Phonons

Phonons are introduced as an example of quasi-particles that can only exist in matter. Debye’s quantum model for heat capacity of solids and comparison with experimentin different temperature ranges is presented. The dispersion relations of lattice vibration (phonons) and quantization for chains of atoms presented, revealing the optical and acoustic modes; anharmonic effects are discussed. Crystal lattice structures and Brillouin zones are introduced. Phonon scattering and the Umklapp process described. The variation of the thermal conductivity of dielectrics with temperature is interpreted. X-ray scattering studies of phonon dispersion relations are described. Coupling between phonons with photons in polaritons is explained: Raman scattering studies of GaN used to exhibit the cross-over of their dispersion relations. The Mössbauer effect, a recoilless process, and its dependence on temperature are explained.