Phonon dispersion relation in LiKSO4

Extensive Raman scattering and neutron-diffraction studies of LiKS${\mathrm{O}}_4$ have recently been carried out in our laboratory at Trombay. In order to understand the experimental observations in Raman scattering, we have resorted to lattice-dynamical calculations. A model based on an atom-atom potential function comprised of the Coulombic and short-range interactions as well as covalent interactions is used to calculate the phonon dispersion relation in LiKS${\mathrm{O}}_4$ [in two space groups ($C_6^6$) and $P31c\left(C_{3v}^4\right)$. The rigid molecular-ion model is used for studying external modes, and an atomic model is used for studying both the external and internal modes in the lattice. Comparison of the theoretical phonon frequencies with those obtained from optical techniques shows that for most of the frequencies the agreement is reasonable. From results of studies in which one of the parameters of the potential function was systematically varied, an incommensurate soft mode belonging to $E_1^{+}$ symmetry is predicted at a wave vector of nearly $0.4{\overrightarrow{\mathrm{c}}}^{*}$. This mode involves librations of sulfate ion about axes in the basal plane. Details of analysis of phonon eigenvectors and LO-TO splittings are presented and compared with experimental results.