Theoretical Lattice-Dynamical Studies of the Incommensurate Phase Transformation in K\u3csub\u3e2\u3c/sub\u3eSeO\u3csub\u3e4\u3c/sub\u3e

We have made detailed lattice-dynamical studies of the origin of the incommensurate phase transition in potassium selenate. These were based on a rigid-ion model with Coulomb interactions, and also short-range interactions between restricted numbers of close neighbors. The associated short-range force constants were determined using the static equilibrium conditions for the crystal and the observed Raman frequencies. The calculations were made for the room temperature structure using the quasiharmonic approximation in which the effects of varying temperature were simulated by varying the short-range force constants. In this way we were able to show that the crystal has a low-frequency optic branch of Σ2 symmetry which displays softening and instability for wave vectors q in the vicinity of q =0.3a* where a* is the first reciprocal-lattice vector along the [l00] direction. This is in agreement with experimental neutron scattering results and implies a transition to an incommensurate phase. Full sets of dispersion curves at 130 K for the [l00] direction are presented. We also present comparisons of the calculated and experimental low-frequency Σ2 and Σ3 branches at 130, 145, and 250 K. We show, by decomposition of the squares of the normal-mode frequencies into a sum of Coulomb and short-range components, that the balance between these two kinds of interatomic forces is very delicate. This decomposition also shows that a transition to an incommensurate phase is very likely for both the selenate and isomorphous structures. Our model also enables us to predict that uniaxial stress will rapidly depress the transition temperature; a result also in accord with experiment