Lattice dynamics ofβ-(silver iodide) by neutron scattering

The dispersion relation for the normal modes of vibration in hexagonal $\beta -\mathrm{AgI}$ has been determined at 160 K along three principal symmetry directions from coherent neutron inelastic scattering data using a triple-axis spectrometer. The most interesting feature is the observation of a very-low-lying dispersionless TO mode which is almost decoupled from the other vibrations. The frequencies have been fitted by a valence-shell model, and a satisfactory agreement was obtained with four short-range parameters, a variable ionic charge, and mechanical and electrical polarizabilities for both ions. A frequency distribution function has been computed, together with the lattice heat capacity and the mean-square ionic displacement for each ion. The temperature dependence of the theoretical values compares well with the relevant experiments. Finally, the model is extended and the lattice vibrations of $\gamma -\mathrm{AgI}$ and $\alpha -\mathrm{AgI}$ are discussed.