Week 1: Crystal structure (I)
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?
Week 2: Crystal structure (II)
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.
Week 3: Bonds and cohesion
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.
Week 4: Diffraction from crystals (I)
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.
Week 5: Diffraction from crystals (II)
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.
Week 6: Magnetism
Magnetic materials have played important technological roles for millennia. This week, we extend our study of structure to consider magnetic structure, the arrangement of magnetic dipole moments within a material: how this can be determined using diffraction methods, and how it responds to an external magnetic field.
Week 8: Lattice vibrations
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.
Week 9: Lattice vibrations and thermal properties
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.
Week 10 (Not examinable 2018): The free electron model
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.
Week 11 (Not examinable 2018): Electronic band structure (I)
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.
Week 12 (Not examinable 2018): Electronic band structure (II)
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.