Structural phase transformation in K2SeO4

Successive phase transformations in K2SeO4 at T1 = 130 K and T/sub c/ = 93 K were studied by the neutron-scattering technique. The superlattice reflections in the intermediate phase were found to be incommensurate with the lattice periodicity. The wave vector characterizing the reflections is q/sub delta/ = (1-delta) a*/3 with delta = 0.07 at 122.5 K. The deviation delta decreases with decreasing temperature with an apparently discontinuous jump to zero at T/sub c/. Below this temperature, the crystal remains commensurate and is known to be ferroelectric. The incommensurate-commensurate transition and the simultaneous occurrence of the commensurate phase and the spontaneous polarization are discussed using a Landau-type expansion of the free energy in which a term proportional to Q3(q/sub delta/) P/sub z/ (q3/sub delta/) plays an essential role in driving the incommensurate-commensurate phase transformation and in inducing the spontaneous polarization. Here, Q (q/sub delta/) is the amplitude of the primary atomic displacements with wave vector q/sub delta/ and P/sub z/(q3/sub delta/) is the polarization wave with wave vector q3/sub delta/ = 3delta (a*/3) and becomes the macroscopic polarization below T/sub c/. Above T/sub i/, a Σ2 optic-phonon branch along (xi,0,0) shows a striking softening and ω/sub j/(q) for q approx. (1/3,0,0) tends to zero at T/sub i/. The softening results from a temperature-dependent decrease of the interlayer forces with ranges a/2 and a (a is one unit-cell length along the a axis) in the presence of strong and persisting forces with a range 3a/2. The intensities of the soft phonon were measured about different reciprocal-lattice points and were used to determine the nature of the soft-phonon mode and suggest a coupled translation of potassium ions with rotational motion of SeO4 groups to be the origin of the lattice instability