OPTIC PHONONS IN A DISORDERED IONIC-CRYSTAL

We investigate tile absorption of infra-red radiation by an impure ion ic crystal, due to coupling with phonon modes. By means of a standard diagrammatic perturbation theory, the phonon Green's function and henc e the infra-red spectrum is calculated. The two absorption peaks corre sponding to longitudinal and transverse modes are broadened by disorde r into bands of finite width. This behaviour is very similar to that o f electrons in a dirty metal with a magnetic field, with the phonon mo des playing a similar role to the Landau levels of the electrons. This suggests that the diagrammatic formalism can be used to study the tra nsport properties of phonons in a crystal with impurities and long-ran ged dipole-dipole interactions, by analogy with the methods used in th e transport theory of electrons in disordered metals.