *Fundamentals of Condensed Matter and Crystalline Physics* (pictured left). This was not announced when this module was first described, as it was only published in July 2012! If you are going to buy any book this is the one; it will also be helpful if you go on to study third-year condensed matter physics modules. In this module we will mainly be looking at chapters 1, 4–6, and 10–13, plus selected topics in chapters 15 and 17.

Also recommended are three specialist books on individual topics that go well beyond the material covered in this module, but will make excellent references if you choose to continue in the field. They are all part of the (highly recommended) *Oxford Master Series in Condensed Matter Physics*:

- Dove,
*Structure and Dynamics*covers the first two quarters of the module, on (oddly enough) atomic structure and dynamics respectively. We will look at sections of chapters 2–4, 6, and 8–10. - Singleton,
*Band Theory and Electronic Properties of Solids*covers the third quarter, on electronic structure. We will look at sections of chapters 2–6. - Blundell,
*Magnetism in Condensed Matter*covers the fourth quarter, on magnetism. We will look at sections of chapters 1, 2, 4, and 5, and if time permits perhaps venture a little into chapter 6.

Finally, a general reference, aimed at a higher level than the other three, is Ibach and Lüth, *Solid State Physics*. I find their explanations clearer than other general texts; however, their coverage is fast and at times mathematically involved, and they assume a good working knowledge of quantum and statistical physics. The material for this module is in chapters 2–4 and 6–8; I hasten to add, though, that these chapters cover more than we could hope to discuss in a single term, so we will be looking only at carefully selected topics.

In short: the best approach for this module's reading will be to use your class notes (and the summary sheets I will provide) as your primary reference, and to consult the recommended books either beforehand in preparation, or when you find yourself confused by a particular topic.

## FAQ

- Why was this module created?
- All of the Condensed Matter modules are currently being revised, to ensure that we offer a complete course in fundamental condensed matter physics and to provide better links to research in the Centre for Condensed Matter and Materials Physics. This is the first of the revised modules to be run.
- What can I do in third year after taking this module?
- Details of the third-year modules to be offered in 2013–14 are still being finalised. However, you can expect an optional module focusing on “real-world” physics, in which some of the assumptions in SPFM—such as considering only defect-free, infinite crystals or isotropic materials—will be relaxed in order to treat more complex but realistic situations. The third-year module will also feature some topics under active research within the School.
- Is the syllabus similar to the old Condensed Matter 2?
- No, the syllabus of this module is entirely new, although some parts are similar to the old third-year Solid State Physics module (which will run for the last time in 2012–13).
- What can I do if I have a question that isn’t answered here?
- Please feel free to contact the module organiser, Dr Anthony Phillips.