The overall aim of this MSc module is to explain the salient points of higher-symmetry space groups, namely those belonging to the tetragonal, trigonal, hexagonal, and cubic crystal systems.

The objectives of each lecture are given below:

• Lecture 1
  To explain the solution to symmetry problems set for the vacation;
  To revise the basic principles involved for orthorhombic space groups;
  To give students confidence in deriving space group information from single-crystal diffraction data.
• Lecture 2
  To illustrate the additional symmetry elements present in centred orthorhombic space groups;
  To discuss the concept of extended space-group symbols;
  To teach the students how to deduce space-group symmetry from diffraction data of a crystal possessing a centred lattice;
  To introduce the concept of d-glide planes with reference to space groups Fdd2 and Fddd.
• Lecture 3
  To develop the concepts involved in tetragonal space groups belonging to the Laue class 4/m;
  To briefly survey the higher-symmetry tetragonal space groups belonging to the Laue class 4/mmm;
  To show how the two Laue classes may be distinguished in a diffraction experiment;
  To introduce the concept of enantiomorphic pairs of space groups.
• Lecture 4
  To develop the concepts involved in cubic symmetry;
  To discuss the differences between the two cubic Laue classes m-3 and m-3m.
• Lecture 5
  To introduce the concept of trigonal symmetry and the diamond-shaped unit cell associated with it;
  To introduce the symmetry operators resulting from threefold symmetry;
  To introduce the concept of the reciprocal-space coordinates hkil;
  To develop the concepts involved with the Laue classes -3m1 and -31m and to demonstrate the relationship between them;
  To show how the different Laue classes may be distinguished in a diffraction experiment;
  To introduce the concept of rhombohedral symmetry and the relationship between the R-centred hexagonal and primitive rhombohedral unit cells;
  To relate the rhombohedral and cubic unit cells.
• Lecture 6
  To extend the concepts of trigonal symmetry to hexagonal space groups;
  To show additional uses for hkil indices in hexagonal systems;
  To discuss the differences between the two hexagonal Laue classes 6/m and 6/mmm.
• Lecture 7
  To revise space-group symmetry from low to high symmetry;
  To illustrate sub-group and super-group relationships;
  To very briefly discuss the concept of higher-symmetry systems;
  To illustrate the latter with colour symmetry and magnetic spin.