Anharmonic crystals

The study of anharmonic effects in crystals has received considerable attention in the last few years. As a result of this it has been shown that many properties can be understood by expanding the interatomic potential and keeping only the lowest-order terms in the anharmonicity. The theory of thermal expansion, elastic and dielectric properties, Raman and neutron scattering, and specific heat at low temperatures are all discussed from this point of view. The main lack in our understanding of these properties is uncertainty in the interatomic potentials, and some of the approximations used in calculations are discussed. The theory of the thermodynamic behaviour, including thermal conductivity and second sound, is developed from the phonon Boltzmann equation. The theory of these properties is considerably more complicated, particularly from a microscopic point of view, than that of those properties described above, and few detailed calculations have been made. There are some examples of where the anharmonic effects are large and low-order perturbation theory is inadequate. One of these is close to displacive phase transitions, another is in solid helium and a third occurs in all solids close to their melting point. The theoretical work which has been done on these systems is described, although there remains a great deal to be done before our understanding of these is in any sense complete.