## SPA5228 - Condensed Matter A - 2016/17

Year: 2 | Semester: B | Level: 5 | Units: 1 | Credits: 15

Prerequisites: None

Lectures: 44 hours | Lectures Mon 9 (Fogg), Tue 9 and 12 (GOJ), Thu 11 (Fogg)

Problems classes: 12 | Fridays for one hour at 9 am, 10 am, 11 am or 12 noon, as allocated

Exam: 2.5 hours

Module organiser: Dr Anthony Phillips

Office hours: Tuesdays and Thursdays, 10-11, in room 215, or by appointment

Deputy module organiser: Dr Andrei Sapelkin

Demonstrators: Mr James Kneller and Ms Ying Liu

Markers: Mr Xiaoming Zhao, Mr Hongfei Li, and Ms Ying Liu

Online quizzes: 11 | run for each teaching week from and until Monday 9 a.m. but can be taken as many times as you like during the week. 0.5% each = 5.5%.

Homework: 9 | handed out every teaching Thursday except weeks 6 and 12, due the following Thursday at 4 p.m. in the boxes in Reception on level 1. Total = 7.5%.

Review tests: 4 | will be held in the second half of the lecture slots on Thursdays 26 January, 16 February, 9 March, and 30 March. In each case the format will be 3 part A-style questions based closely on the sample questions for the preceding weeks. 3% each = 12%.

(Coursework is 20% of the module mark but, as shown above, the available marks add up to 25%; the extra 5% are "buffer marks" so that the odd slip doesn't damage your module mark.)

Revision lecture: Friday, 28 April 2017, 2–4 p.m., GO Jones Lecture Theatre

Final exam: worth 80% of the module mark. Friday 19 May, 2:30-5:00 p.m.

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• 1
• 2

We begin the module by looking at the structures of some common crystals. What does it mean to say that a material is crystalline, what are the consequences for material properties – and why do materials form crystals in the first place?

• 3

This week we continue to look at common crystal structures, looking at some slightly more complex materials and their functions. We also consider the role of symmetry in constraining the possible lattices, and show that taking this into account there are only 14 possible lattice types in three dimensions.

• 4

So far we have discussed the ways in which atoms pack together to form materials without worrying about the forces between the atoms. This week we consider these interactions in more detail. Although ultimately, they all originate from the electromagnetic force, they can be divided into five types that behave quite differently – and cause materials to do likewise.

• 5

We have spent a lot of time so far worrying about the structures of materials, but haven’t yet said much about how we know what structure a particular material has! This week we show that crystals diffract radiation – for instance, X-rays, neutrons, or electrons – in a way that depends on their structure. To understand this we will need to use some mathematical formalisms, including the Fourier transform, the operation of convolution, and the Dirac delta function.

• 6

We continue our study of the way in which experimentally observed diffraction data can be used to determine crystal structures. We also consider how the beams of X-rays or neutrons we need for such experiments can themselves be produced.

• 7

Despite the importance of crystals to materials physics, not all materials are crystalline. This week we consider the structures of amorphous materials, and the statistical techniques we use to describe them.

• 9

So far we have assumed that the atoms in a crystal are permanently fixed in position. In fact, of course, they have thermal energy and will vibrate about their average positions. This week we begin by investigating the nature of these vibrations in one dimension; next week we will move on to consider real three-dimensional crystals.

• 10

We continue from last week’s discussion of phonons in 1D to consider real three-dimensional materials. We will also consider the effect of lattice vibrations on materials’ thermal properties, such as specific heat and conductivity.

• 11

So far we have focused on the movement of atoms. But in metals, the electrons themselves can move and are responsible for many characteristic properties. So this week we approach the topic from a different direction, by throwing away the nuclei and considering only the electrons! This simple model turns out to give rather accurate predictions, and we will discover why.

• 12

This week we apply last week’s theory to some real materials. We reintroduce the atomic nuclei and find that they make a small, but very significant difference to our model.

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We conclude the module by considering three types of material with very different electronic properties: metals, insulators, and semiconductors. We show that the simple models we have studied are able to explain these properties rather well.