Lattice dynamics and phonon dispersion in Hg$_2$Br$_2$ model ferroelastic crystals

Interatomic force constants have been determined, acoustic and optical phonon frequencies have been calculated, phonon dispersion curves have been constructed, and the density of states in the phonon spectrum has been obtained for Hg$_2$Br$_2$ model ferroelastic crystals. The effect of hydrostatic pressure on the acoustic and optical phonon frequencies and their dispersion has been theoretically analyzed. It is established that an increase in the pressure leads to significant softening of the slowest acoustic TA branch (soft mode) at the X point of the Brillouin zone, which agrees with the phenomenological Landau theory of phase transitions and is consistent with the available experimental data.