Phase-transition mechanism in (${\mathrm{NH}}_4$${)}_2$${\mathrm{SO}}_4$

The temperature dependence of the midinfrared reflectivity spectra of ammonium sulfate is reported for the two polarizations a and c of the electric field of the infrared wave, in the paraelectric and ferroelectric phases. Strong dynamic disorder of ammonium sulfate is confirmed by the occurrence in the paraelectric phase of vibration modes symmetry allowed only in the ferroelectric phase. Contrary to the molecular distortion-type-model predictions, no softening of the ${\nu }_3$ or ${\nu }_4$ (${\mathrm{SO}}_4^{2\mathrm{-}}$) internal modes is observed. The comparison between low-frequency (50–400 ${\mathrm{cm}}^{\mathrm{-}1}$) reflectivity spectra of (${\mathrm{NH}}_4$ ${)}_2$ ${\mathrm{SO}}_4$ and isomorphous crystals such as ${\mathrm{K}}_2$ ${\mathrm{SO}}_4$, mixed (K-${\mathrm{NH}}_4$ ${)}_2$ ${\mathrm{SO}}_4$, and (Rb-${\mathrm{NH}}_4$ ${)}_2$ ${\mathrm{SO}}_4$, shows that ammonium disorder induces sulfate disorder in the paraelectric phase. This underlines the important role of the librational ${\mathit{B}}_{1\mathit{u}}$ sulfate mode in the phase-transition mechanism. The microscopic origin of the critical relaxation is assigned to reorientation of the whole group ${\mathrm{NH}}_4^{+}$(I)-(${\mathrm{SO}}_4^{2\mathrm{-}}$)-${\mathrm{NH}}_4^{+}$(II) between two equivalent positions with regard to the ab mirror plane. The behavior of the spontaneous polarization is well explained by two contributions, a lattice part and a part due to distortion of all the ions. Finally a softeninglike behavior of the ${\nu }_3$ (${\mathrm{NH}}_4^{+}$) mode is observed and explained in the light of hard-mode spectroscopy.