Introduction

Abstract

One of the most powerful methods to determine phonon dispersion relations in a crystal is inelastic neutron scattering which yields phonon frequencies of all wavevectors with an accuracy of a few percent or better if circumstances are favorable. Infrared and Raman spectra provide optic frequencies only at very long wavelengths with an accuracy of about 0.1%. From these data, and including information obtained from elastic and dielectric constants, it is possible in many cases to calculate phonon dispersion relations which interpolate between the experimental data. In the simplest case, a set of inter-ionic force constants is fitted, usually by a least-square procedure, to the data in such a way as to give agreement within the limits of experimental error. The number of force constants which is required in such a procedure becomes, however, often rather high (≳20) even in simple cubic crystals. Therefore, phonon models are widely used which start from a parametrized “model” description of the electron-ion interaction before going, via the adiabatic condition, to the “formal” force constants. This leads usually to a drastic reduction of parameters (<10 for diatomic crystals) and facilitates considerably the physical interpretation of the phonon spectra. A summary of the most important models and a short discussion of the underlying physical ideas is given in Part I.