ABSTRACT
This chapter reviews the phonon Hamiltonian of a general three-dimensional crystal, with a view to analysing the lowest order anharmonicity. It also reviews the Hamiltonian of an elastic continuum, again with a view to analysing the lowest order anharmonicity. The chapter explains the expression for the Fourier transform of the anharmonic force tensor and derive an expression for the Griineisen constant in the isotropic continuum approximation. In the harmonic approximation phonons are independent of each other. The vibrations of a real crystal, however, are not purely harmonic and the meaning of independent phonons breaks down. Anharmonicity leads to coupling between phonons of the harmonic crystal, which becomes more important as the temperature of the crystal increases. Neutron scattering experiments clearly indicate one-phonon peaks, which suggest that anharmonicity can be viewed as a perturbation on the non-interacting phonon states of a crystal.
