Theory of the quadrupolar deformability in silver halides

Abstract

The tight-binding method of Varma and Weber is used to calculate phonon dispersion curves in silver halides. For this purpose the method is extended to include crystal-field matrix elements in the electron-phonon coupling. It is shown that the quadrupolar deformability of ${\mathrm{Ag}}^{+}$ ions, as proposed in the model of Fischer et al., arises indeed from virtual atomic ${\mathrm{Ag}}^{+}$ $d\ensuremath{-}s$ excitations induced by displacements of the neighboring halide-ion potentials. In the limit of flat bands there is an exact correspondence of model and microscopic quadrupolar terms. Moreover, realistic band-structure calculations do not significantly alter the above results. We use self-consistent ionic wave functions to obtain numerical estimates for the absolute magnitude of the quadrupolar deformability in fcc AgCl, AgBr, and AgI. With these numbers we get good agreement with the phonon dispersion curves, using an otherwise simple shell model. For AgI we predict with reasonable short-range parameters that the crystal is unstable, thus suggesting a reason for the different structure of AgI at atmospheric pressure.