Phonons in low-dimensional systems

An introduction is given to the dynamical properties of crystalline systems having lattice-translational symmetry in less than three dimensions. These include surfaces of and interfaces between crystals, layered structures (2D lattice periodicity), bars and wires (1D lattice periodicity), as well as crystallites and clusters that have no lattice translational symmetry at all. In addition, superlattices are covered as artificial materials, giving rise to interesting dynamical effects. Crystal surfaces and crystalline bars are considered in some detail. For these systems, changes of the atomic equilibrium positions in comparison to the corresponding bulk crystals are also discussed since they frequently affect the dynamical properties.