Molecular-dynamics study of successive phase transitions in potassium selenate

Molecular-dynamics calculations at different temperatures and pressures have been performed to study the sequence of phase transitions: hexagonal (P$6_3$/mmc)-orthorhombic (Pnam)-orthorhombic (Pna$2_1$) in ${\mathrm{K}}_2$ ${\mathrm{SeO}}_4$. The potential model consists of rigid-ion long-range Coulombic and short-range repulsive forces fitted to structural data of the room-temperature phase, the tetrahedral ${\mathrm{SeO}}_4$ groups being reduced to rigid bodies. A method that uses symmetry-adapted coordinates is introduced to separate the phonon spectrum into symmetry classes and to obtain the eigenvectors of the accessible modes. The simulations confirm the thermal stabilization of the mechanically unstable Pnam phase; in particular, they indicate a large thermal renormalization of its lowest ${\mathrm{\Sigma }}_2$ branch. In accordance with experimental results, the model predicts the softening of the lowest ${\mathrm{\Sigma }}_2$ branch at (1/3)${\mathbf{a}}^{\mathrm{*}}$ as the mechanism of the ferroelectric Pnam-Pna$2_1$ phase transition, the intermediate incommensurate phase being obviated by the type of simulation. The transition temperature and the eigenvector of the soft mode are in good agreement with the experimental values. The low-temperature phase has the expected Pna$2_1$ symmetry, but its spontaneous polarization is too small, and only the primary distortion of ${\mathrm{\Sigma }}_2$ symmetry is properly reproduced. The potential model used is also sufficient to explain the existence at the high temperatures of a disordered hexagonal phase, as observed in the real material at 745 K. The molecular dynamics simulations locate this second structural phase transition in the temperature interval 700–800 K and enable us to identify the more plausible structural model for the high-temperature hexagonal phase from the two proposed in the literature.