5. Lattice Systems

The chapter delves into the classification of crystals based on the symmetry of their lattices, distinguishing between lattice systems and crystal systems. It introduces seven lattice systems (cubic, hexagonal, rhombohedral, tetragonal, orthorhombic, monoclinic, triclinic) and their corresponding centring operations, including body centring, face centring, and rhombohedral centring. The text also explores the relationship between lattice systems and crystal systems, highlighting the distinctions and overlaps between them. Additionally, it discusses the concept of Bravais lattices, which are the unique combinations of crystal systems and centring operations, and provides a detailed explanation of the metric tensor, a tool used for geometrical calculations in crystals. The chapter concludes by illustrating the application of the metric tensor in calculating distances and angles within crystals, emphasizing its utility in understanding complex crystal structures.