This paper is devoted to some recent applications of density-functional perturbation theory to the prediction of lattice instabilities occurring in ionic solids at high pressure. We first briefly review some work aimed at understanding the interplay between shear instabilities and phonon softening in the pressure-induced phase transformations of Cesium halides and hydride. We then report on preliminary results of an attempt of ours to apply similar techniques to the long-standing problem of the pressure-induced amorphization of quartz.
