General aim:

To show how interatomic forces determine the structure of simple crystalline materials.

To demonstrate that elementary cubic crystal structures may be determined by performing diffraction experiments.

To show qualitatively how non linear behaviour in oscillatory systems may lead to a variety of novel phenomena including chaotic behaviour.

Objectives

1 On completion of this section you should be able to:

• Understand the concept of a crystal structure being composed of a lattice plus a basis of atoms;
• draw the unit cells of the cubic, tetragonal, orthorhombic and hexagonal lattices;
• draw from co ordinate information diagrams giving atomic positions for simple cubic, tetragonal and orthorhombic structures and calculate interatomic distances;
• understand how different types of atomic bonding give rise to particular crystal structures;
• describe the following crystal structures close packed (fcc and hcp), bcc, diamond.

2 On completion of this section you should be able to:

• describe the concept of crystal planes and define the Miller indices for a set of planes;
• determine the separation of the planes for crystals with orthogonal axes.

3 On completion of this section you should be able to:

• describe the experimental arrangements used for X ray diffraction studies of a polycrystalline sample;
• derive the Bragg law for diffraction from lattice planes;
• appreciate that the distribution of scattering angles from a polycrystalline sample gives information about the lattice type;
• derive the lattice parameter from diffraction data for cubic crystals.

4 On completion of this section you should be able to:

• calculate the wavelength for electrons used in diffraction experiments and for thermal neutrons;
• describe the key features of electron and neutron diffraction apparatus;
• calculate typical diffraction angles for such experiments;
• describe how electrons may be used to image thin samples.

5 On completion of this section you should be able to:

• describe qualitatively how high order terms in the interatomic potential energy lead to thermal expansion;
• discuss the free and forced behaviour of a simple non linear oscillator;
• describe qualitatively the chaotic behaviour of the Van der Pol relaxation oscillator and other non linear oscillatory systems and relate this behaviour to other situations occurring in nature.

Not all topics will necessarily be discussed.